Somesign Aspects On Rf Cmos Lnas And Mixers

郑林全 · 发表于 2008-3-22 08:47:00

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Somesign Aspects On Rf Cmos Lnas And Mixers

郑林全 · 发表于 2008-3-22 08:59:11

Somesign Aspects On Rf Cmos Lnas And Mixers

郑林全 · 发表于 2008-3-22 09:04:50

Contents
1 Introduction 1
2 Low Noise Amplifier 3
2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Basic Amplifier Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2.1 Selection of Amplifier Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2.2 Differential Stage or Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.3 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.4 Using Coupled Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.5 Effects of Transistor Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Noise Analysis of MOS Transistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.1 Noise Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.1.1 Drain Current Thermal Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.1.2 Gate Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1.3 Substrate Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.1.4 Flicker Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.2 Transistor Noise Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.3 Equivalent Noise Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.3.1 Two-Port Model for a MOS-Transistor . . . . . . . . . . . . . . . . . . . . . 18
2.3.3.2 Two-Port Model for an Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.3.3 Noise Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4 Transadmittance Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.1 Input Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.1.1 Calculation Using Simplified MOS Model . . . . . . . . . . . . . . . . . . 23
2.4.1.2 Calculation Using Complete MOS Model . . . . . . . . . . . . . . . . . . . 23
2.4.1.3 Calculation Using New Simplified MOS Model . . . . . . . . . . . . . . 27
2.4.2 Gain of Transadmittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.2.1 Calculation Using Simplified MOS Model . . . . . . . . . . . . . . . . . . 28
2.4.2.2 Calculation Using New Simplified MOS Model . . . . . . . . . . . . . . 28
2.4.3 Noise Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4.3.1 Noise Factor of Simplified MOS Model . . . . . . . . . . . . . . . . . . . . 30
2.4.3.2 Noise Factor of New Simplified MOS Model . . . . . . . . . . . . . . . . 32
2.5 Transresistance Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.1 Input Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.2 Gain of Transresistance Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.6 Voltage Follower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.6.1 Input Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.6.2 Output Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.6.3 Gain of Voltage Follower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.7 Overall Amplifier Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.7.1 Overall Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

[ 本帖最后由郑林全于 2008-3-22 09:11 编辑 ]

郑林全 · 发表于 2008-3-22 09:05:58

2.7.2 Simulating Gain and Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.7.3 Calculating the Noise Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3 Analysis of Conversion Gain Spread in Mixers 45
3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 An Image-Reject Mixer and the Effect of I/Q-Imbalance . . . . . . . . . . . . . . . . . 47
3.2.1 Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.2 Imbalance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.3 Conversion Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.1 Ideal Mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.2 Passive CMOS Mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3.3 Numerical Calculation of the Time-Variant Filter . . . . . . . . . . . . . . . . . . 55
3.3.4 Conversion Gain and the Dependency on the Conductance . . . . . . . . . . . 58
3.4 Modelling and Statistical Properties of Mixer Image Rejection . . . . . . . . . . . . 58
3.4.1 Channel Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.2 Mixer Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.4.3 Image Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.5 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.5.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.5.2 Channel Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.5.3 Image Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.5.4 Additional simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.5.4.1 Changing the IF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.5.4.2 Varying the LO signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

[ 本帖最后由郑林全于 2008-3-22 09:10 编辑 ]

郑林全 · 发表于 2008-3-22 09:08:09

Appendix
A Input Impedance of the Common Source Amplifier 73
A.1 Blackman’s Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
A.2 Complete Small Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
A.3 New Simplified Small Signal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
B Gain of Various Stages 77
B.1 Superposition Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
B.2 Transconductance Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
B.2.1 Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
B.2.2 Gate Drain Capacitance Excluded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
B.2.3 Gate Drain Capacitance Included . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
B.3 Current Follower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
B.4 Voltage Follower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
C Noise 85
C.1 Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
C.2 Calculating the Equivalent Noise Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
C.2.1 Output Noise as a Function of Equivalent Input Noise . . . . . . . . . . . . . . . 85
C.2.1.1 Open Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
C.2.1.2 Short Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
C.2.2 Output Noise as a Function of Transistor Input Noise . . . . . . . . . . . . . . . 89
C.2.2.1 Open Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
C.2.2.2 Short Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
C.2.3 Equivalent Noise as a Function of Transistor Noise . . . . . . . . . . . . . . . . . 94
C.2.3.1 Open Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
C.2.3.2 Short Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
C.3 Total Equivalent Input Noise Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
C.3.1 Gate Drain Capacitance is Zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
C.3.2 Gate Drain Capacitance is not Zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
D Gaussian Approximation 99
E Conductance Model 101
E.1 Transistor Parameters with Mismatch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
E.2 Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
E.2.1 Effective Transistor Width and Length . . . . . . . . . . . . . . . . . . . . . . . . . . 102
E.2.2 Threshold Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
E.2.3 Effective Electron Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
E.2.4 Oxide Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
E.2.5 Effect of Drain and Source Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . 103
F Additional Simulation Results 105

郑林全 · 发表于 2008-3-22 09:14:10

Abstract This thesis deal with two parts of a radio receiver. The low noise amplifier (LNA) and the mixer. A tuned RF front-end amplifier in CMOS with an operating frequency around 1.8 to 2GHz has been investigated. A symmetric design has been used to improve linearity with preserved power consumption. In this case it has been a parallel connection of complementary devices. The symmetric solution allows the use of inductor pairs in transformer configuration to improve the gain of the circuit. The input impedance has been controlled by an inductive series feedback of a transconductance. An extended investigation has been made to determine the effect of the capacitive shunt feedback, traditionally ignored, as well as the effects of other internal parasitics. Simulation results shows that for a required input resistance and operating frequency a maximum transconductance of the transistor can be found. A new approximation of the input resistance where found, valid for low frequencies and for small transconductances. The most important part of the amplifier is the first stage (the inverter) as it will affect both input impedance and noise. Analysis of the optimum noise figure both with the capacitive shunt feedback excluded and included are made to show that it is possible to repeat the calculations in the same manner both times and thereby being able to compare the results. The major conclusion of this paper is that the shunt feedback can not be ignored and that good design methods therefore require a more extended analysis. Imbalances in quadrature demodulators, based on a passive CMOS mixer with capacitive load, has been studied with respect to process spread. A mathematical model of the mixer has been presented which explains the statistical spread in the mixer. The mixer transfer function has been divided into a multiplier, an amplifier and a time-variant filter, where the statistical spread will affect the filtering part of the mixer. The filter is time-invariant if the time constant is large enough compared with the local oscillator frequency. A first approximation of the mixer filter is therefore that it is time-invariant which simplifies the statistical analysis. The model does not require time-consuming transient analysis, as it possible to use the time average of the transfer function, enabling the use of AC simulation instead. The time-invariant model gives a maximum of the minimum image rejection. The time-variance increases the spread and reduces the image rejection. The main conclusion of the investigation is that the time average of the transfer function can be used as the small signal model for the mixer. The model can be used to analyse and simulate the statistical spread and thereby the imbalance and minimum image rejection of a quadrature demodulator.

happylure · 发表于 2008-4-20 22:16:37

The book is so clearly written you can open it practically anywhere and read just the items of interest.

Concepts are supported by properly simplified schematics.

All the math needed for your own designs is shown and explained, but in such a way, that if you do not need the math right now, you can skip it.

Half the reason I bought this book was to learn to build switching power supplies, the other half was to learn analog design in general. The book is excellent for both purposes