Chapter 11 Frequency Response 11 1 11 2
- Slides: 74
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
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 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 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 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 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 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 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 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 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 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), 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 II CH 11 Frequency Response 15
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 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 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
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 -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 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
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 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
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 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
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
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 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 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 Using Miller’s Theorem CH 11 Frequency Response 36
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
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: 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
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 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: Frequency Response of CG Stage CH 11 Frequency Response 47
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 Source Follower Stage CH 11 Frequency Response 50
Example: Frequency Response of Source Follower CH 11 Frequency Response 51
Example: Source Follower CH 11 Frequency Response 52
Input Capacitance of Emitter/Source Follower CH 11 Frequency Response 53
Example: Source Follower Input Capacitance CH 11 Frequency Response 54
Output Impedance of Emitter Follower CH 11 Frequency Response 55
Output Impedance of Source Follower CH 11 Frequency Response 56
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
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 MOS Cascode CH 11 Frequency Response 61
Example: Frequency Response of Cascode CH 11 Frequency Response 62
MOS Cascode Example CH 11 Frequency Response 63
I/O Impedance of Bipolar Cascode CH 11 Frequency Response 64
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 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 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
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 3 Ø Gate-Drain Capacitance of M 3 CH 11 Frequency Response 70
Example: Capacitive Coupling CH 11 Frequency Response 71
Example: IC Amplifier – Low Frequency Design CH 11 Frequency Response 72
Example: IC Amplifier – Midband Design CH 11 Frequency Response 73
Example: IC Amplifier – High Frequency Design CH 11 Frequency Response 74
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