# 频率响应

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1.Chapter 7 Frequency Response Introduction 7.1 s-Domain analysis: poles,zeros and bode plots 7.2 the amplifier transfer function 7.3 Low-frequency response of the common-source and common-emitter amplifier 7.4 High-frequency response of the CS and CE amplifiers 7.5 The CB, CG and cascode configurations

2.Introduction Why shall we study the frequency response? Actual transistors exhibit charge storage phenomena that limit the speed and frequency of their operation. Aims: the emphasis in this chapter is on analysis. focusing attention on the mechanisms that limit frequency response and on methods for extending amplifier bandwidth.

3.Three parts: s-Domain analysis and the amplifier transfer function (April 13,2008) High frequency model of BJT and MOS; Low-frequency and High-frequency response of the common-source and common-emitter amplifier (April 15,2008) Frequency response of cascode , Emitter and source followers and differential amplifier (April 22,2008)

4.Part I: s-Domain analysis Zeros and poles Bode plots The amplifier transfer function

5.7.1 s-Domain analysis– Frequency Response Transfer function: poles, zeros Examples: high pass and low pass Bode plots: Determining the 3-dB frequency

6.Transfer function: poles, zeros Most of our work in this chapter will be concerned with finding amplifier voltage gain as a transfer function of the complex frequency s. A capacitance C: is equivalent an impedance 1/SC An inductance L: is equivalent an impedance SL Voltage transfer function: by replacing S by jw , we can obtain its magnitude response and phase response

7.Transfer function: poles, zeros Z 1 , Z 2 , … Z m are called the transfer-function zeros or transmission zeros . P 1 , P 2 , … P m are called the transfer-function poles or natural modes . The poles and zeros can be either real or complex numbers, the complex poles(zeros ) must occur in conjugate pairs.

8.First-order Functions All the transfer functions encountered in this chapter have real poles and zeros and can be written as the product of first-order transfer functions . ω 0, called the pole frequency , is equal to the inverse of the time constant of circuit network(STC ).

9.Example1: High pass circuit RC is the time constant; ω L =1/RC

10.Example2: Low pass circuit RC is the time constant; ω H =1/RC

11.Bode Plots A simple technique exists for obtaining an approximate plot of the magnitude and phase of a transfer function given its poles and zeros. The resulting diagram is called Bode plots A transfer function consists of A product of factors of the form s+a

12.Bode Plots

13.Bode Plots

14.Example 7.1

15.7.2 the amplifier transfer function (a) a capacitively coupled amplifier (b) a direct-coupled amplifier

16.The Gain Function Gain function Midband : No capacitors in effect Low-frequency band: coupling and bypass capacitors in effect High-frequency band: transistor internal capacitors in effect

17.The low-Frequency Gain Function Gain function ω P1 , ω P2 , …. ω Pn are positive numbers representing the frequencies of the n real poles . ω Z1 , ω Z2 , …. ω Zn are positive, negative, or zero numbers representing the frequencies of the n real transmission zeros.

18.Determining the 3-dB Frequency Definition or Assume ω P1 < ω P2 < ….< ω Pn and ω Z1 < ω Z2 < ….< ω Zn

19.Determining the 3-dB Frequency Dominant pole If the lowest-frequency pole is at least two octaves (a factor of 4) away from the nearest pole or zero, it is called dominant pole. Thus the 3-dB frequency is determined by the dominant pole. Single pole system,

20.The High-Frequency Gain Function Gain function ω P1 , ω P2 , …. ω Pn are positive numbers representing the frequencies of the n real poles . ω Z1 , ω Z2 , …. ω Zn are positive, negative, or infinite numbers representing the frequencies of the n real transmission zeros.

21.The High-Frequency Gain Function Gain function ω P1 , ω P2 , …. ω Pn are positive numbers representing the frequencies of the n real poles . ω Z1 , ω Z2 , …. ω Zn are positive, negative, or infinite numbers representing the frequencies of the n real transmission zeros.

22.The High-Frequency Gain Function Gain function ω P1 , ω P2 , …. ω Pn are positive numbers representing the frequencies of the n real poles . ω Z1 , ω Z2 , …. ω Zn are positive, negative, or infinite numbers representing the frequencies of the n real transmission zeros.

23.approx. determination of corner frequency Using open-circuit time constants for computing high-frequency 3-dB Frequency : reduce all other C to zero; reduce the input source to zero.

24.approx. determination of corner frequency Using short-circuit time constants for computing low-frequency 3-dB Frequency : replace all other C with short circuit; reduce the input source to zero.

25.Example7.3

26.Example7.4

27.summary (The Fouth Edition:P601) (A) Poles and zeros are known or can be easily determined Low-frequency High-frequency (B) Poles and zeros can not be easily determined Low-frequency High-frequency

28.Homework April 17th, 2008 7.1; 7.2; 7.7; 7.10

29.Part II: Internal Capacitances of the BJT BJT High Frequency Model Internal Capacitances of the MOS MOS High Frequency Model Low-frequency of CS and CS amplifiers