Chapter 11 Frequency Response 11 1 11 2

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Chapter 11 Frequency Response Ø Ø Ø Ø Ø 11. 1 11. 2 11.

Chapter 11 Frequency Response Ø Ø Ø Ø Ø 11. 1 11. 2 11. 3 11. 4 11. 5 11. 6 11. 7 11. 8 11. 9 Fundamental Concepts High-Frequency Models of Transistors Analysis Procedure Frequency Response of CE and CS Stages Frequency Response of CB and CG Stages Frequency Response of Followers Frequency Response of Cascode Stage Frequency Response of Differential Pairs Additional Examples 1

Chapter Outline CH 11 Frequency Response 2

Chapter Outline CH 11 Frequency Response 2

High Frequency Roll-off of Amplifier Ø As frequency of operation increases, the gain of

High Frequency Roll-off of Amplifier Ø As frequency of operation increases, the gain of amplifier decreases. This chapter analyzes this problem. CH 11 Frequency Response 3

Example: Human Voice I Natural Voice Telephone System Ø Natural human voice spans a

Example: Human Voice I Natural Voice Telephone System Ø Natural human voice spans a frequency range from 20 Hz to 20 KHz, however conventional telephone system passes frequencies from 400 Hz to 3. 5 KHz. Therefore phone conversation differs from face-to-face conversation. CH 11 Frequency Response 4

Example: Human Voice II Path traveled by the human voice to the voice recorder

Example: Human Voice II Path traveled by the human voice to the voice recorder Mouth Air Recorder Path traveled by the human voice to the human ear Mouth Air Ear Skull Ø Since the paths are different, the results will also be different. CH 11 Frequency Response 5

Example: Video Signal High Bandwidth Low Bandwidth Ø Video signals without sufficient bandwidth become

Example: Video Signal High Bandwidth Low Bandwidth Ø Video signals without sufficient bandwidth become fuzzy as they fail to abruptly change the contrast of pictures from complete white into complete black. CH 11 Frequency Response 6

Gain Roll-off: Simple Low-pass Filter Ø In this simple example, as frequency increases the

Gain Roll-off: Simple Low-pass Filter Ø In this simple example, as frequency increases the impedance of C 1 decreases and the voltage divider consists of C 1 and R 1 attenuates Vin to a greater extent at the output. CH 11 Frequency Response 7

Gain Roll-off: Common Source Ø The capacitive load, CL, is the culprit for gain

Gain Roll-off: Common Source Ø The capacitive load, CL, is the culprit for gain roll-off since at high frequency, it will “steal” away some signal current and shunt it to ground. CH 11 Frequency Response 8

Frequency Response of the CS Stage Ø At low frequency, the capacitor is effectively

Frequency Response of the CS Stage Ø At low frequency, the capacitor is effectively open and the gain is flat. As frequency increases, the capacitor tends to a short and the gain starts to decrease. A special frequency is ω=1/(RDCL), where the gain drops by 3 d. B. CH 11 Frequency Response 9

Example: Figure of Merit Ø This metric quantifies a circuit’s gain, bandwidth, and power

Example: Figure of Merit Ø This metric quantifies a circuit’s gain, bandwidth, and power dissipation. In the bipolar case, low temperature, supply, and load capacitance mark a superior figure of merit. CH 11 Frequency Response 10

Example: Relationship between Frequency Response and Step Response Ø The relationship is such that

Example: Relationship between Frequency Response and Step Response Ø The relationship is such that as R 1 C 1 increases, the bandwidth drops and the step response becomes slower. CH 11 Frequency Response 11

Bode Plot Ø When we hit a zero, ωzj, the Bode magnitude rises with

Bode Plot Ø When we hit a zero, ωzj, the Bode magnitude rises with a slope of +20 d. B/dec. Ø When we hit a pole, ωpj, the Bode magnitude falls with a slope of -20 d. B/dec CH 11 Frequency Response 12

Example: Bode Plot Ø The circuit only has one pole (no zero) at 1/(RDCL),

Example: Bode Plot Ø The circuit only has one pole (no zero) at 1/(RDCL), so the slope drops from 0 to -20 d. B/dec as we pass ωp 1. CH 11 Frequency Response 13

Pole Identification Example I CH 11 Frequency Response 14

Pole Identification Example I CH 11 Frequency Response 14

Pole Identification Example II CH 11 Frequency Response 15

Pole Identification Example II CH 11 Frequency Response 15

Circuit with Floating Capacitor Ø The pole of a circuit is computed by finding

Circuit with Floating Capacitor Ø The pole of a circuit is computed by finding the effective resistance and capacitance from a node to GROUND. Ø The circuit above creates a problem since neither terminal of CF is grounded. CH 11 Frequency Response 16

Miller’s Theorem Ø If Av is the gain from node 1 to 2, then

Miller’s Theorem Ø If Av is the gain from node 1 to 2, then a floating impedance ZF can be converted to two grounded impedances Z 1 and Z 2. CH 11 Frequency Response 17

Miller Multiplication Ø With Miller’s theorem, we can separate the floating capacitor. However, the

Miller Multiplication Ø With Miller’s theorem, we can separate the floating capacitor. However, the input capacitor is larger than the original floating capacitor. We call this Miller multiplication. CH 11 Frequency Response 18

Example: Miller Theorem CH 11 Frequency Response 19

Example: Miller Theorem CH 11 Frequency Response 19

High-Pass Filter Response Ø The voltage division between a resistor and a capacitor can

High-Pass Filter Response Ø The voltage division between a resistor and a capacitor can be configured such that the gain at low frequency is reduced. CH 11 Frequency Response 20

Example: Audio Amplifier Ø In order to successfully pass audio band frequencies (20 Hz

Example: Audio Amplifier Ø In order to successfully pass audio band frequencies (20 Hz -20 KHz), large input and output capacitances are needed. CH 11 Frequency Response 21

Capacitive Coupling vs. Direct Coupling Capacitive Coupling Direct Coupling Ø Capacitive coupling, also known

Capacitive Coupling vs. Direct Coupling Capacitive Coupling Direct Coupling Ø Capacitive coupling, also known as AC coupling, passes AC signals from Y to X while blocking DC contents. Ø This technique allows independent bias conditions between stages. Direct coupling does not. CH 11 Frequency Response 22

Typical Frequency Response Lower Corner CH 11 Frequency Response Upper Corner 23

Typical Frequency Response Lower Corner CH 11 Frequency Response Upper Corner 23

High-Frequency Bipolar Model Ø At high frequency, capacitive effects come into play. Cb represents

High-Frequency Bipolar Model Ø At high frequency, capacitive effects come into play. Cb represents the base charge, whereas C and Cje are the junction capacitances. CH 11 Frequency Response 24

High-Frequency Model of Integrated Bipolar Transistor Ø Since an integrated bipolar circuit is fabricated

High-Frequency Model of Integrated Bipolar Transistor Ø Since an integrated bipolar circuit is fabricated on top of a substrate, another junction capacitance exists between the collector and substrate, namely CCS. CH 11 Frequency Response 25

Example: Capacitance Identification CH 11 Frequency Response 26

Example: Capacitance Identification CH 11 Frequency Response 26

MOS Intrinsic Capacitances Ø For a MOS, there exist oxide capacitance from gate to

MOS Intrinsic Capacitances Ø For a MOS, there exist oxide capacitance from gate to channel, junction capacitances from source/drain to substrate, and overlap capacitance from gate to source/drain. CH 11 Frequency Response 27

Gate Oxide Capacitance Partition and Full Model Ø The gate oxide capacitance is often

Gate Oxide Capacitance Partition and Full Model Ø The gate oxide capacitance is often partitioned between source and drain. In saturation, C 2 ~ Cgate, and C 1 ~ 0. They are in parallel with the overlap capacitance to form CGS and CGD. CH 11 Frequency Response 28

Example: Capacitance Identification CH 11 Frequency Response 29

Example: Capacitance Identification CH 11 Frequency Response 29

Transit Frequency Ø Transit frequency, f. T, is defined as the frequency where the

Transit Frequency Ø Transit frequency, f. T, is defined as the frequency where the current gain from input to output drops to 1. CH 11 Frequency Response 30

Example: Transit Frequency Calculation CH 11 Frequency Response 31

Example: Transit Frequency Calculation CH 11 Frequency Response 31

Analysis Summary Ø The frequency response refers to the magnitude of the transfer function.

Analysis Summary Ø The frequency response refers to the magnitude of the transfer function. Ø Bode’s approximation simplifies the plotting of the frequency response if poles and zeros are known. Ø In general, it is possible to associate a pole with each node in the signal path. Ø Miller’s theorem helps to decompose floating capacitors into grounded elements. Ø Bipolar and MOS devices exhibit various capacitances that limit the speed of circuits. CH 11 Frequency Response 32

High Frequency Circuit Analysis Procedure Ø Determine which capacitor impact the low-frequency region of

High Frequency Circuit Analysis Procedure Ø Determine which capacitor impact the low-frequency region of the response and calculate the low-frequency pole (neglect transistor capacitance). Ø Calculate the midband gain by replacing the capacitors with short circuits (neglect transistor capacitance). Ø Include transistor capacitances. Ø Merge capacitors connected to AC grounds and omit those that play no role in the circuit. Ø Determine the high-frequency poles and zeros. Ø Plot the frequency response using Bode’s rules or exact analysis. CH 11 Frequency Response 33

Frequency Response of CS Stage with Bypassed Degeneration Ø In order to increase the

Frequency Response of CS Stage with Bypassed Degeneration Ø In order to increase the midband gain, a capacitor Cb is placed in parallel with Rs. Ø The pole frequency must be well below the lowest signal frequency to avoid the effect of degeneration. CH 11 Frequency Response 34

Unified Model for CE and CS Stages CH 11 Frequency Response 35

Unified Model for CE and CS Stages CH 11 Frequency Response 35

Unified Model Using Miller’s Theorem CH 11 Frequency Response 36

Unified Model Using Miller’s Theorem CH 11 Frequency Response 36

Example: CE Stage Ø The input pole is the bottleneck for speed. CH 11

Example: CE Stage Ø The input pole is the bottleneck for speed. CH 11 Frequency Response 37

Example: Half Width CS Stage CH 11 Frequency Response 38

Example: Half Width CS Stage CH 11 Frequency Response 38

Direct Analysis of CE and CS Stages Ø Direct analysis yields different pole locations

Direct Analysis of CE and CS Stages Ø Direct analysis yields different pole locations and an extra zero. CH 11 Frequency Response 39

Example: CE and CS Direct Analysis CH 11 Frequency Response 40

Example: CE and CS Direct Analysis CH 11 Frequency Response 40

Example: Comparison Between Different Methods Miller’s CH 11 Frequency Response Exact Dominant Pole 41

Example: Comparison Between Different Methods Miller’s CH 11 Frequency Response Exact Dominant Pole 41

Input Impedance of CE and CS Stages CH 11 Frequency Response 42

Input Impedance of CE and CS Stages CH 11 Frequency Response 42

Low Frequency Response of CB and CG Stages Ø As with CE and CS

Low Frequency Response of CB and CG Stages Ø As with CE and CS stages, the use of capacitive coupling leads to low-frequency roll-off in CB and CG stages (although a CB stage is shown above, a CG stage is similar). CH 11 Frequency Response 43

Frequency Response of CB Stage CH 11 Frequency Response 44

Frequency Response of CB Stage CH 11 Frequency Response 44

Frequency Response of CG Stage Ø Similar to a CB stage, the input pole

Frequency Response of CG Stage Ø Similar to a CB stage, the input pole is on the order of f T, so rarely a speed bottleneck. CH 11 Frequency Response 45

Example: CG Stage Pole Identification CH 11 Frequency Response 46

Example: CG Stage Pole Identification CH 11 Frequency Response 46

Example: Frequency Response of CG Stage CH 11 Frequency Response 47

Example: Frequency Response of CG Stage CH 11 Frequency Response 47

Emitter and Source Followers Ø The following will discuss the frequency response of emitter

Emitter and Source Followers Ø The following will discuss the frequency response of emitter and source followers using direct analysis. Ø Emitter follower is treated first and source follower is derived easily by allowing r to go to infinity. CH 11 Frequency Response 48

Direct Analysis of Emitter Follower CH 11 Frequency Response 49

Direct Analysis of Emitter Follower CH 11 Frequency Response 49

Direct Analysis of Source Follower Stage CH 11 Frequency Response 50

Direct Analysis of Source Follower Stage CH 11 Frequency Response 50

Example: Frequency Response of Source Follower CH 11 Frequency Response 51

Example: Frequency Response of Source Follower CH 11 Frequency Response 51

Example: Source Follower CH 11 Frequency Response 52

Example: Source Follower CH 11 Frequency Response 52

Input Capacitance of Emitter/Source Follower CH 11 Frequency Response 53

Input Capacitance of Emitter/Source Follower CH 11 Frequency Response 53

Example: Source Follower Input Capacitance CH 11 Frequency Response 54

Example: Source Follower Input Capacitance CH 11 Frequency Response 54

Output Impedance of Emitter Follower CH 11 Frequency Response 55

Output Impedance of Emitter Follower CH 11 Frequency Response 55

Output Impedance of Source Follower CH 11 Frequency Response 56

Output Impedance of Source Follower CH 11 Frequency Response 56

Active Inductor Ø The plot above shows the output impedance of emitter and source

Active Inductor Ø The plot above shows the output impedance of emitter and source followers. Since a follower’s primary duty is to lower the driving impedance (RS>1/gm), the “active inductor” characteristic on the right is usually observed. CH 11 Frequency Response 57

Example: Output Impedance CH 11 Frequency Response 58

Example: Output Impedance CH 11 Frequency Response 58

Frequency Response of Cascode Stage Ø For cascode stages, there are three poles and

Frequency Response of Cascode Stage Ø For cascode stages, there are three poles and Miller multiplication is smaller than in the CE/CS stage. CH 11 Frequency Response 59

Poles of Bipolar Cascode CH 11 Frequency Response 60

Poles of Bipolar Cascode CH 11 Frequency Response 60

Poles of MOS Cascode CH 11 Frequency Response 61

Poles of MOS Cascode CH 11 Frequency Response 61

Example: Frequency Response of Cascode CH 11 Frequency Response 62

Example: Frequency Response of Cascode CH 11 Frequency Response 62

MOS Cascode Example CH 11 Frequency Response 63

MOS Cascode Example CH 11 Frequency Response 63

I/O Impedance of Bipolar Cascode CH 11 Frequency Response 64

I/O Impedance of Bipolar Cascode CH 11 Frequency Response 64

I/O Impedance of MOS Cascode CH 11 Frequency Response 65

I/O Impedance of MOS Cascode CH 11 Frequency Response 65

Bipolar Differential Pair Frequency Response Half Circuit Ø Since bipolar differential pair can be

Bipolar Differential Pair Frequency Response Half Circuit Ø Since bipolar differential pair can be analyzed using halfcircuit, its transfer function, I/O impedances, locations of poles/zeros are the same as that of the half circuit’s. CH 11 Frequency Response 66

MOS Differential Pair Frequency Response Half Circuit Ø Since MOS differential pair can be

MOS Differential Pair Frequency Response Half Circuit Ø Since MOS differential pair can be analyzed using halfcircuit, its transfer function, I/O impedances, locations of poles/zeros are the same as that of the half circuit’s. CH 11 Frequency Response 67

Example: MOS Differential Pair CH 11 Frequency Response 68

Example: MOS Differential Pair CH 11 Frequency Response 68

Common Mode Frequency Response Ø Css will lower the total impedance between point P

Common Mode Frequency Response Ø Css will lower the total impedance between point P to ground at high frequency, leading to higher CM gain which degrades the CM rejection ratio. CH 11 Frequency Response 69

Tail Node Capacitance Contribution Ø Source-Body Capacitance of M 1, M 2 and M

Tail Node Capacitance Contribution Ø Source-Body Capacitance of M 1, M 2 and M 3 Ø Gate-Drain Capacitance of M 3 CH 11 Frequency Response 70

Example: Capacitive Coupling CH 11 Frequency Response 71

Example: Capacitive Coupling CH 11 Frequency Response 71

Example: IC Amplifier – Low Frequency Design CH 11 Frequency Response 72

Example: IC Amplifier – Low Frequency Design CH 11 Frequency Response 72

Example: IC Amplifier – Midband Design CH 11 Frequency Response 73

Example: IC Amplifier – Midband Design CH 11 Frequency Response 73

Example: IC Amplifier – High Frequency Design CH 11 Frequency Response 74

Example: IC Amplifier – High Frequency Design CH 11 Frequency Response 74