Wideband Amplifier Design for STO Technology Master of Science Thesis In SystemonChip Design by Chen Tingsu
[email protected]
Stockholm, August, 2011
Supervisor: Examiner:
Prof. Ana Rusu and Dr. Saúl Rodríguez Dueñas Prof. Ana Rusu
August 30, 2011 Master Thesis TRITAICTEX2011:204 i
ACKNOWLEDGEMENTS
First and foremost, I would like to take the opportunity to extend my greatest gratitude to my main supervisor Professor Ana Rusu for welcoming me to the Radio and MixedSignal group at KTH, providing me good suggestions for both research and life, guiding me for research topic definition and the overall research plan, supporting me during these months and reviewing manuscripts. Professor Ana Rusu is an innate scientific leader, an endless source of inspiration and excellent example to follow.
I would like to appreciate my cosupervisor Dr. Saúl Alejandro Rodríguez Dueñas for his patient guidance, frequent troubleshooting and valuable discussion during the whole design. He shows talent, creativity, responsibility and strict discipline at all times. He is a professional model to follow. I also want to thank Professor Eduard Alarcón Cot and Julian Marcos Garcia for providing references, good suggestions and valuable discussion during my thesis work.
My thanks are also to Bengt Molin for sharing his great knowledge and experience in analog and RF electronics. His precise attitude on teaching inspires me.
I would like to thank Professor Johan Åkerman and Anders Eklund for providing me valuable references of novel STO technology.
I also sincerely want to thank Xu Dongdong (bachelor thesis supervisor). He is my respectable teacher and friend.
I would want to acknowledge all the friends in the Radio and MixedSignal group, where is full of passion and intelligence: Sha Tao, Vasileios Manolopoulos, Raul Onet, Milad Razzaghpour and Rocco Grimaldi.
i
I want to thank all my friends in the SystemOnChip Design program.
Last, but not the least, I wish to express my deep appreciation to my parents in China for their infinite love in my life.
 ii 
ABSTRACT Spin Torque Oscillator (STO) is a promising technology for microwave and radar applications due to its large tunability, miniature size, high operation frequency, high integration level, etc. However, the technology comes also with issues and challenges, such as low output power and spectrum impurity. For instance, in order to apply the STO technology into communication systems, an amplifier is required to compensate the STO’s low output power. This thesis presents an amplifier for promising Magnetic Tunnel Junction (MTJ) STO devices. The motional resistance of different MTJ STO devices varies from several Ohms to hundreds Ohms, which makes the design challenging. This thesis focuses first on extracting the amplifier requirements using the stateoftheart MTJ STO devices. The operation frequency of MTJ STO is in the range of 48GHz with a 40～60 dBm output power. Therefore, a wideband amplifier with 4565 dB gain is required. Then based on the amplifier requirements, an amplifier topology is proposed, which is composed of two types of input balunLNA stages depending on the motional resistance of the STO, a broadband limiting amplifier and an output buffer. CGCS architecture is suitable for the input balunLNA in the small motional resistance case and cascodedCS architecture is suitable for the large motional resistance case. The limiting amplifier and the output buffer are the common circuits shared by two cases via switches. The wideband amplifier for STO is implemented using a 65nm CMOS process with 1.2V supply and it exhibits 52.36 dB gain with 1.3411.8 GHz bandwidth in small motional resistance case and 59.29 dB gain with 1.1718.178 GHz bandwidth in large motional resistance case. The simulation results show that the amplifier has very low power consumption and meets the linearity and noise performance requirements.
 iii 
ABBREVIATION TABLE
Abbrev.
Full names
AC
Alternating Current
CCO
CurrentControlled Oscillator
CG
Common Gate
CMOS
Complementary MetalOxide Semiconductor
CS
Common Source
dB
Decibel
dBm
Power ratio in decibels
of the measured power referenced to
one milliwatt DC
Direct Current
ESD
Electrical Static Discharge
Ft
Transit Frequency
gm
Transconductance
GMR
Giant Magnetic Resistance
IIP3
ThirdOrder Input Intercept Point
IP3
Thirdorder Intercept Point
LA
Limiting Amplifier
LNA
Low Noise Amplifier
LSB
Load Stability Circle
MR
MagnetoResistance
MTJ
Magnetic Tunnel Junctions
NF
Noise Figure
OIP3
Output ThirdOrder Intercept Point
PAC
Periodic AC
PCB
Printed Circuit Board
PLL
PhaseLocked Loop
PSS
Periodic SteadyStage
Rds
Drain to Source Resistance
Recn
Resistor for Thermal Noise Enhancement  iv 
RAM
Random Access Memory
RF
Radio Frequency
SRF
SelfResonant Frequency
SSB
Source Stability Circle
STO
Spin Torque Oscillator
TIA
Transimpedance Amplifier
TMR
Tunnel Magnetic Resistance
VCO
VoltageControlled Oscillator
Vdd
Power Supply Voltage
Vpp
Peaktopeak voltage
VSWR
Voltage Standing Wave Ratio
VTH
Threshold voltage of Transistor
v
CONTENTS
ACKNOWLEDGEMENTS ......................................................................................... i ABBREVIATION TABLE ......................................................................................... iv CONTENTS................................................................................................................. vi LIST OF FIGURES ................................................................................................. viii LIST OF TABLES....................................................................................................... xi Chapter 1. Introduction ............................................................................................... 1 1.1 Motivation ......................................................................................................... 1 1.2 Objectives ......................................................................................................... 2 1.3 Thesis Organization .......................................................................................... 3 Chapter 2. Spin Torque Oscillator.............................................................................. 5 2.1 Background ....................................................................................................... 5 2.1.1 Spin momentum transfer torque.............................................................. 5 2.1.2 Magnetoresistance ................................................................................. 6 2.2 Characterization of Spin Torque Oscillator ...................................................... 7 2.2.1. Features and drawbacks ......................................................................... 7 2.2.2. Classification.......................................................................................... 8 2.3 Stateoftheart MTJ STO ................................................................................. 9 2.4 Summary ......................................................................................................... 13 Chapter 3. Amplifier Requirements and Topology ................................................. 14 3.1 Amplifier Requirements.................................................................................. 14 3.2 Cases under investigations .............................................................................. 17 3.2.1. Small motional resistance case ............................................................ 17 3.2.2. Large motional resistance case ............................................................ 19 3.3 Amplifier Topology ........................................................................................ 20 3.4 Summary ......................................................................................................... 23 Chapter 4. Biastee and Current Source/Sink ......................................................... 24 4.1 Biastee ........................................................................................................... 24 4.1.1 Biastee Operation ................................................................................ 24 4.1.2 Transfer function ................................................................................... 25 4.2 Biasing circuit and Current Source/Sink design ............................................. 27  vi 
4.2.1. Small motional resistance case ............................................................ 27 4.2.2. Large motional resistance case ............................................................ 33 4.3 Summary ......................................................................................................... 34 Chapter 5. Input Stage of Amplifier ......................................................................... 35 5.1 Input stage in small motional resistance case ................................................. 35 5.2 Input stage in large motional resistance case .................................................. 46 5.3 Switch ............................................................................................................. 54 5.4 Summary ......................................................................................................... 55 Chapter 6. Limiting amplifier ................................................................................... 56 6.1 Limiting amplifier ........................................................................................... 56 6.2 Case studies ..................................................................................................... 57 6.2.1 Cascaded LA using CS stages ............................................................... 57 6.2.2 Cascaded LA using CS stages with negative Miller capacitors compensation ................................................................................................. 58 6.2.3 Cascaded LA using cascoded CS stages ............................................... 60 6.2.4 Cascaded LA using current mirror ........................................................ 61 6.2.5 Topology discussion.............................................................................. 62 6.3 Limiting amplifier Design for STO amplifier ................................................. 63 6.4 Summary ......................................................................................................... 73 Chapter 7. Output buffer .......................................................................................... 74 7.1 Case studies ..................................................................................................... 74 7.2 Output buffer design ....................................................................................... 75 7.3 Summary ......................................................................................................... 80 Chapter 8. Wideband amplifier Design ................................................................... 81 8.1 Small motional resistance case (50 Ohms system) ......................................... 81 8.2 Large motional resistance case (HighZ system) ............................................ 88 8.3 Summary ......................................................................................................... 94 Chapter 9. Conclusion and Future Work ................................................................ 95 9.1 Conclusion ...................................................................................................... 95 9.2 Future Work .................................................................................................... 96 Reference .................................................................................................................... 97
 vii 
LIST OF FIGURES
Figure 2.1 STO structure and magnetoresistance effect ........................................ 5 Figure 2.2 Spin momentum transfer torque ............................................................ 6 Figure 2.3 Two types of MTJ STO ......................................................................... 9 Figure 2.4 Timetrace of MTJ STO after a 62 dB amplifier .................................. 11 Figure 2.5 PSD over 1us of the MTJ timetrace after a 62 dB amplifier ............... 12 Figure 3.1 Block Diagram of this project ............................................................. 15 Figure 3.2 Modified impedance matching ............................................................ 19 Figure 3.3 Broadband amplifier based on voltagecontrolled current source with resistive feedback .......................................................................................... 20 Figure 3.4 Low noise amplifier with matching networks at input and output ...... 20 Figure 3.5 Basic commongate stage with capacitive coupling at input............... 21 Figure 3.6 Amplifier topology .............................................................................. 22 Figure 4.1 Biastee architecture (a).RC architecture (b).LC architecture ............. 24 Figure 4.2 Biastee LC architecture ...................................................................... 25 Figure 4.3 Biastee RC architecture ...................................................................... 26 Figure 4.4 (a).Model of real inductor L (b).Model of real capacitor C ................ 27 Figure 4.5 Dual current source/sink and biasing topology ................................... 29 Figure 4.6 Biasing and current source/sink in small motional resistance case ..... 30 Figure 4.7 Impedance of biasing and current source/sink .................................... 30 Figure 4.8 Impedance Z11 of biasing and current source/sink ............................. 31 Figure 4.9 Sparameter analysis of biasing and current sink ................................ 32 Figure 4.10 Sparameter analysis of biasing and current source .......................... 33 Figure 5.1 The lumped circuit model of bond wire .............................................. 35 Figure 5.2 Approximate package model ............................................................... 36 Figure 5.3 CGCS balunLNA – input stage ......................................................... 37 Figure 5.4 Input impedance of the balunLNA ..................................................... 40 Figure 5.5 S11 of the balunLNA ......................................................................... 40 Figure 5.6 Biasing circuit for CGCS balunLNA – input stage........................... 41 Figure 5.7 Gain of balunLNA with same gain at CG and CS branches .............. 42 Figure 5.8 Noise performance of LNA ................................................................. 43  viii 
Figure 5.9 Source Stability Circle of the LNA ..................................................... 45 Figure 5.10 Transient analysis of input stage........................................................ 45 Figure 5.11 IIP3 of CGCS LNA .......................................................................... 46 Figure 5.12 Cascoded CS input stage ................................................................... 47 Figure 5.13 Biasing circuit for Cascoded CS balunLNA .................................... 48 Figure 5.14 AC responses of cascoded CS stage .................................................. 50 Figure 5.15 Input impedance with bond wire effect at 5 GHz.............................. 50 Figure 5.16 Input impedance of the cascoded CS stage ....................................... 50 Figure 5.17 Noise performances of cascoded CS stages ...................................... 51 Figure 5.18 Transient analysis of cascoded CS stages .......................................... 52 Figure 5.19 IIP3 of cascoded CS LNA ................................................................. 52 Figure 5.20 gds vs. Vds and Rds vs. Vds characteristics of switch transistor ...... 55 Figure 6.1 CS stage of Limiting amplifier ............................................................ 57 Figure 6.2 Simulation result of CS stage .............................................................. 58 Figure 6.3 CS stage with negative Miller capacitors compensation ..................... 59 Figure 6.4 Simulation result of CS stage with negative Miller capacitors compensation ................................................................................................ 59 Figure 6.5 Cascoded CS stage .............................................................................. 60 Figure 6.6 Simulation result of cascoded CS stage of Limiting amplifier............ 61 Figure 6.7 Current mirror stage ............................................................................ 61 Figure 6.8 Simulation result of current mirror stage............................................. 62 Figure 6.9 Synthesizing wideband frequency responses ...................................... 64 Figure 6.10 LA cell ............................................................................................... 65 Figure 6.11 Model of inductive peaking compensation........................................ 65 Figure 6.12 Simplified model of LA cell .............................................................. 66 Figure 6.13 AC response of CS stage ................................................................... 68 Figure 6.14 Simulation results of 6stage LA ....................................................... 69 Figure 6.15 Noise Figure of 6 cascoded CS stages of LA .................................... 70 Figure 6.16 Transient analysis of LA .................................................................... 71 Figure 7.1 Output buffer ....................................................................................... 75 Figure 7.2 Bond wire at the output ....................................................................... 76 Figure 7.3 Output impedance of output buffer (3 GHz to 10 GHz) ..................... 77 Figure 7.4 Output reflection coefficient S22 of output buffer .............................. 78 Figure 7.5 Gain loss of output buffer .................................................................... 78  ix 
Figure 7.6 Transient analysis of output buffer ...................................................... 79 Figure 8.1Wideband amplifier .............................................................................. 81 Figure 8.2 Sparameter of amplifier...................................................................... 82 Figure 8.3 VSWR of input and output of amplifier in small motional resistance case ................................................................................................................ 82 Figure 8.4 Noise performance of amplifier in small motional resistance case ..... 83 Figure 8.5 SSB and LSB of amplifier in small motional resistance case ............. 83 Figure 8.6 Output voltage distribution of amplifier in small motional resistance case ................................................................................................................ 84 Figure 8.7 1 dB compression point of amplifier in small motional resistance case ....................................................................................................................... 85 Figure 8.8 IIP3 of amplifier in small motional resistance case............................. 86 Figure 8.9 Corner analyses in small motional resistance case .............................. 87 Figure 8.10 Sparameter of amplifier in large motional resistance case............... 88 Figure 8.11 Input impedance of amplifier in large motional resistance case........ 89 Figure 8.12 Noise performance of amplifier in large motional resistance case.... 89 Figure 8.13 SSB and LSB of amplifier in large motional resistance case ............ 90 Figure 8.14 Output voltage distribution of amplifier in large motional resistance case ................................................................................................................ 90 Figure 8.15 1 dB compression point of amplifier in large motional resistance case ....................................................................................................................... 91 Figure 8.16 IIP3 of amplifier in large motional resistance case ........................... 92 Figure 8.17 Corner analysis of amplifier in large motional resistance case ......... 93
x
LIST OF TABLES
Table 2.1 MTJ STO summary ............................................................................... 10 Table 3.1.Summary of the amplifier requirements ............................................... 16 Table 3.2.Amplifier requirements of each stage ................................................... 23 Table 4.1 Transistors’ size of biasing and current source/sink in small motional resistance case ............................................................................................... 30 Table 5.1. Parameters of the input transistors M03 ............................................. 36 Table 5.2 Parameters of the biasing transistors M1M3 ....................................... 41 Table 5.3 Parameters of the transistors of cascoded CS input stage ..................... 47 Table 5.4 Parameters of the biasing transistors M12 ........................................... 49 Table 5.5 Comparison of the proposed LNAs with stateoftheart LNAs and Baluns ........................................................................................................... 53 Table 6.1 Summary of LA stage topologies .......................................................... 62 Table 6.2 Transistor sizes of cascoded CS stage ................................................... 67 Table 6.3 Parameters of the biasing transistors M1, M2....................................... 67 Table 6.4 Transistor sizes of CS stage .................................................................. 68 Table 6.5 Comparison of Limiting amplifier ........................................................ 72 Table 7.1 Parameters of the transistors in output buffer ....................................... 76
 xi 
Chapter 1. Introduction
Chapter 1. Introduction 1.1 Motivation Microwave refers to the signals with frequencies between 300MHz and 300GHz frequency range [1]. Microwave applications such as wireless communication systems and radar communication are developing at a rapid speed. Oscillators play very important role in these microwave applications. In all the communication systems, oscillators generate the carrier or local oscillator signal. Modern microwave oscillator requires the following features: miniature size, low cost, high operation frequency, high quality and stability, low phase noise, large tunability, low power consumption, high output power, high integration level and temperature independence. Unfortunately, there is no microwave oscillator, which assembles all these features together. The typical offchip quartz crystal oscillator has large dimension, large power consumption, temperature dependence, low integration level, high quality only at low frequency, and lack of antivibration, which is no longer suitable for modern microwave applications. CMOS fully integrated LCVCO is competitive due to its low phase noise, low power consumption, large tunable frequency range (12 GHz) [2]. However, the integrated oscillators have very low quality factor. Spin torque oscillator (STO) is a novel tunable nanoscale microwave integrated currentcontrolled oscillator (CCO). The tunability of STO is typically in 540 GHz range, which is suitable for applications in the domain of microwave frequency. The quality factor of magnetic tunnel junctions (MTJ) STO is up to 18000 [3] and is easy to be integrated in CMOS process. These advantages make it a promising microwave oscillator candidate. The nanometersized STO is based on two spintronic effects: spin momentum transfer torque and magnetoresistance (MR). The spin torque effect was first predicted in 1996 by Slonczewski and Berger [4]. One prediction was described as that a spinpolarized current can induce magnetic switching and dynamic excitations in ferromagnetic thin films [5]. Demonstrations of spin torque have so far been focused on ‘currentinduced switching’ for application in harddisk drives and 1
Chapter 1. Introduction Random Access Memories (RAM). The other prediction is that the spintorque can drive steadystate magnetization precession (oscillation) when the applied fields are large enough. MR effect translates the magnetic precession into the microwave signal when an external magnetic field is applied. Nowadays, numerous measurements are carried out to explore the characterization of STO and improve the performance of STO. Bottlenecks of this nanometersized magnetic oscillator that need exploration are low output power and spectrum impurity. The low output power can be compensated by employing an application specific amplifier that provides high gain, wideband, low noise and high linearity.
1.2 Objectives As per knowledge of the author, there is no universal amplifier for MJT STO device with large motional resistance as well as small motional resistance, in literature. The objective of this thesis is to design and implement the required circuit to amplify the microwave signal generated by the MTJ STOs with small/large motional resistance provided by the Applied Spintronics group in KTH. Firstly, this thesis should concentrate on the theoretical, mathematical and physical background behind STO. Secondly, the amplifier requirements should be analyzed based on the stateoftheart STOs’ performance. To reach this goal, the following features of STO have to be analyzed: mechanism, advantages and disadvantages, classification, external and internal influence, output power, motional resistance, noise, operation frequencies. Thirdly, the amplifier must be designed and simulated according to the requirements. The amplifier will be designed using a 65nm CMOS process. The shrinking of transistors size leads to higher cutoff frequency Ft and fast speed. The process shrinking also leads to some disadvantages: lower drainsource voltages, low supply voltage, low gain per stage, mismatch, etc. In this design, gain is influenced heavily by the imperfection of the 65nm process. The output conductance of shortchannel transistors is very large, which leads to a lower intrinsic gain. Besides, the channellength modulation factor is also very large in the 65nm process, which finally results in a very low gain [6]. Furthermore, the reduced supply voltage limits the choice of amplifier topologies. In order to achieve high gain, the combination of 2
Chapter 1. Introduction cascading and cascoding of amplifier stages should be employed. The noise performance is also critical to this project. However, in the 65nm process, the noise performance is limited by the gate current noise, which is caused by the comparatively large gate leakage current. Thus, the low leakage transistors are used in this project. Above all, the tradeoff between gain and bandwidth, the imperfection of the 65nm process and strict requirements for amplifier need careful consideration during the amplifier design.
1.3 Thesis Organization Chapter 1. Introduction: This chapter describes the motivation and the objective of this thesis. Chapter 2. Spin Torque Oscillator: This chapter mainly presents STO operating principle, summarizes the stateoftheart performance and STO’s superiority. The main issues of STO are also raised by investigating the existing references. Chapter 3. Amplifier Requirements and Topology: The requirements of the amplifier for STO depend on the STO performance. The amplifier topology is proposed based on the requirements. Chapter 4. Biastee and Current Source/Sink: This chapter introduces biastee network and its alternatives, and verifies the feasibility of onchip biastee network and current source/current sink. Chapter 5. Input stage of Amplifier: This chapter presents the design of input stage of the whole amplifier in small and large motional resistance cases respectively. Chapter 6. Limiting amplifier: This chapter studies the existing limiting amplifiers and proposes a suitable topology for this project. This is the core part of the amplifier. Chapter 7. Output buffer: This chapter compares several types of output buffer and comes out with a solution of output buffer for this project. Chapter 8. Wideband Amplifier Design: The whole amplifier design is proposed based on the previous 4 chapters. The noise performance, linearity, Sparameter analysis, corner analysis, etc. are simulated and analyzed in Cadence.
3
Chapter 1. Introduction
Chapter 9. Conclusion and Future Work: This chapter summarizes the overall work that has done in this thesis and suggests recommendations for future work.
4
Chapter 2. Spin Torque Oscillator
Chapter 2. Spin Torque Oscillator
2.1 Background In recent years, the intriguing properties of STO make it a promising candidate for microwave and radar applications. STO is based on two spintronic effects: spin momentum transfer torque and MR. The structure of STO [7] is given in Figure 2.1. A nonmagnetic spacer layer is sandwiched between the fixed layer and free layer.
The *Red arrow indicates the direction of the magnetization.
Figure 2.1 STO structure and magnetoresistance effect (a). Parallel case in magnetoresistance effect with small resistance; (b). Antiparallel case in magnetoresistance effect with a large resistance
2.1.1 Spin momentum transfer torque Spin momentum transfer torque is caused by the spin polarized current. Thus, the spin momentum transfer torque acts on the free layer and provides the required energy to maintain the steady state oscillation. When spin polarized current is injected from magnetic layer into a nonmagnetic layer, the spin polarization will be retained over a certain distance [8] as shown in Figure 2.2(a). When spin polarized current is injected 5
Chapter 2. Spin Torque Oscillator from nonmagnetic layer into a magnetic layer, the spin of the injected current will be quickly absorbed by the magnetic layer on the right side in Figure 2.2(b). When the current is large enough (larger than the threshold current Ith), it will cause the change of the magnetization direction of the magnetic layer [8].
Figure 2.2 Spin momentum transfer torque (the red layer is magnetic layer, the blue layer is nonmagnetic layer) (a). Spin polarized current injected from magnetic layer into a nonmagnetic layer (b). Spin polarized current injected from nonmagnetic layer into a magnetic layer
The magnetization direction of the magnetic layer can change continuously when a suitable current is applied, which results in oscillation at GHz frequency.
2.1.2 Magnetoresistance The MR effect is the result of the relative orientation changes of magnetization between the free layer and fixed layer. As discussed above, the magnetization direction of the magnetic layer changes when a suitable DC current is applied. Thus, the value of MR is a function of the DC current and applied magnetic field. When there is no relative orientation between these two ferromagnetic layers shown in Figure 2.1(a), it is called the parallel case. When the magnetization of the free layer is in parallel with that in the fixed layer, the electrons can move from the spacer to the fixed layer easily and the STO device reveals the low resistance. RP represents the 6
Chapter 2. Spin Torque Oscillator resistance value in the parallel case. When there is a relative orientation of the magnetization between the free layer and fixed layer as shown in Figure 2.1(b), it is called antiparallel case. The electrons are hard to move in this case, which results in higher resistance. RAP represents the relatively large resistance in the antiparallel case. Thus, as the relative orientation of magnetization changes between the free layer and the fixed layer, the electrical resistance value of STO oscillates around a DC value, which can be represented as Rdc. The timevariant part of the resistance value, which is caused by the relative orientation of magnetization changes, can be regarded as △R. The electrical resistance or motional resistance of STO can be represented by Rdc+△R, where Rdc lays between RAP and RP, △R is the high frequency term [7]. The combination of spin momentum transfer torque and MR makes STO oscillates at several gigahertzes under the local effective magnetic field and external magnetic field. By tuning the applied DC current and external magnetic field, one can find the optimal conditions of operation for STO.
2.2 Characterization of Spin Torque Oscillator 2.2.1. Features and drawbacks Firstly, the size of STO devices is close to zero chip area. Actually, the size of a STO device is 50 times smaller than that of the conventional LCtank VCO [3]. The nanoscale dimensions and simple structure makes it extremely suitable for integration on silicon. Thus, it can be easily integrated on any kind of semiconductor device, which makes it promising to replace the conventional VCO. Secondly, the line width (3 dB bandwidth) in the STO is down to several hundreds kilohertz. In the condition of room temperature, the narrow line width results in high quality factors of up to 18000 [8]. This high Q characteristic of STO indicates a lower rate of energy loss. In resonating systems, high frequency stability needs high Q devices. Thus, STO became a candidate for microwave applications. Thirdly, STO has superior noise properties due to the high quality factors. Fourthly, the STO has a wide tuning frequency range from 1 to 40 GHz and the central frequency can be tuned by both current and magnetic field [8].
7
Chapter 2. Spin Torque Oscillator Finally, STO can be synchronized with other oscillators that are similar to STO by using both magnetic and current means [8]. The high tunability, miniature size, low energy loss of STO and its compatibility with CMOS technology, make the STO technology a promising candidate for future communication applications. The main issues of STO technology are low output power and spectral impurity. Research has been performed to improve the STO performance. The motional resistance is a function of the applied magnetic field and direct current. In different STO systems, the motional resistance varies from several Ohms to hundreds Ohms. The current improvements of output power are just focusing on one specific type of the motional resistance when specific magnetic field and direct current are applied. Hence, the improvements are restricted to a specific STO device or one type of STO devices. The spectral impurity of STO is still a troublesome issue. The frequency fluctuates at a high speed. Furthermore, the direct current applied to the STO is connected directly to the external current generator, which is noisy and inaccurate.
2.2.2. Classification The STOs suitable for microwave applications are based on two spintronic effects: MR and the spin momentum transfer torque. There are two important types of STO, which can be distinguished by the MR. One is the MTJ type, which is characterized by tunnel magnetic resistance (TMR) and the other spin valve type, which is characterized by giant magnetic resistance (GMR). TMR is much higher than GMR, which causes a higher output power in MTJ devices. However, the larger resistance requires a lower current density in order to prevent from breakdown. The lower current density required in MTJ STO causes that its frequency of operation will be lower compared to all metal (referred to GMR), nano contact STO [3]. Moreover, the MTJ, compared with GMR, has a larger output power while has many unwanted modes near the operation frequency. What should be emphasized here is that both MTJ and GMR STO excite one mode when specific control parameters are set [9]. The free ferromagnetic layer has multimode nature, which does not mean that several modes are excited. All the modes compete for the same energy source provided by the bias current, and only one strongest mode can survive. 8
Chapter 2. Spin Torque Oscillator There are two types of MTJ STO: nano contact type device and nano pillar type device as shown in Figure 2.3 [9]. Nanocontact device in Figure 2.3 (a) refers to that its free magnetic layer is not bounded in the layer plane. Nanopillar device shown in Figure 2.3 (b) is represented as a magnetic stack, which is entirely nanofabricated into a pillar shape of around 100 nm dimensions [7] and has a higher resistance than nano contact type device.
Figure 2.3 Two types of MTJ STO: (a). Nano contact type (b). Pillar type
MTJ STO is attractive because of its larger intrinsic signal and strong tendency for synchronization [10]. Thus, in this project, MTJ STO is considered due to these double benefits. However, larger resistancearea product limits the operation frequency of MTJ STO and increases the noise.
2.3 Stateoftheart MTJ STO MTJ STO has been successfully used in harddisk drives and it is a promising candidate for the next generation recording technology. The intriguing properties of STO suggest that it is also a promising candidate for the next generation microwave generators in communications and radar applications. MTJ STO is newly explored, and it is not yet compatible with the telecommunication standard mainly because of its two drawbacks: low output power and spectral impurity. In Table 1.1, the stateoftheart MTJ STO can be seen.
9
Chapter 2. Spin Torque Oscillator Table 2.1 MTJ STO summary Device
F (GHz)
LWmin (MHz)
Pout (dBm)
MR (Ohms)
I (mA)
Ref
1
5.03
37.4
62.7
3763 ≈50
8
[3]
2
6
10
46
0.75
[8]
3
68
21
47
N/A
N/A
[11]
4
7
21
55
≈100
2
[12]
5
5
30
60
N/A
6
[13]
6
56
N/A
N/A
4270
1
[14]
7
4.78
N/A
0.14uW= 38.5
42.572
N/A
[15]
8
47
21
35nW=44.56
1725
2, ±10
[16]
9
Around 5
N/A
40
Assume 50
8.6
[17]
10
3.5 and 5
100
0.14uW= 38.5
300600
>±0.3
[18]
180270
F is the centre frequency; LWmin is the minimum linewidth or bandwidth; Pout is the output power of STO device; MR is the magnetic resistance; I is the injected DC current; The applied bias magnetic field configuration is not shown in the table
Apart from the parameters listed in Table 2.1, MTJ STO can be characterized by TMR coefficients. Equation (2.1) is used to calculate the TMR coefficients [7]. TMR ⋅ coefficient =
R AP − RP RP
(2.1)
MTJ STOs exhibit TMR coefficient in the range of 50%  100%. The resistance Rdc of MTJ STO varies from 100 to 1000 Ohms [8]. The output power is proportional to the square of the bias current and can be estimated [7], which will be discussed in the Chapter 3. As the bias current increases, the output power increases. However, according to [19], at least in a certain range of supercritical bias current I/Ith ≤1.5, only one mode is excited by STO. In order to
 10 
Chapter 2. Spin Torque Oscillator excite only one mode unconditionally, upper limit of the bias current is confined by I/Ith ≤1.5. The timetraces are shown in Figure 2.4. The STO followed by a 62 dB amplifier results in a higher background RMS voltage of 75 mV, but the signal power of 412 mV is still considerably stronger than the noise [13], which shows that the STO has superior noise properties. The oscillation of STO can be clearly identified although it is partially sustained [8]. From the STO signal in time domain, it is also easy to see that there are amplitude variations, frequency variations and phase shifting. This indicates that the performance of STO needs improvement.
2000 signal noise 1500
1000
Voltage [mV]
500
0
−500
−1000
−1500
−2000
0
1
2
3 Time [ns]
4
5
6
Figure 2.4 Timetrace of MTJ STO after a 62 dB amplifier [13]
The PSD of a typical MTJ STO followed by a 62 dB amplifier can be seen in Figure 2.5. From Figure 2.5, one can see that the central frequency is around 5 GHz and the second harmonic is around 10 GHz. There are several peaks in the range of 5.6 – 6.6 GHz, which indicates that the MTJ STO oscillates in several modes at different frequencies near the central frequency. The second strongest mode happens at 5.512 GHz, which is 16 dB/Hz lower than the strongest mode. Around the center frequency of 4.993 GHz, one can see the narrow linewidth which shows a high quality factor. The noise floor is 26 dB/Hz lower than the signal.
 11 
Chapter 2. Spin Torque Oscillator
Figure 2.5 PSD over 1us of the MTJ timetrace after a 62 dB amplifier [13]
Apart from the time and frequency domain of the STO output signal, the figure of frequency spectra versus time is also important in characterizing the STO. According to the frequency spectra versus time [8], one can easily find the frequency fluctuation or frequency hooping within ±10 MHz. In order to check the influence of amplitude variations, frequency variations and phase shifting，a test on locking the phase of STO was carried out [20]. Due to the frequency hooping, the STO signal frequency is varying from time to time. Sometimes the STO signal frequency is higher and sometimes it is lower than the center frequency when DC current and magnetic field are fixed. The expecting result is the amplified STO output signal cannot be locked by PLL within 15 ns. Based on the result in [20], in author’s opinion the possible causes of the signal locking failure are: The amplitude of the amplified STO signal is not stable, which can also be seen in the time domain. In the test [20], the lower limit of output power level of the amplified STO signal that can be locked by the given PLL is60 dBm. If the signal is too small to reach the limitation, the raising and falling edges of the signal cannot be detected. This should be the main reason which leads to the  12 
Chapter 2. Spin Torque Oscillator signal locking failure. The phase shifting of the STO is obvious, which also contributes to the failure. In Figure 2.4, one can see several phase shifting in such a short time. The frequency fluctuates at a fast speed, which should be taken into consideration as well.
2.4 Summary STO is a novel currentcontrolled oscillator device, which is a good candidate for the microwave applications due to its advantages, such as miniature size, high quality, high frequency, large tunability, high integration level, etc. However, the issues of STO are low output power and spectrum impurity, which need more exploration in the future.
 13 
Chapter 3. Amplifier Requirements and Topology
Chapter 3. Amplifier Requirements and Topology
3.1 Amplifier Requirements The output power of STO followed by a 62 dB amplifier can be calculated from Figure 2.5 by using the bandwidth that refers to the 3dB bandwidth. The output power is around 60 dBm in this case. The background noise can also be calculated in the same way. The background noise power of STO followed by a 62 dB amplifier is 94 dBm. In order to connect the amplified signal to a mixer in the future work, the output power of amplified STO signal should be at least 0 dBm. In order to connect the amplified signal to a PLL in the coming stage, the output power should be at least 10 dBm. Besides, the compensation for microwave losses from the board and cable should also be taken into consideration. If the output power of the MTJ STO (input power of amplifier) is 60 dBm, the required gain of the amplifier should be 65 dB. As it can be seen in Table 2.1, highpower microwave oscillations in MTJ devices have been observed in [15] [18]. The output power of MTJ STO is up to 38.5 dBm, which calls for less than 40 dB amplifier. The direct current requirements are different from case to case, as shown in Table 2.1. But in all cases, an accurate and tunable direct current source is needed. It can be connected to the STO via the biastee. Feasibility of onchip biastee will be examined in the Chapter 4. The MTJ STO device is placed on the physical transmission line or resonator[21]. The proposed amplifier IC can be connected to MTJ STO device by using RF probe pads or bond wires. The block diagram of the proposed approach can be seen in Figure 3.1.
 14 
Chapter 3. Amplifier Requirements and Topology
Figure 3.1 Block Diagram of this project (only the current source case is shown)
From Table 2.1, one can find that the central frequency of MTJ STO varies from 4 GHz to 8 GHz due to the specified device, DC current and magnetic field. Therefore, the bandwidth of the proposed amplifier should cover the range of 48 GHz. In this project, bandwidth B is 4 GHz (from 4 GHz to 8 GHz).
fU = f C +
B = 8GHz 2
(3.1)
f L = fC −
B = 4GHz 2
(3.2)
fU 8 = =2 fL 4
(3.3)
where fU is the upper limit of bandwidth, fL is the lower limit of bandwidth and fC is the center frequency. Highfrequency amplifiers are called wideband amplifiers when they meet the criterion of fU/fL≥2. Equation (3.3) indicates that a wideband amplifier is needed in this project. Nonlinearity is harmful in this project because of two reasons. One reason is that several modes are closed to operation frequency and the other one is that frequency hoops at a high speed. Thus, good linearity is required. In order to achieve good linearity, clipping distortion should be prevented in time domain, which appears as odd order harmonics in frequency domain. The efficient way to prevent clipping distortion is to keep the output voltage swing sufficient and avoid saturation on transistors. However, the 1.2V supply voltage limits the output voltage swing to 1.2V  15 
Chapter 3. Amplifier Requirements and Topology at maximum. Thus, specific topology with large output swing should be employed in the amplifier, specially in the latter stages of the amplifier. Moreover, the reflection coefficient S11 and return loss S22 should be below 10 dB to prevent degrading of the signal. Above all, the amplifier requirements are summarized in Table 3.1
Table 3.1.Summary of the amplifier requirements Item
Specific requirement
STO Technology
MTJ
Measured max. output level
40～60dBm [8] [11] [13] [15] [16] [18]
Required
total
gain
of Required 4565 dB amplification depending on the
amplifier
STO device* (including compensation for microwave losses from the board and cable)
DC current
Accurate tunable current
Frequency range
48 GHz
Output resistance of STO
Around 50 Ohms [11] or larger/smaller than 50 Ohms [3] [8] [12] [14] [16]
Output impedance of
Matches to 50 Ohms
amplifier S11
<10 dB
S22
<10 dB
Noise of STO
≈94 dBm at central frequency [13]
NF of STO
≈5.23 dB [13]
NF of amplifier
<6dB
* In this project, we target to design an amplifier with as high as possible gain (if possible else to 65 dB)
The specific gain, bandwidth, linearity, noise figure, etc. requirements will be discussed later in this chapter.
 16 
Chapter 3. Amplifier Requirements and Topology
3.2 Cases under investigations The output power delivered by STO can be calculated according to Equation (3.4), proposed in [8]. Pout = (
∆R 2 β 2 ) ⋅ ⋅ R ⋅ I DC 2 (1 + β ) R
(3.4)
where β stands for the ratio between the motional resistance R of STO and amplifier input impedance Zin. In order to maximize the power delivered to the amplifier, one should maximize magnetoresistance coefficient matching ratio
β (1 + β ) 2
∆R R
and impedance
. Magnetoresistance coefficient is a property of a specific
STO device and cannot be changed. Thus, only impedance matching ratio should be maximized. By calculating the derivative of impedance matching ratio, the maximum power delivery can be achieved when β =1. Thus, the impedance matching between the motional resistance and amplifier input impedance is needed.
3.2.1. Small motional resistance case In [3], the motional resistance of STO is around 50 Ohms. In this type of STO devices, the input impedance of the amplifier should match 50 Ohms in order to obtain maximum power and minimum reflection. It should be stressed that the magnetoresistance coefficient is large, in another words, the high frequency term △R of motional resistance varies in a large range. Thus, the input impedance of the amplifier cannot be matched perfectly at any time. The losses and reflections due to impedance mismatch should also be taken into consideration [ 22 ]. The input reflection coefficient can be estimated by Equation (3.5). In practical case, the reflection can be measured in the form of S11. Γ=
R − Z in R + Z in
(3.5)
In this design, both the STO output impedance and amplifier input impedance are varying. Assume that the input impedance is purely resistive, then the Equation (3.5) can be rewritten as:
 17 
Chapter 3. Amplifier Requirements and Topology Γ=
( Rdc + ∆R) − ( Rin + ∆Rin ) Rdc − Rin + ∆R − ∆Rin = ( Rdc + ∆R) + ( Rin + ∆Rin ) Rdc + Rin + ∆R + ∆Rin
(3.6)
where Rdc is the DC term and △R is the high frequency term of STO resistance discussed in Chapter 2, Rin is the desired amplifier input resistance of 50 Ohm in a 50 Ohms system and △Rin is the variation between practical input resistance of amplifier and the desired 50 Ohms. The resistance of STO is a function of the applied magnetic field and DC current and according to Table 3.1 it varies from several Ohms to hundreds Ohms. The MTJ STO provided in [3] has a 50 Ohms Rdc, which is equal to Rin, and Equation (3.6) can be rewritten as: Γ=
∆R − ∆Rin 100 + ∆R + ∆Rin
(3.7)
In [3], △R is varied from 13 Ohms to +13 Ohms and the total variation of △ R is 26 Ohms. If we only consider the 26 Ohms variation of STO motional resistance, it leads to 0.206 reflection coefficient according to Equation (3.7). The return loss (RL) is the negative part of the magnitude of the reflection coefficient in dB and it is given by [23]: RL(dB) = −20 log10  Γ 
(3.8)
In typical LNAs, the requirement of return loss is 15 dB to 20 dB[24], and the reflection coefficient calculated by Equation (3.8) is around 0.1. In high frequency LNAs, the requirement of reflection coefficient is 0.2 as
∆R − ∆Rin ≤ 0.2 100 + ∆R + ∆Rin
(3.9)
whose return loss is around 14 dB. The return loss of LNA for STO device in [3] is at least 0.206, which cannot meet the return loss requirement given by Pin1 = Vin ( 2
Z in1 2 ) / Z in1 Z in1 + R
(3.10)
due to the large variation of the STO motional resistance. Zin1 is the modified input impedance seen from the transmission line as shown in Figure 3.2. Vin is the RF signal of STO and Pin1 is the power obtained on Zin1 before the transmission line. The impedance mismatch brings inband power loss as well. Equations (3.10)(3.12) are the derivations of power loss: Pout 1 = Vth ( 2
Z out 1 ) 2 / Z out 1 Z in + Z out 1  18 
(3.11)
Chapter 3. Amplifier Requirements and Topology
Ploss = Pin1 − Pout 1
(3.12)
where Zout1 is the impedance seen from the end of the transmission line and Pout1 is the power obtained at the end of biastee network as shown in Figure 3.2.
Figure 3.2 Modified impedance matching
Equation (3.12) indicates the power loss during energy transfer from the generated signal of the MTJ STO to the input of the amplifier as shown in Figure 3.2. In practical case, the power loss can be measured by spectrum analyzer at the output port when an input microwave signal is injected at the input port.
3.2.2. Large motional resistance case One should notice that for large motional resistance case, the solution could be different. In ref [8], amplifiers with 50 Ohms input impedance and high input impedance are applied respectively when the output impedance of STO is up to several hundreds Ohms. Based on the comparison in [8], a proper power transfer from the STO to the amplifier requires the amplifier to exhibit sufficiently high input impedance. However, due to the large input impedance of amplifier, the reflection coefficient is increased. The larger reflection coefficient is harmful when taken the frequency hooping of STO into consideration because the reflected signal may modulate the current STO signal. The input impedance of amplifier will be discussed in Chapter 5. In [8], the STO device with large motional resistance is placed on the waveguide top and bottom electrodes and contacted by RF probes. The dominant  19 
Chapter 3. Amplifier Requirements and Topology inductance of RF probes can be neglected and the output impedance of STO device is close to the varied motional resistance of STO.
3.3 Amplifier Topology For the small motional resistance, there are many topologies that can be investigated. For instance, the broadband amplifier based on voltagecontrolled current source with resistive feedback which matches both the input and output impedance as shown in Figure 3.3 and the low noise amplifier with matching networks as shown in Figure 3.4 are possible topologies. However, since in this design a high gain amplifier with large bandwidth is required, both these topologies cannot meet the gain and bandwidth requirements at the same time. The broadband amplifier based on voltagecontrolled current source with resistive feedback cannot obtain high gain and the amplifier with matching network and low noise figure cannot achieve wide bandwidth at the input. Furthermore, the practical resistors, capacitors and inductors make the matching network even harder at high frequency [25].
Figure 3.3 Broadband amplifier based on voltagecontrolled current source with resistive feedback
Figure 3.4 Low noise amplifier with matching networks at input and output  20 
Chapter 3. Amplifier Requirements and Topology Therefore, the approach in this case is based on common gate (CG) stage, which has large bandwidth, as shown in Figure 3.5. The disadvantage of CG input stage is the poor noise performance, which requires special attention.
Figure 3.5 Basic commongate stage with capacitive coupling at input
For large motional resistance, it seems that TIA (Transimpedance amplifier) is a good choice. It is suitable for gigahertz oscillators that use highQ lateral micromechanical resonators with large motional resistance and large shunt parasitic capacitance. However, the output signal of STO is a voltage signal. Common source (CS) stage is wellknown for its low noise performance. However, CS stages have lower bandwidth, which requires analysis of the tradeoff between gain and bandwidth. Cascoded CS stage has better performance in gain and bandwidth, which is suitable in this case. The output signal of STO is unbalanced. In both small and large motional resistance cases, the first stage is responsible for gain, impedance matching, as well as unbalancebalance conversion. Balanced signal (differential pair) brings a lot of benefits. For example, differential pairs have higher immunity to “environment” noise, the current reuse technology can be applied, etc. There are several methods to convert the unbalanced signal into balanced signal. One method is to use external balun. However, it is expensive and there will be approximately 1.5 dB loss. A suitable method in the small motional resistance case is to use balunLNA topology. In the later case of large motional resistance, singletodifferential cascoded CS stages can be used.  21 
Chapter 3. Amplifier Requirements and Topology However, in both cases, the motional resistance (Rdc+△R) of STO varies in a large range. Thus, the design of impedance matching becomes tricky in such wide frequency range. Apart from the input stage, the following stages for both cases can be reused in both cases. According to the analysis of the amplifier requirements above, the input stage is a balunLNA with impedance matching. The following stages are limiting amplifier and buffer. Both cascading and cascoding techniques are utilized due to high gain requirement. The amplifier must also exhibit a 50 Ohms output impedance and an acceptable noise figure. The output buffer is required to match the output impedance and convert the balanced output to single output for testing at the same time. The topology of the amplifier can be seen in Figure 3.6.
Figure 3.6 Amplifier topology
The gain assignment of each stage can be seen in Table 3.2. The input LNA stages require around 10 dB gain, which is not large. Much of the gain can be obtained in LA chain stage. According to the requirement in Table 3.1, around 45 dB gain is required in the LA chain stage because that the gain loss of impedance matching and design imperfection should be taken into consideration. However, the gain is not the larger the better because that the 1.2V power supply limits the output
 22 
Chapter 3. Amplifier Requirements and Topology swing then governs the gain. Ideally, output buffer should have an unity gain, which cannot achieve in practical. Thus, the gain of output buffer should be as closest to unity as possible. The bandwidth of each stage should be larger than 9GHz in order to achieve the entire bandwidth requirement. Moreover, the test results are always worse than simulation results, which requires redundancy of bandwidth. The linearity of the latter stages of the amplifier is crucial for the entire linearity of the amplifier. The >10 dBm Output ThirdOrder Intercept Point (OIP3) of the latter stages makes it possible for dynamic range and intercept point requirements of PLL. On the contrary, the noise performance mainly depends on the first LNA stage. Based on the existing products of microwave amplifiers with 48 GHz frequency range, the possible maximum noise figure can be 5 dB [26]. Table 3.2 summarizes the amplifier requirements of each stage.
Table 3.2.Amplifier requirements of each stage gain
BW
OIP3
NF
S11
S22
LNA
≈10 dB
>9 GHz

<5 dB
<10 dB

LA
≈45 dB
>10 GHz >10 dBm



Buffer
≈0 dB
>9 GHz


<10 dB
3.4 Summary Based on the summary of the stateoftheart STO technology, requirements and amplifier topology for STO devices is proposed in this chapter. In the following chapters, the detailed amplifier design will be presented.
 23 
Chapter 4. Biastee and Current Source/Sink
Chapter 4. Biastee and Current Source/Sink
4.1 Biastee 4.1.1 Biastee Operation Biastee is an essential part in RF circuits. It is widely used when a DC source must be injected to a RF signal path. DC source should have no influence on the RF transmission when a proper biastee is applied. In another words, the impedance of DC path should be large enough to prevent loading. Thus, three ports are needed for a normal biastee. They are DC port, RF port and mixed port. These three ports are characterized in term of input and output RF impedance matching, isolation between RF and DC ports, insertion loss, bandwidth, DC current handling, RF power handling and size [27]. Biastees are usually with 50 Ohms impedance matching at both RF input and output. Simple and common biastee can be designed with RC or LC architectures. In this project, two types of biastee are required. One is designed for 50 Ohms system, while the other one is designed for high impedance. The choice of RC or LC architectures in Figure 4.1 is determined by the applied DC current. When a small DC current is injected (e.g. I < 10mA), RC architecture is used. In this case, the value of R should be much larger than 50 Ohms. This resistor can provide flat impedance over a wide frequency range compared to inductor [28]. For large current applications (e.g. I > 10mA), LC architecture is reasonable because that the voltage drop across R or power dissipation will be too large.
Figure 4.1 Biastee architecture (a).RC architecture (b).LC architecture  24 
Chapter 4. Biastee and Current Source/Sink Moreover, in the gigahertz systems, the low frequency cutoffs of biastees must be extended out into the megahertz domain or it should be down to 2 decades below the operation frequency. The low frequency cutoffs of biastee can be determined by Equation 4.1 and 4.2. fo =
1 2Π ( RsCs )
(4.1)
fo =
1 2Π LsCs
(4.2)
The choices of Rs, Cs and Ls should fulfill the requirement introduced above.
4.1.2 Transfer function The required DC current of STO varies from device to device. Thus, both large current and small current are possible in the STO applications. Correspondingly, both LC and RC architectures will be used. A formal analysis of the biastee transfer function requires the load to be included in the calculation. Thus, 50 Ohms and 1K Ohms loads will be considered in small and large motional resistance cases respectively in the following calculations.
A. LC architecture The small signal path of LC biastee can be seen in Figure 4.2. Zin is the input impedance of amplifier.
Figure 4.2 Biastee LC architecture The transfer function is: 1 Zin + + Ls ⋅ S Vout Ls ⋅ S Cs ⋅ S = Zin ⋅ ⋅ 1 1 Vin Zin + + Ls ⋅ S ( Zin + ) ⋅ Ls ⋅ S Cs ⋅ S Cs ⋅ S  25 
(4.3)
Chapter 4. Biastee and Current Source/Sink The input impedance Zin of amplifier is matched to 50 Ohms and 1K Ohms in small and large motional resistance cases respectively. According to Equation (4.3), in order to obtain a transfer function of unity gain, it requires: 1 →0 Cs ⋅ S
(4.4)
Therefore, Cs should be large enough to achieve unity gain and Ls should be much larger than Zin to prevent loading at high frequency. In practice, the input impedance of amplifier at high frequency is finite, which will be discussed in Chapter 5.
B. RC architecture The small signal path of RC biastee can be seen in Figure 4.3.
Figure 4.3 Biastee RC architecture
The transfer function is: 1 + Rs Vout Rs Cs ⋅ S = Zin ⋅ ⋅ 1 1 Vin Zin + + Rs ( Zin + ) ⋅ Rs Cs ⋅ S Cs ⋅ S Zin +
(4.5)
As in the large DC current case, in order to obtain a transfer function of unity gain, it requires: 1 →0 Cs ⋅ S
(4.6)
According to Equation (4.6), Cs should be large enough, at the same time, Rs should also be much larger than Zin to prevent loading.
 26 
Chapter 4. Biastee and Current Source/Sink
4.2 Biasing circuit and Current Source/Sink design As described in Chapter 3, a wideband amplifier is required for STO devices. Therefore, wideband biastee is required. Wideband biastees are relatively complicated to design. The reason is that the performance of biastee is heavily dependent on the parasitic inductance of DC blocking capacitor and parasitic capacitance of AC blocking inductor. Real inductor model and capacitor model can be seen in Figure 4.4[29]. Due to the parasitic capacitance or inductance, the applied inductor or capacitor should work under the Selfresonant frequency (SRF) to prevent oscillating.
Figure 4.4 (a).Model of real inductor L (b).Model of real capacitor C
4.2.1. Small motional resistance case Wideband biastees require large coupling capacitors Cs in order to reduce the effect on AC signal. The reactance Zs of this capacitor should fulfill the requirement of: ZS ≈
1 ≤ 50Ω ωC C S
(4.7)
where ωc is the cutoff frequency. The bandwidth requirement for STO amplifier is at least from 4 GHz to 8 GHz. According to the frequency cutoffs requirement in section 4.1.1., ωc should be lower than 2∏×200 MHz (200 MHz is 2 decades below 4 GHz). According to Equation (4.7), Cs should be larger than 15.9pF. For wideband biastees, the inductors must be large enough at the lowest required frequency. Ls is at least j500 Ohms at lowest frequency in this case of 4 GHz. Therefore, Ls is at least 19.89nH, which costs extensive onchip area. In addition, the inductor must definitely look like an inductor at 8 GHz in this application. In another words, the shunt parasitic capacitance of large  27 
Chapter 4. Biastee and Current Source/Sink inductor will cause the selfresonance at specific frequency and the SRF must be larger than 8 GHz. Apart from the selfresonance, this parasitic capacitance will also shunt the high frequency signal to ground. The loss of signal indicates the biastee is no more effective. Thus, the inductor is an uncertain element and a key issue in biastee. The inductor’s manufacture process will affect the circuit significantly. Apart from the parasitic effect of the inductor, it also brings nonlinearity to the amplifier, which is in form of the third order intermodulation. One should also make sure that the RF choke should not degrade the thirdorder intercept point (IP3) of the device. In [28], several inductors in series are used to cover a wideband frequency. Moreover, extra circuits need to be used in wideband biastees to avoid the shunt path. Thus, a proper broadband biastee is a very complex network. The inductor or resistor can be replaced by transistor. By using the transistors, the biastee and current source/ current sink can be designed together. Note that it is a conventional biasing circuit, not biastee now. Current source/current sink is a critical part of STO device as explained in Chapter 2. In different STO devices, the injected DC currents are different. According to the analysis in Chapter 3, the DC current varies from 0.1mA to several milliamps. Several milliamps current source/current sink requires very large size transistors and high power supply. Apart from the large variation in DC current value, some of the STO devices need a current source while the others require current sink. Thus, a dual current source/sink topology as shown in Figure 4.5 is necessary and it calls for an up to 100uA high accuracy, large current handling capacity and low noise. In Figure 4.5, Port 1 is an AC/DC mixed signal port, which is the output of STO and the AC input of the biastee. Port 2 is the injected DC current source/sink, which should flow into Port 1. By controlling the gate voltage of the transistors, the dual current source/sink device is switched to current source or current sink asynchronously. Port 3 is the input of amplifier, which is the AC output of the bias tee.
 28 
Chapter 4. Biastee and Current Source/Sink
Figure 4.5 Dual current source/sink and biasing topology
Due to the relatively small Rds of transistors in 65nm CMOS process, to increase the output resistance, cascode topology is used as it can be seen in Figure 4.6. In order to prevent the signal shunting to ground through the capacitance of transistor, Cgs and Cds of transistors M0/M2 in Figure 4.6 should be small enough. The total impedance can be calculated by: Rout = [1 + ( g m0 + g mb 0 ) ⋅ Rds 0 ] ⋅ Rds1 + Rds 0
(4.8)
The impedance of Cgs and Cds should be much larger than 50 Ohms at highest operation frequency. Cgs and Cds should be less than 20 fF in order to reveal 1KOhms impedance at 8 GHz. In order to relieve the voltage requirement of the transistor when a relatively large current is injected, a wide transistor M1 is needed. All the transistors are using double contact row in order to increase the current handling capacity. The schematic can be seen in Figure 4.6 and the transistors’ size is given in Table 4.1. The impedances of cascoded transistors, which are seen from AC & DC port in current source and current sink cases are given by the Smith Chart shown in Figure 4.7, Z11 is given in Figure 4.8.
 29 
Chapter 4. Biastee and Current Source/Sink
Figure 4.6 Biasing and current source/sink in small motional resistance case
Table 4.1 Transistors’ size of biasing and current source/sink in small motional resistance case M0/M1
M2/M3
PM0/PM1
PM2/PM3
type
N_12_LLLVTRF N_BPW_12_LLNVT P_12_LLLVTRF P_12_LLLVT
L
60nm
200nm
60nm
120nm
W_tot 24um
240um
32um
300um
Figure 4.7 Impedance of biasing and current source/sink
 30 
Chapter 4. Biastee and Current Source/Sink
Figure 4.8 Impedance Z11 of biasing and current source/sink
In these figures, the impedance drops from 728.6 Ohms at 4 GHz to 395.4 Ohms at 8 GHz in current sink case and from 635.5 Ohms at 4 GHz to 369 Ohms at 8 GHz in current source case. Compared to the 50 Ohms STO, the AC blocking impedance is acceptable. The Sparameter analysis can be seen in Figure 4.9 (current sink case) and 4.10 (current source case). The DC current handling capacity is 8mA in this design due to the supply voltage of 1.2V. In both current source and current sink cases, the lower the injected DC current is; the better the biastee performance is. However, in the current source case, the performance is worse due to the PMOS devices limitations. The Sparameter analysis given in Figure 4.9 (current sink case) and 4.10 (current source case) is extremely necessary for the biastee network. S11 and S33 are the input and output return losses, which are always less than 17.5 dB at the required frequency when the injected DC current source is in the range of 02.5 mA and DC current sink is in the range of 08mA. S13 and S31 indicate the cutoff frequency fc, which is around 100 MHz, which is much less than required 200 MHz. The DC bias port isolation S12 is around 75 dB in both current source and current sink cases. The input of biastee (output of STO) and output of biastee (input of amplifier) nearly have no influence on DC port according to the S21 and S23.
 31 
Chapter 4. Biastee and Current Source/Sink
Figure 4.9 Sparameter analysis of biasing and current sink
From these simulation results it can be seen that the small current handling capacity has a maximum of 8 mA in current sink case and 2.5 mA in current source case, which cannot meet the current requirement in small motional resistance case of 9 mA in [3]. This is mainly caused by the limitation of the supply voltage.
 32 
Chapter 4. Biastee and Current Source/Sink
Figure 4.10 Sparameter analysis of biasing and current source
4.2.2. Large motional resistance case The motional resistance of STO devices can be up to 1K Ohms. In this case, a biastee, which exhibits j10K Ohms in the required frequency range, is necessary. Onchip inductor is infeasible due to the large area and uncertainty. Several kilo Ohms resistor should be also avoided due to the DC current requirement and supply voltage. According to the simulation result in Figure 4.8, the cascoded MOS topology is also infeasible due to the small impedance at high frequency.
 33 
Chapter 4. Biastee and Current Source/Sink
4.3 Summary Biastee/biasing for injected DC current is infeasible in 65nm process with 1.2V power supply in both small motional resistance and large motional resistance cases. Offchip wideband biastee will be designed in the future work.
 34 
Chapter 5. Input Stage of Amplifier
Chapter 5. Input Stage of Amplifier
5.1 Input stage in small motional resistance case As described in Chapter 3, the balunLNA is employed to meet the requirements. In order to reach a high gm of CG stage, which is equal to 20mS, a large product of W/L and drain current (ID) are required. One method is to increase the current ID, which results in smaller load and lower gain. The other method is to increase the ratio W/L of the input transistor, which causes that the Ft corner moves toward the direction of larger drain current. As a result, Ft is reduced when the current is small. In another words, the bandwidth will be reduced. Thus, there is a tradeoff between gain and bandwidth. In a 65nm process, the small Rds should be also taken into account. Fortunately, the relatively small Rds relieves the requirement of gm in the input stage. Furthermore, the bond wire has high impedance, which causes inductive discontinuities. The inductive discontinuities lead to impedance mismatch and bring unwanted reflection. In order to match the input impedance to 50 Ohms, the bond wire should be taken into consideration along with the input stage. The lumped circuit model for bond wire can be seen in Figure 5.1 [30]. The parasitic capacitance and resistance can be regarded as constant with respect to the inductance value. R is 0.2 Ohms and 0.3 Ohms for 15 and 25 mil wires respectively. The optimized L’ and C are 0.05nH and 17.5 fF, respectively. L is dominant at high frequency.
Figure 5.1 The lumped circuit model of bond wire
 35 
Chapter 5. Input Stage of Amplifier The freespace inductance L is given by Equation (5.1) [31] [32] [33]:
L = 2 × 10 −4 l[ln{
2l 2l d d + l + ( ) 2 } + − 1 + ( ) 2 + C ] (nH) d d 2l 2l
(5.1)
where d and l (in microns) are diameter and length of the wire and C is frequencydependent correction factor, which is a function of bond wire diameter and its material’s skin depth. A rule of thumb is that bond wires have an inductance of 1 nH/mm [34]. Assume small dieattach area package is applied, approximate 1.5 nH to 2 nH inductance is used in the model. Along with the parasitic capacitances of bond pad and Electrical Static Discharge (ESD) protection diodes, the approximate package model is given in Figure 5.2. The ESD protection diodes are embedded within the IC package. Total shunt capacitances are assumed 120 fF.
≈ Figure 5.2 Approximate package model
Based on the analysis above, the transistors’ size of input LNA can be seen in Table 5.1.
Table 5.1. Parameters of the input transistors M03 Transistor(s) M0
(current M2
M1, M3
source) Transistor
N_12_LLLVT N_BPW_12_LLLVTRF N_BPW_12_LLLVTRF
type VDS
0.3 V
0.3 V
0.3 V
IDS
1.223 mA
1.242 mA
1.907 mA
L
180 nm
60 nm
60 nm
 36 
Chapter 5. Input Stage of Amplifier Transistor(s) M0
M2
M1, M3
W
1.8 um
1 um
2 um
NF
10
16
12
W_tot
18 um
16 um
24 um
gm
6.5 mS
9.36 mS
14.12 mS
Rds
1187.8 Ohms
600.01 Ohms
393.31 Ohms
Cgs
33.84 fF
10.03 fF
15.02 fF
Cgd
4.13 fF
3.97 fF
5.91 fF
Cds
0.27 fF
2.11 fF
3.18 fF
Cdb
0.07 fF
0.07 fF
0.10 fF
Vgs
0.7028 V
0.6 V
0.6 V
Intrinsic
7.72
5.61
5.55
gain
In this case of small motional resistance, CG (M2) and CS stages (M1) are used as input stage as shown in Figure 5.3. The CG stage achieves wideband input impedance matching while the CS stage generates an antiphase output signal [35]. CS stage is cascoded (M3) in order to achieve a high voltage gain via R1. Cascoded CS also helps to reduce the Miller effect, which leads to larger bandwidth.
Figure 5.3 CGCS balunLNA – input stage  37 
Chapter 5. Input Stage of Amplifier Noise performance is improved [36] thanks to the introduction of crosscoupling Cc1/Cc2 (1 pF) as shown in Figure 5.3. The noise figure of CG stage without crosscoupling capacitor can be written as:
(Vn + In ⋅ R ) NF = 1 + 4kTR
2
(5.2)
where R refers to the source impedance, which is the motional resistance of STO, Vn is the input referred noise voltage and In is the input referred noise current. The gate noise of CG stage is insignificant. Neglecting the effect of gate noise of CG stage, the noise figure can be rewritten as: 2
1
=R γ gm 1 γ gm NF ≈ 1 + ⋅ ⋅ →1 + 1 α α gm ⋅ R
(5.3)
R where α and γ are biasdependent parameters: α is the ratio between the voltage signal obtained at the input of amplifier and the voltage source generated by STO devices, γ is the coefficient, which depends on the channellength of the transistor. Equation (5.3) can be rewritten as:
γ gm 1 NF ≈ 1 + ⋅ ⋅ α 1 Gm ⋅ R
2
(5.4)
R
where gm in (gm·R) product is replaced by effective transconductance Gm because that noise figure changes as Gm changes. In the conventional CG stage, the effective transconductance is equal to gm. If the effective Gm can be increased, the noise figure will be reduced. Thus, a feedback with gain Afb is required. The noise performance improvement requires a passive component, which will not introduce extra noise into the CG stage. Thus, the method of crosscoupling capacitor is introduced. As shown in Figure 5.3, Afb can be calculated as:
A fb =
Cc Cc + C gs
(5.5)
If Cc is large enough compared to Cgs, Afb is nearly to unity. The effective Gm with crosscoupling capacitor is:
Gm = (1 + A fb ) ⋅ gm The noise figure in this case can be derived based on Equation (5.4):
 38 
(5.6)
Chapter 5. Input Stage of Amplifier 1 γ gm NF ≈ 1 + ⋅ ⋅ α 1 (1 + A fb ) ⋅ gm ⋅ R
2
(5.7)
R
In order to keep the impedance matching, Gm should match to R. Thus, gm is two times smaller than that with crosscoupling capacitor, which relieves the requirement of gm as well. Equation (5.7) can be rewritten as: 1
=R
Gm NF →1 +
1 γ γ ⋅ ≈ 1+ α 1 + A fb 2 ⋅α
(5.8)
From Equation (5.8), one can find that the noise performance is better compared to Equation (5.3). In addition, this capacitive crosscoupling technique helps to boost the transistor transconductance, which results in gain boosting at the same time. The effective transconductance is doubled according to [37]. Furthermore, the power consumption is reduced due to the lower transconductance gm. The CG stage will be biased by the current source M0. The transistor size of current source M0 should also be small enough to avoid the parasitic effect. Note that the current source should have a large Rds to reduce the common mode disturbance. R0, R1 are chosen to be 500 and 325 Ohms respectively in order to obtain same gain on both branches. Cout is a DC blocking capacitor. Inductive peaking is introduced by inductor I0 to increase the bandwidth. Equation (5.9) gives the ratio between two time constants RC and L/R: m=
RC L/R
(5.9)
According to Equation (5.9), when m=2, it has the significant bandwidth enhancement without excessive frequency response peaking [38]. Thus, the inductor I0 is chosen to be 3 nH and m is 1.76 in this case. The input impedance can be estimated by using the parameters in Table 5.1 and Equation (5.10): Rin = Rds 0 // Rds 2 //
1 gm2
(5.10)
where Rds0 and Rds2 are 600 Ohms and gm2 is 9.3mS. The calculated input impedance is around 91 Ohms. The input impedance with the bond wire effect can be verified by using Z11 and Smith Chart as shown in Figure 5.4. In the figure, one can see that the  39 
Chapter 5. Input Stage of Amplifier normalized input impedance is close to unity in Smith Chart. As the frequency increases, reactance tends to be inductive, which indicates the inductance of bond wire is dominant at high frequency. The input impedance matching can be characterized by S11, which is always lower than 11.5 dB in the required frequency range 48 GHz as shown in Figure 5.5, which means that the input impedance matching meets the requirement given in Chapter 3.
Figure 5.4 Input impedance of the balunLNA
Figure 5.5 S11 of the balunLNA
 40 
Chapter 5. Input Stage of Amplifier The biasing circuit for Vb1,Vb2 and Vb3 can be seen in Figure 5.6. They are biased by the current mirrors. The entire current mirror is not drawn in Figure 5.6. The transistors size of biasing circuit can be seen in Table 5.2. Due to the channel length modulation, the current source M0 in Figure 5.3 cannot accurately copy the current from M3 in Figure 5.6. Thus, R1 of 444 Ohms is employed in order to reduce the impact of channel length modulation.
Figure 5.6 Biasing circuit for CGCS balunLNA – input stage
Table 5.2 Parameters of the biasing transistors M1M3 Item
M1
M2
M3
Transistor type
N_12_LLLVT
N_12_LLHVT
N_12_LLRVT
W
4 um
2.4 um
2.7 um
L
500 nm
500 nm
500 nm
NF
10
10
10
W_tot
40 um
24 um
27 um
A total 25 fF capacitive load, which represents the total output capacitance and the input capacitance of the coming stage (switch), is added at the output. The total AC gain is up to 14.23 dB (with bonding wire model and 50 Ohms source impedance) at 2.8 GHz with 0.111.65 GHz bandwidth, which is shown in Figure 5.7. There is a gain mismatch of maximum 0.7dB at 11.65GHz between CG and CS branches. From this result, it can be concluded that the proposed input stage has a slight gain imbalance.
 41 
Chapter 5. Input Stage of Amplifier
Figure 5.7 Gain of balunLNA with same gain at CG and CS branches
Thanks to the introduction of balun, the differential output pair helps to reduce considerably the noise when CG is employed. The input referred noise of the whole LNA stage is given in Figure 5.8 (a). Compared to the single CS and CG stages, a part of noise is cancelled by the differential pair. At 5 GHz, the input referred noise is around 766pV/sqrt(Hz). In Figure 5.8 (a), it can be seen that the noise figure is less than 4.8 dB in required frequency range which meets the requirement presented in Chapter 3. The noise figure in Figure 5.8 (a) is taken out to compare with that without capacitive crosscoupling technique. Figure 5.8 (b) presents the noise performance improvement when capacitive crosscoupling technique is used. The noise figure is improved more than 1 dB in the required frequency range.
Figure 5.8(a)
 42 
Chapter 5. Input Stage of Amplifier
Figure 5.8(b)
Figure 5.8 Noise performance of LNA (a). The input referred noise and noise figure (b). Noise figures with and without capacitive cross coupling
Compared with [35], higher noise figure in this case is because this topology suffers from a tradeoff between noise performance and source impedance matching. In [35] [39], the noise cancellation technique is proposed based on the negligible noise generated by other transistors except M2 in Figure 5.3. It requires large sizes of other transistors except M2, which results in less than 6 GHz bandwidth in [35] [39]. Due to the bandwidth requirement, the sizes of all transistors in this case should be small. Thus, the noise generated by transistors M0 and M1 can not be neglected anymore, which makes the noise cancellation extremely hard. The most dominant noise contributors are: 1) external resistor for thermal noise enhancement of transistor M1 in Figure 5.3; 2) the thermal noise of current source transistor M0 in Figure 5.3; 3) the thermal noise of M1. The first noise contributor cannot be eliminated or reduced because it depends on the process. The second and third noise contributors can be reduced by using large transistors, which increase the parasitic capacitance at the input and indirectly reduce the gain and bandwidth. Reducing the bias current can help to reduce the second noise contributor too. But this is also at the cost of reduction of gain. The gain reduction of the input stage will affect the total noise figure of the amplifier. In order to obtain enough gain in the input stage, the load resistor should be increased, which will reduce the bandwidth and also increase the noise of the load resistor. To conclude, there is a tradeoff between the noise performance and  43 
Chapter 5. Input Stage of Amplifier requirements of gain and bandwidth. The requirements of noise cancellation in this design include: no compromise of the source impedance matching and no feedback which may cause instability and gain loss. In addition, the output signal of CG stage and cascoded CS stage should be balanced. In [40], onchip transformer is used to improve the noise performance, which costs large onchip area. In some specific topologies, a method that utilizes the different sign for noise and signal is used [41], which is also applicable in this case. Based on this method and [35], a scaling factor n can be used to improve the noise performance. The scaling factor n is referred to the ratio between the W/L of CS transistor and that of CG transistor. The noise figure decreases as n increases. At the same time, the gain also increases as n increases. However, as n increases, the gain mismatch is also increasing due to the increasing gain of CS and constant gain of CG. In this case, the scaling factor is chosen to be 1.5 with a good tradeoff between gain matching and noise performance. The scaling factor cannot be increased further in this design due to the gain and bandwidth requirements. The NF can be reduced further in this design by increasing the fingers of the transistors, which is also at the cost of slight bandwidth shrinking due to the increasing parasitic effect. The source stability circle (SSB) presented in Figure 5.9 illustrates the boundary between values of source impedance that cause instability and values without instability. In a 50 Ohms impedance system, the center of the normalized Smith Chart is in the stable region. The unstable regions in the required frequency range can be seen as Figure 5.9. From the figure, one can see that all the circles resides completely outside the  Γs = 1 region, which indicates it is unconditionally stable in required frequency range. The stability and gain can also be verified by the transient analysis as it can be seen in Figure 5.10. The voltage gain of 16 dB can be calculated from Figure 10(b) and Figure 10(e), which is verified by Figure 5.7 with 14.23 dB gain.
 44 
Chapter 5. Input Stage of Amplifier
Figure 5.9 Source Stability Circle of the LNA
Figure 5.10 Transient analysis of input stage (a). A 1mVpp test signal at input port. (b). The signal 1.5mVpp at the input of amplifier, after bonding wire. (c),(d). The output signal of CG and cascoded CS branches respectively. (e). The differential output signal 9.765mVpp
 45 
Chapter 5. Input Stage of Amplifier A figure of merit of linearity is thirdorder input intercept point (IIP3). Twotone test is applied to calculate the IIP3 of the CGCS LNA with two tones at 5GHz and 5.02 GHz. IIP3 is 3.5 dBm as shown in Figure 5.11.
Figure 5.11 IIP3 of CGCS LNA
5.2 Input stage in large motional resistance case As described in the Chapter 2, the singledifferential CS input stage is employed in this case. A resistor of 1K Ohms represents the large motional resistance at the source. The dominant pole in the CS stage is the output node. If the load resistor is large to achieve a high gain, the pole at the output node will be close to axis, which indicates that the bandwidth will shrink. CS stages have acceptable gain while the bandwidth cannot meet the requirement. Therefore, the CS stages are cascoded to reduce the Miller effect, hence to increase the bandwidth. The proposed input stage is shown in Figure 5.12.
 46 
Chapter 5. Input Stage of Amplifier
Figure 5.12 Cascoded CS input stage
The differential pair is biased by the current source. A modification is required based on the conventional singledifferential cascoded CS stage to relieve the size requirement of the current source transistor M0. A large size current source transistor M0 is required to reduce the common mode disturbance. However, the parasitic capacitance will shunt the signal to ground in singledifferential stage. For this reason, a modification is proposed to provide a reversed sign of input signal. Due to the fact that signal obtained at node X is close to input signal (gain is close to unity) and the sign is opposite, the signal of node X can be transferred to the other branch of the differential pair. However, node X suffers from a large parasitic capacitance, which will be the dominant pole and will shrink the bandwidth. Reducing the transistors sizes of M1M4 in the signal path can help to keep the bandwidth, at the price of reduction on gain. The parameters chosen for transistors in cascoded CS stage are listed in Table 5.3.
Table 5.3 Parameters of the transistors of cascoded CS input stage Item
M1M4
M0
Transistors type
N_BPW_12_LLLVTRF
N_12_LLLVT
VDS
0.3 V
0.3V
 47 
Chapter 5. Input Stage of Amplifier Item
M1M4
M0
IDS
1.074 mA
2.15mA
L
60 nm
500nm
W
2 um
10um
NF
8
12
W_tot
16 um
120um
gm
8.66 mS
15.65 mS
Rds
662.89 Ohms
1150.41 Ohms
Cgs
9.46 fF
589.43 fF
Cgd
3.66 fF
26.42 fF
Cds
2.03 fF
0.74 fF
Cdb
0.07 fF
1.41 fF
Vgs
0.58 V
0.597 V
Intrinsic gain
5.74
18.01
In Figure 5.12, the load resistors R0 and R1 are 247 Ohms. The inductor is chosen to be 1.5 nH in order to achieve the maximum bandwidth without excessive frequency response peaking. Vb2 of the input stage is biased to 0.9V by current mirror as shown in Figure 5.13. The entire current mirror is not drawn in Figure 5.13. The transistor sizes of the biasing circuit can be seen in Table 5.4.
Figure 5.13 Biasing circuit for Cascoded CS balunLNA
 48 
Chapter 5. Input Stage of Amplifier Table 5.4 Parameters of the biasing transistors M12 Item
M1 (current source)
M2
Transistor type
N_12_LLLVT
N_12_LLHVT
W
3 um
2.4 um
L
500 nm
500 nm
NF
8
10
W_tot
24 um
24 um
The maximum total AC gain is approximately 8.4 dB (≈2.63) at approximately 1 GHz with 0.059 GHz bandwidth when 1K Ohms source impedance is employed and it is 9.1dB (≈3) with 0.0516 GHz bandwidth when 50 Ohms source impedance is added, as it can be seen in Figure 5.14. The bond wire model is not taken into consideration in this case. The input port will be connected to the RF probe pad, where the dominant inductance can be neglected. When the input port is connected to the bond wire, the input impedance will drop severely as shown in Figure 5.15. At 5 GHz, due to the bond wire effect, the input impedance is around 120 Ohms, which is much smaller than motional resistance of STO. The signal obtained at the input of amplifier is a very small portion of the signal generated by STO. Furthermore, the unwanted reflections increase and the noise performance deteriorate sharply. As in ref [8], the STO device with large motional resistance, which requires high input impedance amplifier, is connected via RF probe pad as well. Thus, STO device can be placed very close to the input of the amplifier and connected together via RF probe pads. As shown in Figure 5.16, the input impedance of cascoded CS stage drops from 1.91K Ohms at 4 GHz to 1K Ohms at 8 GHz.
 49 
Chapter 5. Input Stage of Amplifier
Figure 5.14 AC responses of cascoded CS stage
Figure 5.15 Input impedance with bond wire effect at 5 GHz
Figure 5.16 Input impedance of the cascoded CS stage  50 
Chapter 5. Input Stage of Amplifier The noise performance can be seen in the Figure 5.17. The input referred noise of balunLNA input stage in large motional resistance case (1K Ohms motional resistance) is around 2.5 nV/sqrt(Hz). The noise figure is less than 2.3 dB in the required frequency range of 48 GHz. Comparing the noise figure of the cascoded CS stage with the CGCS stage, the noise performance is much better in cascoded CS stages.
Figure 5.17 Noise performances of cascoded CS stages Finally, the transient analysis is carried out to verify that the LNA is working properly. 1mVpp test signal is applied, about 1.5mVpp is obtained at the input of the amplifier due to the signal reflection as it can be seen in Figure 5.18(a). The gain can be calculated from Figure 5.18, which is approximate 9 dB when 1K source impedance is used. This is verified by Figure 5.14 with 8.4 dB gain. In Figure 5.18 (c) and (d), one can see that there is only a slight gain mismatch between two branches. The small motional resistance case is only applicable for STO devices with around 50 Ohms motional resistance. When a STO device with larger than 50 Ohms motional resistance is applied, the large motional resistance case should be applied. Moreover, it is important to use 50 Ohms motional resistance in the simulation to compare the simulation results with that of other works with 50 Ohms source impedances. Thus, the lower limit of input impedance for large motional resistance case is 50 Ohms, and the upper limit is 1K Ohms due to the input impedance dropping of cascoded CS stage. Both of the lower limit and upper limit of motional resistances  51 
Chapter 5. Input Stage of Amplifier are used in the IIP3 simulation. The IIP3 in this case is 3.5 dBm when the motional resistance is 50 Ohms and it is 13.5 dBm when the motional resistance is 1K Ohms, which is given in Figure 5.19.
Figure 5.18 Transient analysis of cascoded CS stages (a). A 1.5mVpp signal obtained at the input of amplifier when 1mV test signal is applied. (b). (c). 2.2mVpp signals obtained at positive and negative outputs. (d). The 4.3mVpp differential output signal
Figure 5.19 IIP3 of cascoded CS LNA  52 
Chapter 5. Input Stage of Amplifier In order to analyze the performance of proposed LNAs, comparisons of the proposed LNAs and stateoftheart LNAs and Baluns are given in Table 5.5. The LNAs proposed in this design are competitive in bandwidth, power consumption, noise performance and balun integration as shown in Table 5.5. In this work, 25 fF capacitive load is applied during the simulation. This 25 fF capacitive load is composed of the total output capacitance of the LNA stages, the total input capacitance of the next stage and the parasitic capacitance of DC blocking capacitors. What should be stressed is that this work is specific for two types of systems: 50 Ohms system and HighZ system (1K Ohms).
Table 5.5 Comparison of the proposed LNAs with stateoftheart LNAs and Baluns Ref
Freq.
NF
Gain
IIP3
Power
Proc.
Band
[dB]
[dB]
[dBm]
[mW]
Vsupply
Balun
Gain
?
imbal.
[GHz] This work
[dB]
0.111.65 5.2
14.23
(50 Ohms) This work 0.059
3.13
8.4
(1K
3.5 at 6.3
65nm
5GHz
1.2V
13.5at
4.1
5GHz
65nm
YES
<0.7
YES
<0.45
YES
<0.7
N/A
1.2V
Ohms) [35]
0.25.2
3.5
JSSC
13
0
21
15.6
65nm 1.2V
2008 [42]
0.55.6
4.3
30*
24
19
130nm YES
RFIC
(core:
(core:
(core:
1.2V
2009
19)*
12) at 8) 4 GHz
[43]
0.82.5
4
4
high
MTTS
passive
180nm YES
balun

12.5
90nm
<0.4
2005 [39]
0.86
3.5
1820
3.5
JSSC
2.5V
2006
 53 
YES
>6
Chapter 5. Input Stage of Amplifier Ref
Freq.
NF
Gain
IIP3
Power
Proc.
Band
[dB]
[dB]
[dBm]
[mW]
Vsupply
Balun
Gain
?
imbal.
[GHz] [44]
2.39.2
[dB] 7
9.3*
JSSC
6.7 at 9
180nm NO
6 GHz

N/A
2004 [45]
0.58.2
2.6
25
4/16
42
NO
N/A
3 at 2 9
180nm NO
N/A
GHz

ISSCC
90nm 2.7V
2006 [46]
0.047
6.2
8*
JSSC 2006 * present in S21
Based on the comparison in Table 5.5, the proposed LNAs in this work have larger bandwidth while the power consumption is much lower than other LNAs. Besides, two proposed LNAs have competitive noise performance and linearity in such wideband. In addition, compared with [44][46], active baluns are integrated with LNAs to avoid the external passive baluns. Furthermore, compared with [35] who used the same CMOS process, proposed CGCS LNA in this work is superior in gain and bandwidth product.
5.3 Switch In order to reuse the following stages, switches are necessary in this design. A transistor is employed as a switch and it is working in deep triode region, where the linear resistor is given by [47]: Ron =
1 W µ n Cox (VGS − VTH ) L
(5.11)
The gate of the transistor is used as control port, which is connected to 1.2V supply voltage when it is on and to ground when it is off. In order to reduce the voltage drop and noise contribution of transistor, the ratio W/L should be maximized.  54 
Chapter 5. Input Stage of Amplifier However, the parasitic capacitance is the killer at such high frequency. Thus, it is a tradeoff here between bandwidth and switch performance. The size of the transistor is 12um/60nm with 12 fingers. The gds and Rds characteristics of chosen transistor can be seen in Figure 5.20. When Vds is 0, the Rds is around 38 Ohms. As the ratio of W/L increases, Rds decreases. The switch in this case slightly degrades the amplifier performance of bandwidth and noise.
Figure 5.20 gds vs. Vds and Rds vs. Vds characteristics of switch transistor
5.4 Summary Two balunLNAs were proposed for the input stages of amplifier: CGCS LNA, which is suitable for small motional resistance case, and cascoded CS LNA, for the large motional resistance case. The two LNAs proposed in this design are competitive in bandwidth, power, noise performance and input balun. However, CGCS stage has inferior noise performance compared to other topologies, which can be investigated further. The gain requirement as discussed in Chapter 3 is larger than 45 dB. The voltage gain obtained in the input stages is far from enough. Thus, limiting amplifier will be employed to achieve the gain requirement.
 55 
Chapter 6. Limiting amplifier
Chapter 6. Limiting amplifier
6.1 Limiting amplifier Due to the low output level of STO, an amplifier with large gain is required. A cascade of several amplifier stages can be used to achieve the high gain. In such cascade topology, each stage should exhibit high linearity, large bandwidth and large gain. Limiting amplifier (LA) is employed to meet the requirements. LA is a cascade of broadband gain stages, which is implemented in an openloop configuration [48]. Openloop amplifier suffers from nonlinearity issue [47]. Fully differential topology should be employed to eliminate the evenorder harmonics, which results in better linearity. LA has advantages, such as, easier design, low supply voltage, low power consumption, good noise performance, etc [49]. Assume that each stage of LA has a bandwidth of BW, the relationship between BW and the total bandwidth BWtot of cascaded stages can be calculated by [50]: BWtot = BW ⋅ m 21/ n − 1
(6.1)
where n is the number of identical stages, m is 2 for firstorder circuits and 4 for secondorder circuits. The total bandwidth requirement in this project is 8 GHz, then the total bandwidth of LA should be at least 10 GHz. The gain of each stage cannot excess 10 dB at such high frequency due to the large output conductance in 65 nm process. Besides, for a large number of stages, noise will be accumulated rapidly. According to [51], n should be lower than 5 when a good noise performance is needed in the design. Thus, 5 stages are needed for LA. According to Equation (6.1), BW per stage should be at least 16 GHz when 5 stages of secondorder circuits are required. Assume that the gainbandwidth product per stage can be represented by GBW, the relationship between GBW and total gainbandwidth product GBWtot of cascaded stages can be expressed as: GBW =
GBWtot Atot (1−1/ n ) ⋅ m 21/ n − 1  56 
(6.2)
Chapter 6. Limiting amplifier where GBWtot = Atot ⋅ BWtot and GBW = Atot 1/ n ⋅ BW . An around 50 GHz GBW is required when a 10 GHz total bandwidth and 50 dB gain are needed. Approximately 10 dB (≈3.125) gain is required per stage. However, the performance in practical is much worse. It is hard to obtain 10 dB per stage in 65 nm process due to the large output conductance and low intrinsic gain. In order to achieve higher gain, the load resistor should be large enough, which leads to narrow bandwidth. The tradeoff between bandwidth and gain will be discussed further considering the case studies in section 6.2. In addition, the optimal LA approach will be proposed in section 6.3.
6.2 Case studies 6.2.1 Cascaded LA using CS stages The choices of amplifier topologies are limited due to the low supply voltage in 65nm process. First, the simplest LA topology, which is composed of several CS stages, is considered. The schematic can be seen in Figure 6.1. The load capacitance is not shown in the following schematics, but a 20 fF capacitive load (the total parasitic capacitance at output node) is taken into consideration during the simulation. The load resistors R0 and R1 are 600 Ohms in order to obtain high gain. The CS stages are biased at 1mA. Due to the bandwidth requirements, only the NMOS solutions are feasible.
Figure 6.1 CS stage of Limiting amplifier  57 
Chapter 6. Limiting amplifier The AC simulation results of single CS stage and 5 cascaded stages can be seen in Figure 6.2. According to the Equation (6.1), 8 GHz total bandwidth can be achieved when the bandwidth of single CS stage is around 18.56 GHz. However, the imperfections of the process degrade the performance of the amplifier severely as it can be seen in Figure 6.2. The total gain of 5 cascaded stages is around 41.25 dB and the bandwidth is only 5.6 GHz, which cannot meet the bandwidth requirement.
Figure 6.2 Simulation result of CS stage
In this LA, composed of 5 CS stages, Miller effect is the dominant reason of bandwidth shrinkage. Methods should be proposed to mitigate or eliminate Miller effect. In section 6.2.2 and 6.2.3, two methods will be proposed to mitigate Miller effect.
6.2.2 Cascaded LA using CS stages with negative Miller capacitors compensation Negative Miller capacitor is often used in LNA compensation to enhance the bandwidth. The CS stage is compensated by using a crosscoupled capacitor between the input and output of the stage. The negative Miller capacitors introduce a peaking at the required frequency range, at the same time increase the input transconductance [52], which will increase the gain. The mechanism of the negative Miller capacitance is the reduction of effective capacitive load [48]. The single CS stage with negative  58 
Chapter 6. Limiting amplifier Miller capacitors can be seen in Figure 6.3. However, it degrades the linearity and causes the stability issue in cascading limiting amplifiers.
Figure 6.3 CS stage with negative Miller capacitors compensation
The compensation effect of negative Miller capacitors can be seen in AC simulation result in Figure 6.4. The gainbandwidth product increases due to the peaking introduced by negative Miller capacitors. The gain is up to 52 dB while the bandwidth is around 13 GHz when 5 stages are cascaded. However, the issue behind this satisfactory result is instability, which is dangerous in LA. The circuit may oscillate in the desired frequency range, and the cascaded stages act as a ring oscillator.
Figure 6.4 Simulation result of CS stage with negative Miller capacitors compensation  59 
Chapter 6. Limiting amplifier
6.2.3 Cascaded LA using cascoded CS stages Cascoded stages can help to reduce the Miller effect, which results in larger bandwidth. In addition, Cascoded CS stage achieves a higher voltage gain via the load resistors compared with CS stage. Gain is increased due to the higher output impedance. In CS stage, the dominant pole is at the output node. In order to alleviate the effect caused by the dominant pole, the load resistors should be reduced. However, the gain will be reduced as the load resistors reduce. A large bias current is needed to compensate the gain loss.
Figure 6.5 Cascoded CS stage
The AC simulation result can be seen in Figure 6.6. The gain is decreased slightly compared with the CS stage while the bandwidth is around 6 GHz which is larger than that of CS stage. The relationship between the bandwidth per stage and the total bandwidth is in accordance with Equation (6.1). However, the bandwidth of 6 GHz cannot meet the requirement of 8 GHz (at least 8 GHz, but excessiveness of bandwidth is strongly needed). Methods to further enhance the bandwidth are required.
 60 
Chapter 6. Limiting amplifier
Figure 6.6 Simulation result of cascoded CS stage of Limiting amplifier
6.2.4 Cascaded LA using current mirror In a basic current mirror, the relationship between mirrored current and reference current can be written as Equation (6.3) when neglecting the channellength modulation. Iout =
(W / L) 2 ⋅ Iref (W / L)1
(6.3)
where Iout is the mirrored current and Iref refers to reference current. By choosing the suitable size of transistors, the current mirror can be used as wideband limiting amplifier. In order to meet the bandwidth requirement, the transistors that compose the current mirror should be small in sizes. The current mirror can be seen in Figure 6.7. The ratio between PM1 (PM3) and PM2 (PM4) is chosen 2. PM1 and PM2 are very small transistors.
Figure 6.7 Current mirror stage  61 
Chapter 6. Limiting amplifier The AC simulation result of one current mirror stage of LA can be seen in Figure 6.8, whose bandwidth is only 14.26 GHz. According to Equation (6.1), the total bandwidth of 5 cascaded current mirror stages cannot meet the bandwidth requirement of 8 GHz.
Figure 6.8 Simulation result of current mirror stage
6.2.5 Topology discussion Based on the topologies discussed above and proposed in other works, the summary of possible LA stage topologies can be seen in Table 6.1, where bandwidth, gain and drawbacks are mainly concerned. It can be concluded from the simulation results that cascaded stages using basic topologies cannot meet the requirements of gain and bandwidth. Thus, bandwidth enhancement techniques should be employed. The common bandwidth enhancement techniques are given in Table 6.1, one or some of which will be combined with the basic topology to enhance the bandwidth.
Table 6.1 Summary of LA stage topologies Topologies
Bandwidth
Gain
Drawback
CS stage
−
−
/
Basic
Cascoded CS stage
+
+
Low linearity
topology
Current mirror stage
−
−
/
 62 
Chapter 6. Limiting amplifier −
+
/
Miller +
+
Instability and
Inverter stage Negative
capacitors compensation
Capacitance mismatching +
+
Large area
Capacitive degeneration +
−
Gain
Inductive peaking [38] Bandwidth
[38]
enhancement
CherryHooper [48]
reduction +
−
techniques
Gain reduction and Low voltage headroom
Active feedback [51]
+
+
Relatively high complexity
+ — good −. — poor
6.3 Limiting amplifier Design for STO amplifier The low supply voltage (1.2V) limits the feasible LA topologies. Based on the summary of LA in Table 6.1, Cascoded CS stage will be employed in this design for its double benefits of large gain and large bandwidth. Besides, according to the linearity requirement presented in Chapter 3, CS stage will also be used in latter LA stages in this design for its larger output swing compared to cascoded CS stage. Apart from the benefit of large output swing, CS stage can also bring the benefit of saving area because the inductive peaking technique is not necessary. Inverter stage has largest output swing and best linearity among basic topologies. However, it is hard to be cascaded due to the large parasitic capacitance, which results in small bandwidth. According to the comparisons between different bandwidth enhancement techniques, the negative Miller capacitors compensation should be avoided mainly due to instability issue. Inductive peaking can enhance the bandwidth efficiently at the price of large silicon area. Capacitive degeneration and CherryHooper should also be avoided because the bandwidth enhancement is at the cost of gain reduction. In [51],  63 
Chapter 6. Limiting amplifier the considerable bandwidth of 9.4 GHz is based on the combination of activefeedback, inductive peaking and negative Miller capacitor. Apart from the instability issue of negative Miller capacitor, more transistors are employed to form the activefeedback topology to enhance the bandwidth. Considering the tradeoff between bandwidth and gain, cascoded CS stages with inductive peaking is the optimal technique in this design. Compared with [51], this topology requires fewer transistors, lower power and does not cause instability. The cascoded CS stages increase the gain slightly due to the larger output impedance, while they also increase the bandwidth due to the suppression of Miller effect. Inductive peaking is introduced to provide an impedance component that increases with frequency. The synthesizing response of cascoded CS stage and inductive peaking can be seen in Figure 6.9.
Figure 6.9 Synthesizing wideband frequency responses
With the help of current tail, the large common mode disturbance can be rejected in differential pairs. However, the current tail reduces the voltage headroom, followed by gain reduction. Thus, 6 stages maybe needed to meet the gain requirement. However, the noise should be carefully considered when more than 5 stages are employed. The cascoded CS stage is shown in Figure 6.10. As the balunLNA of large motional resistance case presented in Chapter 5, the noise performance of this topology is acceptable compared to other topologies. R0 or R1 is 300 Ohms. I0 is 1.5 nH inductor in order to obtain significant bandwidth enhancement without excessive frequency response peaking.
 64 
Chapter 6. Limiting amplifier
Figure 6.10 LA cell Transfer function gives insight into the circuit behavior that can be used for synthesizing the wideband frequency response of the circuit. The transfer function of output node impedance can be written as [38]: Z ( s ) = ( Ls + R ) //
1 R[( L / R ) s + 1] = 2 Cs s LC + sRC + 1
(6.4)
based on the model in Figure 6.11.
Figure 6.11 Model of inductive peaking compensation
The transfer function can be derived based on the simplified model of LA cell in Figure 6.12. Zx and Zy are the total impedances seen from node X and node Y respectively. Iin refers to the drain to source current of M1. ro1 and ro2 refer to the drain to source resistances of M1 and M2.
 65 
Chapter 6. Limiting amplifier
Figure 6.12 Simplified model of LA cell
Capacitance at node X and node Y can be represented as: C X ≈ 2 ⋅ CGD1 + C DB1 + C SB 2 + CGS 2 CY ≈ C DB 2 + CGD 2 + Cload
(6.5) (6.6)
where Cload consists of Cgs and Cgd of the next stage. Thus, the total impedance seen from node X and node Y in Figure 6.12 can be written as: Z X ≈ ro1 // Z Y ≈ ( Ls + R ) //
1 CX s
1 R ⋅ [( L / R ) s + 1] = 2 CY s s LCY + sRCY + 1
(6.7)
(6.8)
From Figure 6.12, one can write: Vout 1 = −( gm2 ro1 + 1) ⋅ Z X ( s ) ⋅ Z Y ( s ) ⋅ Iin Z Y ( s ) + (1 + gm2 r o 2 ) Z X ( s ) + ro 2
(6.9)
where gm1, gm2 are the transconductance of transistor M1 and M2. The transfer function of cascoded CS stage with inductive peaking can be written as: Vout 1 = − gm1 ( gm2 ro1 + 1) ⋅ Z X ( s ) ⋅ Z Y ( s ) ⋅ Vin Z Y ( s ) + (1 + gm2 r o 2 ) Z X ( s ) + ro 2
(6.10)
The output impedance is: Zout = Z Y ( s ) + (1 + gm2 r o 2 ) Z X ( s ) + ro 2
(6.11)
In the small motoinal resistance case, there will be always at least 6 dB loss at input port due to the input impedance matching. In the large motional resistance case,  66 
Chapter 6. Limiting amplifier the gain of first stage is only 9dB, which also requires large gain in the following stages. 6 stages are required in order to obtain more than 40 dB gain. According to Equation (6.1), BW per stage should be at least 17 GHz when 6 stages are required. The transistor sizes chosen for cascoded CS LA cells can be seen in Table 6.2. If the transistors are larger, the bandwidth will be reduced due to larger parasitic capacitance. If the transistors are smaller, the gain will be reduced due to the lower transconductance. The cascoded differential pairs are biased around 1mA in each branch.
Table 6.2 Transistor sizes of cascoded CS stage Stage number
15
Current source
W
5 um
10 um
L
60 nm
500 nm
N
4
12
Wtot
20 um
120 um
The biasing circuits are the same as in Figure 5.13. Vb3 in Figure 6.10 is connected to supply voltage. Vb2 of the first LA stage is biased to 0.875V. Inputs of the following LA stages can be biased by the outputs of previous stages directly. The transistor sizes of biasing circuit can be seen in Table 6.3.
Table 6.3 Parameters of the biasing transistors M1, M2 Item
M1 (current source)
M2 (input)
Transistor type
N_12_LLLVT
N_12_LLLVT
W
6 um
2.8 um
L
500 nm
500 nm
NF
4
10
W_tot
24 um
28 um
In order to increase the output swing of LA, CS stage is employed in the latter stages of LA. CS stage has lower gain compared to cascoded CS stage. Thus, there is a tradeoff between linearity and gain. Due to the small output power of STO, 5  67 
Chapter 6. Limiting amplifier cascoded CS stages and 1 CS stage is the optimal choice in this design. The CS stage is given in Figure 6.1. R0 and R1 is chosen 300 Ohms to avoid bandwidth shrinking. Due to the small load resistances R0 and R1, CS stage is biased at 2 mA to increase the gain. The transistor size of CS stage is given in Table 6.4.
Table 6.4 Transistor sizes of CS stage Stage number
6
Current source
W
5 um
10 um
L
60 nm
500 nm
N
4
32
Wtot
20 um
320 um
Finally, the gain provided by one CS stage is only 6.333dB (with 20fF load capacitance) and the bandwidth is 26GHz as it can be seen in Figure 6.13.
Figure 6.13 AC response of CS stage
The total gain and bandwidth of the proposed 6stage LA can be seen in Figure 6.14.
 68 
Chapter 6. Limiting amplifier
Figure 6.14 Simulation results of 6stage LA
From Figure 6.14, it can be seen that the gain is around 46.58dB (with 20fF load capacitance), which meets the requirement of around 45dB presented in Chapter 3. In addition, the bandwidth is around 0.1315GHz, which also fulfills the requirement. For a single stage of cascoded CS LA cell, the noise figure is less than 1.5 dB in required frequency range, which is given in Figure 6.15. The noise accumulates fast when 6 stages are employed as we expected. The noise figure of this LA chain can be estimated using the expression [24]:
NFtot = 1 + ( NF1 − 1) +
NFm − 1 NF2 − 1 + ... + AP1 AP1 × ... × AP( m−1)
(6.12)
which shows a Nftot of around 2.1dB. The simulation result of noise figure can be seen in Figure 6.15 which shows a noise figure less than 1.7 dB in the required frequency range. When the switches (discussed at the end of Chapter 5) are taken into account, the total noise figure is up to 2.6 dB within the required frequency range.
 69 
Chapter 6. Limiting amplifier
Figure 6.15 Noise Figure of 6 cascoded CS stages of LA
The maximum output swing of LA can be calculated by: [Vdd − (Vgs1 − Vth1 + Vds 0)] × 2
(6.13)
where Vgs1 and Vth1 are the gatesource voltage and threshold voltage of input transistor M1/M2 in Figure 6.1, Vds0 is the drainsource voltage of current source M0 in Figure 6.0. (Vgs1Vth1) is around 130mV and Vds0 is around 250mV. Therefore, the maximum output swing is 1.64Vpp. The transient response is shown in Figure 6.16. From Figure 6.16 (a) and 6.16(b). Figure 6.16(a) illustrates the 1Vpp test sine wave injected at the input of limiting amplifier. Figure 6.16(b) shows the amplified signal obtained at the output of limiting amplifier when the input signal is 1Vpp. The voltage gain can be calculated 45.3 dB at 5GHz approximately, which is verified by the AC analysis in Figure 6.14. In addition, the maximum differential output swing of LA is 1.67Vpp, as it can be seen in Figure 6.16(c). According to the transient response, the proposed LA has a large output swing.
 70 
Chapter 6. Limiting amplifier
Figure 6.16 Transient analysis of LA (a). A 5GHz 1mVpp test voltage is applied (b).Differential signal with around 183.5mVpp obtained at the output of LA (c). Maximum 1.67Vpp output swing can be obtained
To evaluate the LA performance, comparison of the proposed LA and stateoftheart LAs is given in Table 6.5. Based on Table 6.5, it can be concluded that the proposed LA is competitive for its power and bandwidth compared to other works.
 71 
Chapter 6. Limiting amplifier Table 6.5 Comparison of Limiting amplifier Ref
Freq.
Gain
Power
Proc.
Bandwidth
Inductor
Band
[dB]
[mW]
Vsupply
enhancement technique
?
46.6
20
65nm
Inductive peaking
YES
180nm
Active feedback,
YES
1.8V
inductive peaking and
[GHz] This
0.131
work
5
[51]
9.4
1.2V
50
150
JSSC 2003
negative Miller capacitor 0.18.6 42
[53]
72
SOPO
180nm
thirdorder Interleaving NO
1.8V
active feedback
180nm
thirdorder
1.8V
Interleaving active
2010 [54]
9
42
189
JSSC 2007 [55]
NO
feedback 26.2
38
125
CDTP
130nm
Cascaded distributed
YES
1.5V
amplifiers
SiGe
N/A
NO
Inductive peaking
YES
2006 [56]
15
60
600
JSSC
HBT
1994
3.55.5 V
[57]
3
JSSC
32
53
250nm 2.5 V
2000
The power consumption of proposed limiting amplifier is only 20 mW with considerable gain and bandwidth. Thirdorder interleaving active feedback technique is proposed in [53][54], which has flat gain over a comparatively large bandwidth. However, it suffers from potential instability issue. Compared with [48], which also
 72 
Chapter 6. Limiting amplifier employs the same inductive peaking technique, lower power and larger bandwidth is obtained with fewer transistors and inductors in this work.
6.4 Summary Based on the case studies in this chapter, a broadband limiting amplifier is designed to amplify the signal after BalunLNAs. Considerable gain and bandwidth is obtained by applying inductive peaking technique. The LA gives a differential output with 1.67Vpp. The gain and bandwidth of the amplifier for STO now meet the requirements, and an output buffer is required to convert the differential signal to singleended signal and match the output impedance to 50 Ohms.
 73 
Chapter 7. Output buffer
Chapter 7. Output buffer
7.1 Case studies Output buffer is a necessary and vital building block of the amplifier to transmit power to the following devices. In order to normalize the amplifier interface, a 50 Ohms standard impedance matching is adopted in the design. There are several ways to implement the output buffer [58]: LC based impedance network: LC based impedance network is common used in circuit design because there is no power loss in the LC impedance network. However, there are several drawbacks of this method. Firstly, the onchip inductor consumes a lot of area. Secondly, the parasitic reactance of the LC components degrades the matching performance. Thirdly, the matching network is not suitable for wideband impedance matching. Transmission line: A transmission line with
λ 4
long (quarterwave transmission
line) will help to match the load impedance to desired input impedance [29]. However, the real transmission line is lossy, and there will be undesired power loss on transmission line. Transformer: Transformer can be used to match the impedance, but it is bulky and lossy. It also degrades the circuit performance. CS stage: CS stage can be used to match the impedance in a wide frequency range. And CS stage is well known for its high linearity and it is suitable for the output stage. The output capacitance is negligible. The load resistance can be designed around 75 Ohms (in parallel with Rds of the transistor). In order to obtain unity gain at the output stage, gm of the transistor should be 20mS. However, the transconductance of small size transistors can hardly reach 20 mS in 65nm process, leading to gain loss. Besides, the bandwidth of CS stage does not satisfy the requirements. Super source follower [59]: This approach uses a negative feedback to reduce the output impedance, which could be matched to 50 Ohms in wideband. However, it  74 
Chapter 7. Output buffer cannot convert differential output to single ended output, which calls for an external converter for testing. In this project, a wideband inductorless output buffer is required. The output buffer should convert the differential output to singleended output for testing and give a 50 Ohms output impedance matching. Because there is always 6.02 dB gain loss when the output impedance is perfectly matched, the gain loss should be as little as possible.
7.2 Output buffer design A conventional buffer is used in this design. This output buffer can match the output impedance and convert the differential output to singleended output at the same time. The output buffer is given in Figure 7.1.
Figure 7.1 Output buffer
The input of the proposed buffer is the differential output of limiting amplifier. The upper transistor acts as a source follower while the other transistor works as a common source stage. Ideally, the gain of the source follower and common source stage in this case should be unity, which results in an unity transfer function of the output buffer. The choice of transistor size is critical for output impedance matching. The output impedance of this buffer can be expressed by: Rout =
1 // Rds 0 // Rds1 gm0
 75 
(7.1)
Chapter 7. Output buffer where gm0 is the transconductance of both transistors, Rds0 and Rds1 are the resistance between drain and source of M1 and M2. The output transconductance of transistors are large in 65 nm process, which results in small Rds. Thus, in order to match the output impedance accurately, gm should be chosen less than 20 mS. In addition, the bond wire effect should be also considered at the output of buffer as shown in Figure 7.2. The bond wire model has been proposed in Chapter 5. Fortunately, the bond wire relieves the requirement of gm as well. Therefore, the transistor size chosen for output buffer can be seen in Table 7.1.
Figure 7.2 Bond wire at the output Table 7.1 Parameters of the transistors in output buffer Item
M0, M1
Biasing NMOS transistor
Transistors type
N_BPW_12_LLLVTRF
N_ 12_LLLVT
VDS
0.6 V
0.6 V
IDS
1.7 mA
0.707 mA
L
60 nm
500nm
W
2 um
4um
NF
8
10
W_tot
16 um
40um
gm
11.31 mS
5.14m
Rds
463.41 Ohms
3265.9 Ohms
Cgs
10.24 fF
195.47 fF
Cgd
3.97 fF
8.98 fF
Cds
2.18 fF
0.38 fF
Cdb
0.07 fF
0.51 fF
Vgs
0.64 V
0.6 V
Intrinsic gain
5.24
16.8
 76 
Chapter 7. Output buffer The output stage can be simply biased by current mirror, which is the same as Figure 5.6. The output impedance matching of the output buffer with bond wire can be seen in Figure 7.3. Figure 7.3 (a) illustrates that the output impedance of the buffer varies from 56.92 Ohms to 70.45 Ohms in required frequency range of 48 GHz. In Figure 7.3 (b), the Smith Chart indicates that the output impedance of the output buffer is close to normalized unity (50 Ohms). However, the output impedance first exhibits capacitive then inductive behaviors due to the bond wire effect.
Figure 7.3 Output impedance of output buffer (3 GHz to 10 GHz)
When a test port with 50 Ohms impedance is added at the end of bond wire, the S22 parameter in Figure 7.4 can be used to characterize the output impedance matching of this output buffer. As it can be seen in Figure 7.4, the reflection coefficient is always less than 12.94 dB in required bandwidth, which indicates that the output impedance matching meets the requirement of 10dB in such a wide frequency range. Around 5 GHz, the impedance closely matches to 50 Ohms. In Figure 7.5, there are 9.5dB loss on the output buffer in total. Apart from the loss caused by the impedance matching, there is about 2.85dB loss caused by the chosen transconductance. Due to the large output transconductance of transistors in 65nm process, the Rds cannot be ignored, which requires lower input
 77 
Chapter 7. Output buffer transconductance to match the output impedance to 50 Ohms. According to Equation (7.1), the product of input transconductance and total output impedance is always less than unity in practice. Thus, there is a tradeoff between the perfect impedance matching and gain due to the imperfection of the process. The reduction of power loss and reflection is at the price of losing 2.85 dB gain.
Figure 7.4 Output reflection coefficient S22 of output buffer
Figure 7.5 Gain loss of output buffer
 78 
Chapter 7. Output buffer The transient analysis of output buffer can be seen in Figure 7.6. Due to the limit of 1.2V supply voltage, the maximum differential signal that can be obtained at the input of buffer is 2.4V. Therefore, a 2.4Vpp test sine wave is injected at the input of the buffer as shown in Figure 7.6 (a). The signal obtained at the output of the buffer and before the bond wire is composed of two parts: the degraded signal transferred from the previous stage and the reflected signal from the output port through the bond wire. The degraded signal is caused by the imperfection of the buffer and the reflected signal results from the output impedance mismatch. Due to the time delay generated by the bond wire, the entire signal obtained at the output of buffer is distorted and can be seen in Figure 7.6(b). Figure 7.6 (c) shows the final signal after the bond wire and pad. The output swing of the final signal reaches to 0.6Vpp.
Figure 7.6 Transient analysis of output buffer (a). 2.4Vpp input signal (b). 808mVpp signal obtained before the bond wire (c). 600mVpp obtained after bond wire
 79 
Chapter 7. Output buffer
7.3 Summary This output buffer can convert the differential signals to singleended signal while match the output impedance to 50 Ohms. The power consumption of the output buffer is only 4mW. It has large output swing, wideband output impedance matching and onchip balun. The required building blocks from the input stage to output buffer have been proposed. In the coming chapter, all steps involved in designing the amplifier for STO will be given.
 80 
Chapter 8. Wideband amplifier Design
Chapter 8. Wideband amplifier Design Based on the analysis presented in the previous four chapters, the whole proposed amplifier is shown in Figure 8.1. Note that biasing circuit is not shown in the figure. In this chapter, all the characteristics of the amplifier in two cases will be analyzed, covering Sparameter, linearity, noise performance, corner analysis, stability analysis, etc.
Figure 8.1Wideband amplifier
8.1 Small motional resistance case (50 Ohms system) When Vctl signal is set to Vdd in Figure 8.1, the CGCS LNA operates while the cascoded CS LNA is off. In this case, the input impedance of the amplifier is matched to 50 Ohms in the required frequency range (48 GHz). The Sparameter analysis can be seen in Figure 8.2. S11 reaches its maximum value of 12.48 dB at 4 GHz This meets the requirement of 10 dB and exhibits an acceptable input impedance matching. The reverse voltage gain S12 is always less than 144 dB leading to a perfect isolation. Forward voltage gain S21 is 52.36 dB with a 1.3411.8 GHz bandwidth. The bandwidth and available gain reach the requirements presented in Chapter 3. S22 is less than 12 dB in the required frequency range as shown in Figure 8.2. At 5 GHz, S22 is around 21 dB, which indicates an excellent output impedance matching. The  81 
Chapter 8. Wideband amplifier Design input and output impedance matching can also be characterized by voltage standing wave ratio (VSWR) as shown in Figure 8.3. The input VSWR is less than 1.6 and the output VSWR is less than 1.52 in the required frequency range. Note that a VSWR of 1.2 is considered excellent [24].
Figure 8.2 Sparameter of amplifier
Figure 8.3 VSWR of input and output of amplifier in small motional resistance case
 82 
Chapter 8. Wideband amplifier Design The noise performance is characterized by noise figure and input referred noise as shown in Figure 8.4. The noise figure is below 5.92 dB in required frequency range and the corresponding input referred noise is below 883.7 pV/sqrt(Hz), which meets the requirement of 6 dB. The dominant noise sources are: 1) the thermal noise enhancement of the CS transistor in LNA stage; 2) the thermal noise of current source transistor in LNA stage; 3) the thermal noise of CS transistor in LNA stage.
Figure 8.4 Noise performance of amplifier in small motional resistance case
Basically, SSB and LSB reflect the stability of an amplifier, and as it can be seen in Figure 8.5, the amplifier is unconditionally stable in the required frequency range.
Figure 8.5 SSB and LSB of amplifier in small motional resistance case  83 
Chapter 8. Wideband amplifier Design Wideband applications require wideband amplifiers with high linearity. In this project, the linearity is critical because of the intrinsic performance of the STO, as discussed in the Chapter 2. Linearity includes harmonics, gain compression, desensitization and blocking, cross modulation and intermodulation. Intermodulation is the most critical one in this case due to the performance of STO. The gain compression and harmonics will also be analyzed in this section. The output voltage distribution of an amplifier is important in analyzing intermodulation distortion when the two RF input signals are close. During the Periodic SteadyState (PSS) analysis, the centre frequency and second strongest mode frequency should be multiple of beat frequency. In order to simplify the simulation, it is assumed that the center frequency is 5 GHz (In [13], the centre frequency is 4.993 GHz), and the second strongest mode frequency is 5.5 GHz (In [13], the second strongest mode frequency is 5.512 GHz). The 3rd order intermodulation is 6.031 GHz and 4.474 GHz. However, 6 GHz and 4.5 GHz will be used in simplified simulation. Output voltage distribution is used to analyze the intermodulation distortion when the main mode and second strongest mode of STO signals are close. As shown in Figure 8.6, the intermodulation between the strongest mode and second strongest mode does not affect the linearity considerably. The strongest harmonic is lower than 56 dB and occurs at 4.5 GHz.
Figure 8.6 Output voltage distribution of amplifier in small motional resistance case  84 
Chapter 8. Wideband amplifier Design As the signal amplitude increases, the gain becomes compressed, which results in nonlinearity. The gain compression is characterized by 1dB compression point. Larger 1dB compression point results in better linearity. As illustrated in Figure 8.7, 1 dB compression point is around 57.4 dBm when a 60 dBm input signal is applied.
Figure 8.7 1 dB compression point of amplifier in small motional resistance case
The IP3 is obtained by using swept PSS analysis (SPSS) and SPSS with Periodic AC (PAC). The input signal is 60 dBm. Based on the frequency hooping of STO device discussed in Chapter 2, the maximum spacing between the hooping frequencies is 20 MHz (±10MHz). Figure 8.8 presents the twotone test with 20MHz tone spacing. Because the center frequency is 5 GHz, the two tones are 5 GHz and 5.02 GHz. The third order frequencies are 4.98GHz and 5.04 GHz. From Figure 8.8, IIP3 is calculated around 48.9 dBm. OIP3 is always larger than 10dBm and it is up to 5.295 dBm when the input signal is larger than 59 dBm, which almost meets the requirement. As the spacing between hooping frequencies becomes narrower, the nonlinearity becomes more serious. The nonlinearity is mainly caused by the limiting amplifier. On one hand, due to the high voltage gain of limiting amplifier, the output swing is limited by the power supply of 1.2V then leads to linearity degradation. On the other hand, the openloop topology has intrinsic nonlinearity, which is mainly caused by the nonlinear relation between ID and Vgs of
 85 
Chapter 8. Wideband amplifier Design the transistors in signal paths.
Figure 8.8 IIP3 of amplifier in small motional resistance case
Corner analysis is carried out by changing the corners of the process along with the temperature and supply voltage [60]. All the transistor and capacitor models will be changed according to the corresponding corners settings. The default corner in this design is ◇ tt, 1.2V, 27℃ The other simulated corners are as follows: ◇ ff, 1.3V, 25℃ ◇ ss, 1.1V, 85℃ The simulation result can be seen in Figure 8.9. The red lines represent simulation results in the default corner. The blue lines and red lines represent the simulation results in (ff, 1.3V, 25℃) and (ss, 1.1V, 85℃), respectively. From the simulation result, it can be concluded that the designed amplifier design in small motional resistance case (50 Ohms system) is working properly in the worse cases. S11 and S12 are always less than 10dB, which meets the requirement and shows an acceptable impedance matching at both input and output. S12 has maximum value of 144.2 dB, which presents a perfect isolation in all the corners. S21 is up to 63.16 dB within 48GHz in corner (ff, 1.3V, 25℃). However, the gain in worst case of (ss,  86 
Chapter 8. Wideband amplifier Design 1.1V, 85℃) is only 41.33dB. This cannot meet the requirement of 45 dB, which is mainly caused by the lower mobility at high temperature.
Figure 8.9 Corner analyses in small motional resistance case (a).S11; (b).S12; (c).S21; (d).S22; (e).NF
 87 
Chapter 8. Wideband amplifier Design
8.2 Large motional resistance case (HighZ system) When Vctl signal is set to gnd in Figure 8.1, the CS LNA operates while the CGCS LNA is off. This case is applicable when the output impedance of STO is larger than 50 Ohms. 1K Ohms, 500 Ohms, 50 Ohms input impedances are added to represent the output impedance of STO in order to cover the whole range of motional resistance. In Figure 8.10, S11 is close to 0 dB in required frequency range. The input impedance of the amplifier varies from 2K Ohms at 4 GHz to 1K Ohms at 8 GHz as shown in Figure 8.11. S12 in Figure 8.10 is less than 148 dB, which indicates an excellent isolation. The available gain S21 is 59.29 dB with 1.1718.178 GHz bandwidth when 1K Ohms source impedance is connected, and 47.65dB with larger bandwidth when 50 Ohms source impedance is added. This fulfills the requirements presented in Chapter 3. The output impedance matching is less than 10 dB as in the previous case.
Figure 8.10 Sparameter of amplifier in large motional resistance case  88 
Chapter 8. Wideband amplifier Design
Figure 8.11 Input impedance of amplifier in large motional resistance case
The noise performance is shown in Figure 8.12. The noise figure is below 2.916 dB in required frequency range when 1K Ohms source impedance is added, and the corresponding input referred noise is below 2.8 nV/sqrt(Hz). The noise performance is much better in this case mainly because of employment of CS LNA.
Figure 8.12 Noise performance of amplifier in large motional resistance case
 89 
Chapter 8. Wideband amplifier Design As shown in Figure 8.13, since the SSB and LSB are out of  Γs = 1 , the amplifier is unconditionally stable in the required frequency range.
Figure 8.13 SSB and LSB of amplifier in large motional resistance case
The linearity is analyzed from the output voltage distribution in Figure 8.14. It can be concluded from Figure 8.14 that the intermodulation between the strongest mode and second strongest mode does not affect the linearity much.
Figure 8.14 Output voltage distribution of amplifier in large motional resistance case  90 
Chapter 8. Wideband amplifier Design In Figure 8.15, 1 dB compression point is used to check the gain compression. When the input signal is around 60 dBm with a 50 Ohms motional resistance, 1 dB compression point is around 55.2 dBm. The linear dynamic range in this case is larger than that in the small motional resistance case. When the input signal is 60 dBm with 1K Ohms motional resistance, 1 dB compression point is 58.7 dB, which indicates worse linearity and smaller dynamic range of input signal.
Figure 8.15 1 dB compression point of amplifier in large motional resistance case (a) 1K Ohms source impedance (b) 50 Ohms source impedance
The input signal is 60 dBm. Figure 8.16 is the spectrum of the twotone test with 20MHz tone spacing in large motional resistance case. Because the central frequency is 5 GHz, the two tones are 5 GHz and 5.02 GHz. The simulation result in Figure 8.16 illustrates that when the motional resistance reaches 1K Ohms, the IIP3 is 51.9 dB.
 91 
Chapter 8. Wideband amplifier Design
Figure 8.16 IIP3 of amplifier in large motional resistance case
In this case, a 1K Ohms RF port is used as the large motional resistance of STO device to analyze corners. The simulation result can be seen in Figure 8.17. The purple lines represent the simulation results in the default corner. The blue lines and red lines represent the simulation results in (ff, 1.3V, 25℃) and (ss, 1.1V, 85℃), respectively. It can be concluded that the designed amplifier in large motional resistance case (HighZ system) can also work properly in the worse cases. However, the bandwidth of 1.246.86 GHz in corner (ff, 1.3V, 25℃) cannot meet the requirement. The reason is that the scatting effect is weakened at low temperature, leading to high mobility. The increasing mobility causes larger gain. Due to the tradeoff between gain and bandwidth, as the gain increases, the bandwidth shrinks.
 92 
Chapter 8. Wideband amplifier Design
Figure 8.17 Corner analysis of amplifier in large motional resistance case (a).S11; (b).S12; (c).S21; (d).S22; (e).NF
 93 
Chapter 8. Wideband amplifier Design
8.3 Summary Sparameters, linearity, noise performance, corner analysis, stability analysis of the whole amplifier for STO were presented in this chapter. The amplifier in small motional resistance case shows a gain of 52.36 dB with a 1.2311.8 GHz bandwidth. The amplifier in large motional resistance case results in a 59.29 dB gain with 1.1718.178 GHz bandwidth when a STO device with 1KOhms output impedance is connected to the input. The amplifier is competitive for its very low power consumption, which is less than 30mW in both small and large motional resistance cases.
 94 
Chapter 9. Conclusion and Future Work
Chapter 9. Conclusion and Future Work
9.1 Conclusion The intriguing properties of STO, such as large tunability, miniature size, high operation frequency, high integration level, etc., make it a promising candidate for microwave and radar applications. However, STO is an immature technology with its low output power that is not yet compatible with telecommunication applications. This thesis work presented a universal amplifier for MTJ STO devices with both small motional resistance and large motional resistance. The amplifier requirements are extracted according to the stateoftheart MTJ STO technology. To satisfy the amplifier requirements, the proposed topology is composed of two types of input balunLNA stages, which are suitable for small and large motional resistance cases, and a common circuitry consisting of LA and output buffer. A switch is designed to select between two input balunLNAs according to the requirement. The two proposed input balunLNAs have large bandwidth, good linearity, satisfactory noise performance, low power consumption and input active balun. The proposed CGCS LNA in this work is superior to other works in gain and gain mismatch due the crosscoupling capacitors. In addition, CGCS LNA has acceptable input impedance matched to 50 Ohms in required frequency range. The topology of LA is presented based on the studies and comparisons of several cases. Finally, a 6stage broadband LA, which is composed of 5 cascoded CS stages with inductive peaking technique and one CS stage, is employed to obtain the required gain. The LA gives a large differential output swing of 1.6Vpp. The proposed LA is competitive for its low power consumption and large bandwidth. A conventional buffer is used in this design. It has high linearity, wideband output impedance matching, low power consumption, simple topology and onchip active balun. With the effect of bond wire, the output buffer has an acceptable output impedance matching to 50 Ohms in required frequency range. Solutions to onchip biastee/biasing and current source/sink were also discussed in this thesis. However, simulation results show that the onchip biastee/biasing for  95 
Chapter 9. Conclusion and Future Work injected DC current of STO within the required bandwidth is infeasible in 65nm process with 1.2V power supply in both small motional resistance and large motional resistance cases. Finally, the simulation results show that the whole amplifier exhibits 52.36 dB gain with 1.2311.8 GHz bandwidth in small motional resistance case and 59.29 dB gain with 1.1718.178 GHz bandwidth in large motional resistance (1K Ohms). The proposed amplifier meets the requirements for both MTJ STO devices. In addition, the amplifier has acceptable noise performance and very low power consumption, compared to stateoftheart of the out solutions.
9.2 Future Work This thesis work covered circuit design and simulations. The future work includes: Layout, DRC and LVS check, post layout simulation, fabrication, PCB design, final test and evaluation. Offchip biastee design and test.
 96 
Reference
Reference
[1] Pozar David M, Microwave Engineering, AddisonWesley Publishing Company, 1993 [2] Tang Zhangwen, “LC VoltageControlled Oscillators”, Ph.D. Dissertation, Fudan University, Shanghai, 2004 [3] Johan Persson, Stefano Bonetti, Johan Åkerman, “WP3400MTJ STO Characterization Report”, NanOsc STOLO, 2008.12.04 [4] L. Berger , “ Emission of spin waves by a magnetic multilayer traversed by a current”, Physical Review B, vol 54, issue 13, pp93539358, 1996 [5] W. H. Rippard, M. R. Pufall, S. Kaka, S. E. Russek, and T. J. Silva, “DirectCurrent Induced Dynamics in Co90Fe10/Ni80Fe20 Point Contacts”, Physical Review Letters, vol. 92, Issue 2, id. 027201, 2003 [6] Franz Schlogl and Horst Zimmermann, “A design example of a 65 nm CMOS operational amplifier”, International Journal of Circuit Theory and applications, pp343354, 2007.03.02. [7] Patrick Villard, “A GHz SpintronicBased RF Oscillator”, IEEE Journal of SolidState Circuits, vol. 45, no. 1, pp 214223, January 2010 [8] TUNAMOS, “Tunable NanoMagnetic Oscillators for integrated transceiver applcations”, 01.07.2005 30.8.2008 [9] Slavin Andrei, Tiberkevich Vasil, “Advances in Magnetics Nonlinear AutoOscillator Theory of Microwave Generation by SpinPolarized Current”, IEEE Transactions on Magnetics, vol. 45, no. 4, pp18751917, April 2009 [10] Johan Persson, Zhou Yan, Johan Åkerman, “WP3500MTJ Simulation Report”, NanOsc STOLO, 2008.12.04 [11] D. Houssameddine, S. H. Florez, J. A. Katine, J.P. Michel, U. Ebels, D. Mauri, O. Ozatay, B. Delaet, B.Viala, L. Folks, B. D. Terris, and M.C. Cyrille, “Spin transfer induced coherent microwave emission with large power from nanoscale MgO tunnel junctions,” Applied Physics Letters, vol. 93, no. 1, p.022505, 2008. [12] A. Nazarov, H. Olson, H. Cho, “Spin transfer stimulated microwave emission in MgO magnetic tunnel junctions”, Applied Physics Letters, vol. 88, no.16, p.162504,
 97 
Reference
2006 [13] Anders Eklund, “TimeDomain Study of NanoContact Spin Torque Oscillator”, January 2011 [14] P.K. Muduli, O.G. Heinonen, Johan Åkerman, “Bias dependence of perpendicular spin torque and of free and fixed layer eigenmodes in MgObased nanopillar”, Physical Review B, vol. 83, id. 184410, arXiv:1101.2401v2, 2011.01.12 [15] P.K. Muduli, S. Bonetti, Y. Zhou, Johan Åkerman, Olle G.Heinonen “MgObased Spin Torque Oscillators with above 0.1 uW output power”, IEEE international Magnetics Conference, 2009 [16] A. Nazarov, K. Nikolaev, Z. Gao, “Microwave generation in MgO magnetic tunnel junctions due to spin transfer effects”, Journal of Applied Physics, vol.103, no.7, p.07A503, 2008 [17] Wim Michielsen, “WP3600MTJ test board design”, NanOsc STOLO, 2009. 06.14 [18] A. M. Deac, A. Fukushima, H. Kubota, H. Maehara, Y. Suzuki, S. Yuasa, Y. Nagamine, K. Tsunekawa, D. D. Djayaprawira, and N. Watanabe, “Biasdriven large power microwave emission from MgObased tunnel magnetoresistance devices,” Nature Physics, vol. 4, pp.803809, 10 August 2008 [19] Tiberkevich Vasil, Slavin Andrei, Kim JooVon, “ Microwave power generated by a spintorque oscillator in the presence of noise”, Applied Physics Letters, vol. 91, no.19, p.192506, 2007 [20] Wim Michielsen, “WP4200MTJ test report”, NanOsc STOLO, 2009.06.14 [21] Prokopenko Oleksandr, Bankowski Elena, Meitzler Thomas, Tiberkevich Vasil, Slavin Andrei, “Spintorque nanooscillator as a microwave signal source”, IEEE Magnetics Letters, vol. 2, p.3000104, 2011 [22] Muduli P. K., Pogoryelov Ye., Bonetti S., Mancoff Fred, Åkerman Johan, “Nonlinear frequency and amplitude modulation of a nanocontactbased spintorque oscillator”, Physical Review B, vol.81, p.140408(R), 2010 [23] Trevor S. Bird, “Definition and Misuse of Return Loss”, IEEE Antennas & Propagation Magazine, vol.51, iss.2, pp.166167, April 2009. [24] Behzad Razavi, RF Microelectronics, Pearson Education, Inc, 1998 [25] Brian C. Wadell, “Smith Charts Are Easy”, IEEE Instrumentation & Measurement Magazine, vol.2 iss.13, 1999.03  98 
Reference
[26] Elisra Electronic Systems Ltd. Microwave amplifiers. [Online]. Available: http://www.mwelisra.com/pdf/Microwave%20Amplifiers.pdf, pp13. [27] Cullens Evan, Vanhille Kenneth, “Miniature BiasTee Networks Integrated in Microcoaxial Lines”, Proceedings of the 40th European Microwave Conference, pp413416, 201009 [28] Tiggelman M.P.J., Reimann K. Schmitz J., “Reducing AC impedance measurement errors caused by the DC voltage dependence of broadband highvoltage biastees”, IEEE International Conference on Microelectronic Test Structures, pp200205, 2007 [29] Reinhold Ludwig, Pavel Bretchko, RF Circuit Design Theory and Applications, PrenticeHall, New Jersey, 2000. [30] Albert Sutono, N. Gio Cafaro, Joy Laskar, Manos M. Tentzeris, “Experimental Modeling, Repeatability Investigation and Optimization of Microwave Bond Wire Interconnects”, IEEE Transactions on advanced packaging, vol. 24, no. 4, PP.595603, NOVEMBER 2001 [31] Gupta, K. C., R. Garg, and R. Chadha, ComputerAided Design of Microwave Circuits, Dedham, MA: Artech House, 1981. [32] Wheeler, H. A., ‘‘Simple Inductance Formulas for Radio Coils,’’ Proc. IRE, vol. 16, pp. 1398–1400, October 1928. [33] March, S. L., ‘‘Simple Equations Characterize Bond Wires,’’ Microwaves & RF, vol. 30, pp. 105–110, November 1991. [34] John Rogers, Calvin Plett, Radio frequency integrated circuit design, Artech House microwave library, 2003 [35] Blaakmeer Stephan C, Klumperink Eric A M, Leenaerts Domine M W, Nauta Bram, “Wideband BalunLNA With Simultaneous Output Balancing, NoiseCanceling and DistortionCanceling”, IEEE Journal of SolidState Circuits, vol. 43, no. 6, pp13411350, June 2008 [36] W. Zhuo, X. Li, S. Shekhar, S. H. K. Embabi, J. Pineda de Gyvez, D. J. Allstot, and E. SanchezSinencio, “A Capacitor CrossCoupled CommonGate LowNoise Amplifier”, IEEE Transactions on Circuits and Systems, vol. 52, no. 12, pp875879, December 2005 [37] Xiaohua Fan, Heng Zhang, Edgar SánchezSinencio, “A Noise Reduction and Linearity Improvement Technique for a Differential Cascode LNA”, IEEE Journal of  99 
Reference
SolidState Circuits, vol. 43, no. 3, pp588599, March 2008 [38] Thomas H. Lee, The Design of CMOS RadioFrequency Integrated Circuits, Second Edition, Cambridge University Press, USA, 2004. [39] Rahim Bagheri, Ahmad Mirzaei, Saeed Chehrazi, Mohammad E. Heidari, Minjae Lee, Mohyee Mikhemar, Wai Tang, Asad A. Abidi, “An 800MHz–6GHz SoftwareDefined Wireless Receiver in 90nm CMOS”, IEEE Journal of SolidState Circuits, vol. 41, no. 12, pp28602876, December 2006 [40] Stephan C. Blaakmeer1, Eric A.M. Klumperink, Domine M.W. Leenaerts, Bram Nauta“A wideband NoiseCanceling CMOS LNA exploiting a transformer”, IEEE Radio Frequency Integrated Circuits (RFIC) Symposium, 2006 [41] Federico Bruccoleri, Eric A. M. Klumperink, Bram Nauta, “WideBand CMOS LowNoise Amplifier Exploiting Thermal Noise Canceling”, IEEE Journal of SolidState Circuits, vol. 39, no. 2, pp275282, February 2004 [42] Sanghoon Joo, TaeYoung Choi, JaeYoung Kim, Byunghoo Jung, “A 3to5 GHz UWB LNA with a LowPower Balanced Active Balun”, IEEE Radio Frequency Integrated Circuits Symposium, pp303306, 79 June 2009 [43] Kaixue Ma et al., “800MHz ~ 2.5GHz miniaturized multilayer symmetrical stacked baluns for silicon based RF ICs,” MTTS, International Microwave Symposium Digest, pp. 283286, June 2005. [44] A. Bevilacqua and A. M. Niknejad, “An ultra wideband CMOS low noise amplifier for 3.1  10.6 GHz wireless receiver,” IEEE Journal of SolidState Circuits, vol. 39, no. 12, pp. 2259–2268, Dec. 2004. [45] J.H. C. Zhan and S. S. Taylor, “A 5GHz resistivefeedback CMOS LNA for lowcost multistandard applications,” IEEE ISSCC Dig. Tech. Papers, pp. 200–201, Feb 2006. [46] F. Zhang and P. R. Kinget, “Lowpower programmable gain CMOS distributed LNA,” IEEE Journal of SolidState Circuits, vol. 41, no. 6, pp. 1333– 1343, June 2006. [47] Behzad Razavi, Design of Analog CMOS Integrated Circuits, McGRAWHILL INTERNATIONAL EDITION, 2001. [48] Paul Müller,Yusuf Leblebici, CMOS Multichannel SingleChip Receiver for MultiGigabit Optical Data Communications, Spinger, 2007. [49] Samadi B, M.R., Karsilayan, A.I., SilvaMartinez, J., “Design of transimpedance  100 
Reference
and limiting amplifiers for 10 Gb/s optical communication systems”, Circuits and Systems, MWSCAS, The 2002 45th Midwest Symposium on, vol.3, pp164167, 2002 [50] R.P. Jingal, “Gigahertzband high gain low noise AGC amplifiers in fineline NMOS”, IEEE Journal of SolidState Circuits, vol. SC22, pp. 512521, August 1987. [51] Sherif Galal, Behzad Razavi, “10Gb/s Limiting Amplifier and Laser Modulator Driver in 0.18um CMOS technology”, IEEE Journal of SolidState Circuits, vol. 38, no.12, pp.21382146, Dec. 2003. [52] Zhuo Wei, Embabi Sherif, Gyvez José Pineda De, S Edgar, “Using Capacitive CrossCoupling Technique in RF Low Noise Amplifiers and DownConversion Mixer Design”, SolidState Circuits Conference, 2000. ESSCIRC '00. Proceedings of the 26th European, pp7780, 2000 [53] Lili Chen, Zhiqun Li, Zhigong Wang, “A 10Gb/s Inductorless CMOS Limiting Amplifier for OpticFiber Transmission System”, Photonics and Optoelectronic (SOPO), 2010 Symposium on, pp.14, 1921 June 2010 [54] HueiYan Huang, JunChau Chien, LiangHung Lu, “A 10Gb/s Inductorless CMOS Limiting Amplifier With ThirdOrder Interleaving Active Feedback”, IEEE Journal of SolidState Circuits, vol. 42, no. 5, pp11111120, MAY 2007. [55] C.H. Lee and S.I. Liu, “A 35Gb/s limiting amplifier in 0.13um CMOS technology”, Symp. VLSI Circuits Dig. Tech. Papers, pp. 152–153, Jun. 2006. [56] H. M. Rein, R. Schmid, P. Weger, T. Smith, T. Herzog, and R. Lachner, “A versatile Sibipolar driver circuit with high output voltage swing for external and direct laser modulation in 10 Gb/s opticalfiber links,” IEEE Journal of SolidState Circuits, vol. 29, pp. 1014–1021, Sept. 1994. [57] E. Sackinger and W. C. Fischer, “A 3GHz 32dB CMOS limiting amplifier for SONET OC48 receivers,” IEEE Journal of SolidState Circuits, vol.35, pp. 1884–1888, Dec. 2000. [58] Godara Balwant, Fabre Alain, “The First AllTransistor Wideband (0  5GHz) Impedance Matching Network”, 2007 14th IEEE International Conference on Electronics, Circuits and Systems, pp. 12171219, 2007 [59] Paul R. Gray, Paul J. Hurst, Stephen H. Lewis, Robert G. Meyer, Analysis and Design of Analog Integrated Circuits, fourth edition, John Wiley & Sons, the United States of America, 2001, pp. 213215 [60]Saúl Rodríguez, Sha Tao, Julian Marcos Garcia, Ana Ruru, “Tutorial 5Schematic  101 
Reference
level analysis in Cadence”, HT2010 IL2221 Advanced Topics in Mixed Mode Design, The Royal Institute of Technology, Sweden, v.1.0, 2010.
 102 