Chapter 16 CMOS Amplifiers 16.1 General Considerations 16.2 Operating Point Analysis and Design 16.3 CMOS Amplifier Topologies 16.4 Common-Source Topology 16.5 Summary and Additional Examples 16.6 Chapter Summary

Chapter Outline CH 16 CMOS Amplifiers

Example: Desired I/O Impedances CH 16 CMOS Amplifiers

Method to Measure the I/O Impedances To measure Rin(Rout), deactivate all the other independent sources in the circuit and find the ratio of vX/iX. CH 16 CMOS Amplifiers 4

Example: Input Impedance of a Simple Amplifier CH 16 CMOS Amplifiers 5

The Concept of Impedance at a Node When the other node of a port is grounded, it is more convenient to use the concept of impedance at a node. CH 16 CMOS Amplifiers 6

Example: Impedance Seen at Drain CH 16 CMOS Amplifiers 7

Example: Impedance Seen at Source CH 16 CMOS Amplifiers 8

Impedance Summary Looking into the gate, we see infinity. Looking into the drain, we see rO if the source is (ac) grounded. Looking into the source, we see 1/gm if the gate is (ac) grounded and rO is neglected. CH 16 CMOS Amplifiers 9

Bias and Signal Levels for a MOS Transistor Bias point analysis establishes the region of operation and the small-signal parameters. On top of the bias point, small signals are applied to the circuit. CH 16 CMOS Amplifiers 10

General Steps in Circuit Analysis First, the effects of constant voltage/current sources are analyzed when signal sources are deactivated. Second, small-signal analysis is done when constant sources are set to zero. CH 16 CMOS Amplifiers 11

Simplification of Supply Voltage Notation CH 16 CMOS Amplifiers 12

Example: Amplifier Driven by a Microphone Since the DC (average) value is at zero, and 20mV is not sufficient to turn on M1, M1 is off and Vout is at VDD. CH 16 CMOS Amplifiers 13

Example: Amplifier with Gate Tied to VDD Since the gate voltage level is fixed at VDD, no signal current will be produced my M1, leading to no amplification. CH 16 CMOS Amplifiers 14

Example: Amplifier with Gate Bias With proper value of VB, M1 can operate in the desired saturation region and amplify the incoming voice signal. CH 16 CMOS Amplifiers 15

Simple Biasing In (a), VGS=VDD, whereas in (b) VGS equals to a fraction of VDD. CH 16 CMOS Amplifiers 16

Example: Bias Current and Maximum RD CH 16 CMOS Amplifiers 17

Capacitive Coupling Capacitive coupling is used to block the zero DC output value of the microphone and pass the voice signal to the amplifier. CH 16 CMOS Amplifiers 18

Biasing with Source Degeneration CH 16 CMOS Amplifiers 19

Example: ID and Maximum RD for Source Degeneration Biasing CH 16 CMOS Amplifiers 20

Example: Maximum W/L and Minimum RS CH 16 CMOS Amplifiers 21

Self-Biased MOS Stage The gate voltage is provided by the drain with no voltage drop across RG and M1 is always in saturation. CH 16 CMOS Amplifiers 22

Example: Self-Biased MOS Stage CH 16 CMOS Amplifiers 23

Example: PMOS Stage with Biasing CH 16 CMOS Amplifiers 24

Example: PMOS Stage with Self-Biasing CH 16 CMOS Amplifiers 25

Good Example of Current Source As long as a MOS transistor is in saturation region and λ=0, the current is independent of the drain voltage and it behaves as an ideal current source seen from the drain terminal. CH 16 CMOS Amplifiers 26

Bad Example of Current Source Since the variation of the source voltage directly affects the current of a MOS transistor, it does not operate as a good current source if seen from the source terminal CH 16 CMOS Amplifiers 27

Possible I/O Connections to a MOS Transistor Of all the possible I/O connections to a MOS transistor, only (a,d), (a,e) and (b,d) are functional. CH 16 CMOS Amplifiers 28

Common Source (CS) Stage If the input is applied to the gate and the output is sensed at the drain, the circuit is called a “common-source” (CS) stage. CH 16 CMOS Amplifiers 29

Small-Signal Model of CS Stage CH 16 CMOS Amplifiers 30

Example: CS Stage CH 16 CMOS Amplifiers 31

Example: Faulty CS Stage Design However, no solution exists since M1 is out of the saturation region (VDD-IDRD<VGS-VTH). CH 16 CMOS Amplifiers 32

CS Stage I/O Impedance Calculation CH 16 CMOS Amplifiers 33

CS Stage Including Channel-Length Modulation CH 16 CMOS Amplifiers 34

Example: ½ Gain No Channel-Length Modulation With Channel-Length Modulation CH 16 CMOS Amplifiers 35

Example: RD → ∞ CH 16 CMOS Amplifiers 36

CS Stage with Current Source Load CH 16 CMOS Amplifiers 37

Example: CS Stage with Current Source Load CH 16 CMOS Amplifiers 38

CS Stage with Diode-Connected Load CH 16 CMOS Amplifiers 39

Example: CS Stage with Diode-Connected PMOS CH 16 CMOS Amplifiers 40

CS Stage with Source Degeneration CH 16 CMOS Amplifiers 41

Example: CS Stage with Source Degeneration CH 16 CMOS Amplifiers 42

Example: Degeneration Resistor Without Degeneration With Degeneration CH 16 CMOS Amplifiers 43

Effective Transconductance CH 16 CMOS Amplifiers 44

Effect of Transistor Output Resistance CH 16 CMOS Amplifiers 45

Stage with Explicit Depiction of rO Sometimes, the transistor’s output resistance is explicitly drawn to emphasize its significance. CH 16 CMOS Amplifiers 46

Example: NMOS Current Source Design CH 16 CMOS Amplifiers 47

Example: Output Resistance of CS Stage with Degeneration I CH 16 CMOS Amplifiers 48

Example: Output Resistance of CS Stage with Degeneration II CH 16 CMOS Amplifiers 49

Example: Failing Microphone Amplifier No Amplification!! Because of the microphone’s small low-frequency output resistance (100Ω), the bias voltage at the gate is not sufficient to turn on M1. CH 16 CMOS Amplifiers 50

Capacitive Coupling To fix the problem in the previous example, a method known as capacitive coupling is used to block the DC content of the microphone and pass the AC signal to the amplifier. CH 16 CMOS Amplifiers 51

Capacitive Coupling: Bias Analysis Since a capacitor is an open at DC, it can be replaced by an open during bias point analysis. CH 16 CMOS Amplifiers 52

Capacitive Coupling: AC Analysis Since a capacitor is a short at AC, it can be replaced by a short during AC analysis. CH 16 CMOS Amplifiers 53

Capacitive Coupling: I/O Impedances CH 16 CMOS Amplifiers 54

Example: Amplifier with Direction Connection of Speaker This amplifier design still fails because the solenoid of the speaker shorts the drain to ground. CH 16 CMOS Amplifiers 55

Example: Amplifier with Capacitive Coupling at I/O This amplifier design produces very little gain because its equivalent output resistance is too small. CH 16 CMOS Amplifiers 56

Source Degeneration with Bypass Capacitor It is possible to utilize degeneration for biasing but eliminate its effect on the small-signal by adding a bypass capacitor. CH 16 CMOS Amplifiers 57

Example: Source Degeneration with Bypass Capacitor Design CH 16 CMOS Amplifiers 58

Concept Summary CH 16 CMOS Amplifiers 59

Common-Gate Stage In a common-gate stage, the input is applied at the source while the output is taken at the drain. CH 16 CMOS Amplifiers 60

Small Signal Analysis of Common-Gate Stage CH 16 CMOS Amplifiers 61

Example: Common-Gate Stage Design CH 16 CMOS Amplifiers 62

Input Impedance of Common-Gate Stage CH 16 CMOS Amplifiers 63

The Use of Low Input Impedance The low input impedance of a common-gate stage can be used to impedance match a 50-Ω transmission line. CH 16 CMOS Amplifiers 64

Output Impedance of Common-Gate Stage CH 16 CMOS Amplifiers 65

Example: Alternate Av Expression of CG Stage CH 16 CMOS Amplifiers 66

CG Stage in the Presence of Finite Source Resistance CH 16 CMOS Amplifiers 67

Output Impedance of a General CG Stage CH 16 CMOS Amplifiers 68

CG and CS Stages Output Impedance Comparison Since when calculating the output impedance, the input voltage source of the CG stage is grounded, the result will be identical to that of a CS stage if the same assumptions are made for both circuits. CH 16 CMOS Amplifiers 69

Example: AV and Rout λ = 0 λ > 0 CH 16 CMOS Amplifiers 70

Example: CG Stage Lacking Bias Current Although the capacitor C1 isolates the DC content of the signal source, it also blocks the bias current of M1, hence turning it OFF. CH 16 CMOS Amplifiers 71

Example: CG Stage with Source Shorted to Ground Although there is now a path for bias current to flow to ground, the signal current also goes with it, hence producing no gain. CH 16 CMOS Amplifiers 72

CG Stage with Proper Bias Circuitry R1 is used to provide a path for bias current to flow without directly shorting the source to ground. However, it also lowers the input impedance of the circuit CH 16 CMOS Amplifiers 73

Input Current Flowing Paths To maximize the useful current i2, R1 needs to be much larger than 1/gm. CH 16 CMOS Amplifiers 74

Example: CG with Complete Bias Network CH 16 CMOS Amplifiers 75

Example: Min W/L CH 16 CMOS Amplifiers 76

Source Follower Source follower sense the input at the gate and produces the output at the source. CH 16 CMOS Amplifiers 77

Source Follower’s Response to an Input Change As the input changes by a small amount, the output will follow the input and changes by a smaller amount, hence the name source follower. CH 16 CMOS Amplifiers 78

Small-Signal Model and Voltage Gain for Source Follower CH 16 CMOS Amplifiers 79

Example: Source Follower with Current Source CH 16 CMOS Amplifiers 80

Source Follower Acting as a Voltage Divider CH 16 CMOS Amplifiers 81

Complete Small-Signal Model with rO CH 16 CMOS Amplifiers 82

Example: Source Follower with a Real Current Source CH 16 CMOS Amplifiers 83

Example: Source Follower with a Real Current Source CH 16 CMOS Amplifiers 84

Output Resistance of Source Follower CH 16 CMOS Amplifiers 85

Example: Source Follower with Biasing CH 16 CMOS Amplifiers 86

Source Follower with Current Source Biasing In IC technology, source follower is often biased by a current source to avoid the bias current’s dependence on the supply voltage. CH 16 CMOS Amplifiers 87

Summary of MOS Amplifier Topologies CH 16 CMOS Amplifiers 88

Example: Common Source Stage I CH 16 CMOS Amplifiers 89

Example: Common Source Stage II CH 16 CMOS Amplifiers 90

Example: CS and CG Stages CH 16 CMOS Amplifiers 91

Example: Composite Stage I CH 16 CMOS Amplifiers 92

Example: Composite Stage II CH 16 CMOS Amplifiers 93

Chapter Summary The impedances looking into the gate, drain, and source of a MOS are equal to ∞, rO and 1/gm respectively (under proper conditions). The transistor has to be properly biased before small-signal can be applied. Resistive path between the supply rails establishes the gate bias voltage. Only three amplifiers topologies are possible. CS stage provides moderate AV, high Rin and moderate Rout. Source degeneration improves linearity but lower AV. Source degeneration raises the Rout of CS stage considerably. CG stage provides moderate AV, low Rin and moderate Rout. AV for CS and CG stages are similar but for a sign. Source follower provides AV less than 1, high Rin and low Rout, serving as a good voltage buffer. CH 16 CMOS Amplifiers 94