Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Chirp spectrum wikipedia , lookup
Utility frequency wikipedia , lookup
Electronic engineering wikipedia , lookup
Opto-isolator wikipedia , lookup
Regenerative circuit wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Wien bridge oscillator wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
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 Microelectronic Circuits SJTU Yang Hua 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. Microelectronic Circuits SJTU Yang Hua 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) Microelectronic Circuits SJTU Yang Hua Part I: s-Domain analysis Zeros and poles Bode plots The amplifier transfer function Microelectronic Circuits SJTU Yang Hua 7.1 s-Domain analysis– Frequency Response Transfer function: poles, zeros Examples: high pass and low pass Bode plots: Determining the 3-dB frequency Microelectronic Circuits SJTU Yang Hua 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 am s m am1s m1 ... a0 T ( s) Vo ( s) / Vi ( s) s n bn 1s n 1 ... b0 Microelectronic Circuits SJTU Yang Hua Transfer function: poles, zeros ( s Z1 )( s Z 2 )......( s Z m ) T ( s ) Vo ( s ) / Vi ( s ) am ( s P1 )( s P2 )......( s Pn ) Z1, Z2, … Zm are called the transfer-function zeros or transmission zeros. P1, P2, … Pm 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. Microelectronic Circuits SJTU Yang Hua 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. ω0, called the pole frequency, is Low pass : T ( s ) equal to the inverse of the time constant of circuit network(STC). a0 s 0 High pass : T ( s ) a1s s 0 Microelectronic Circuits a1s a0 T ( s) s 0 SJTU Yang Hua Example1: High pass circuit Au f fL f 1 fL 90 arctan 2 f fL jRC RCs s T ( s) jRC 1 RCs 1 s 1 / RC RC is the time constant; ωL=1/RC Microelectronic Circuits SJTU Yang Hua Example2: Low pass circuit 1 / RC T ( s) s 1 / RC RC is the time constant; ωH=1/RC Au 1 f 1 fH arctan Microelectronic Circuits 2 f fH SJTU Yang Hua 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 20 log 10 a 2 2 20 log 10 1 ( / a) 2 Microelectronic Circuits SJTU Yang Hua Bode Plots Microelectronic Circuits SJTU Yang Hua Bode Plots Microelectronic Circuits SJTU Yang Hua Example 7.1 Microelectronic Circuits SJTU Yang Hua 7.2 the amplifier transfer function (a) a capacitively coupled amplifier (b) a direct-coupled amplifier Bandwidth : BW H L Gain - bandwidth product : GB AM BW AM H Microelectronic Circuits SJTU Yang Hua The Gain Function A(s) AM FL (s) FH (s) Gain function Midband: No capacitors in effect A(s) AM Low-frequency band: coupling and bypass capacitors in effect A(s) AM FL (s) High-frequency band: transistor internal capacitors in effect A(s) AM FH (s) Microelectronic Circuits SJTU Yang Hua The low-Frequency Gain Function Gain function A( s) AM FL ( s) s Z 1 s Z 2 .....s ZnL F ( s) L s s .....s p1 p2 pnL ωP1 , ωP2 , ….ωPn are positive numbers representing the frequencies of the n real poles. ωZ1 , ωZ2 , ….ωZn are positive, negative, or zero numbers representing the frequencies of the n real transmission zeros. Microelectronic Circuits SJTU Yang Hua Determining the 3-dB Frequency Definition A(L ) AM 3dB or A( L ) AM 2 Assume ωP1< ωP2 < ….<ωPn and ωZ1 < ωZ2 < ….<ωZn L 2 P1 P 2 ... 2( Microelectronic Circuits 2 2 Z1 Z 2 ...) 2 SJTU Yang Hua 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, AM s A( s ) s P1 L P1 Microelectronic Circuits SJTU Yang Hua The High-Frequency Gain Function Gain function A( s ) AM FH ( s ) (1 s Z 1 )(1 s Z 2 ) .....(1 s Zn ) FH ( s ) (1 s P1 ) (1 s P 2 )..... (1 s Pn ) ωP1 , ωP2 , ….ωPn are positive numbers representing the frequencies of the n real poles. ωZ1 , ωZ2 , ….ωZn are positive, negative, or infinite numbers representing the frequencies of the n real transmission zeros. Microelectronic Circuits SJTU Yang Hua Determining the 3-dB Frequency Definition or A( H ) AM A(H ) AM 3dB 2 Assume ωP1< ωP2 < ….<ωPn and ωZ1 < ωZ2 < ….<ωZn H 1 ( 1 P1 2 Microelectronic Circuits 1 P 2 2 ....) 2( 1 Z 1 2 1 Z 2 2 ....) SJTU Yang Hua 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, AM A( s ) 1 s / P1 H P1 Microelectronic Circuits SJTU Yang Hua 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. 1 a1s a2 s 2 ... anH s nH FH ( s ) 1 b1s b2 s 2 ... bnH s nH b1 1 1 1 ... p1 p2 pnH nH 1 b1 Ci Rio p1 i 1 H 1 nH C R i 1 i io Microelectronic Circuits SJTU Yang Hua 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. s nL d1s nL1 d 2 s 2 ... FL ( s) nL s e1s nL1 e2 s 2 ... e1 p1 p2 ... pnL nL 1 p1 if dominant pole exists e1 i 1 Ci Rio nL 1 L i 1 Ci Rio Microelectronic Circuits SJTU Yang Hua Example7.3 FL ( s) Microelectronic Circuits s( s 10) ( s 100)( s 25) SJTU Yang Hua Example7.4 1 s / 10 5 FH ( s) (1 s / 10 4 )(1 s / 4 10 4 ) Microelectronic Circuits SJTU Yang Hua summary (The Fouth Edition:P601) (A) Poles and zeros are known or can be easily determined Low-frequency High-frequency A( s) AM FL ( s) A( s ) AM FH ( s ) FL ( s) FH ( s ) s Z1 s Z 2 .....s ZnL s s .....s p1 A( s ) (1 s Z 1 )(1 s Z 2 ) .....(1 s Zn ) (1 s P1 ) (1 s P 2 )..... (1 s Pn ) AM A( s ) 1 s / P1 p2 pnL AM s s P1 H P1 L P1 L 2 P1 P 2 ... 2( 2 2 Z1 Z 2 ...) 2 H 1 ( 1 P1 2 1 P 2 2 ....) 2( 1 Z 1 2 1 Z 2 2 ....) (B) Poles and zeros can not be easily determined Low-frequency s nL d1s nL1 d 2 s 2 ... FL ( s) nL s e1s nL1 e2 s 2 ... e1 p1 p2 ... pnL nL e1 i 1 1 p1 if dominant pole exists Ci Rio nL L i 1 1 Ci Rio Microelectronic Circuits High-frequency FH ( s ) b1 1 a1s a2 s 2 ... anH s nH 1 b1s b2 s 2 ... bnH s nH 1 1 1 ... p1 p2 pnH nH b1 Ci Rio i 1 H 1 if dominant pole exists p1 1 nH C R i 1 i io SJTU Yang Hua Homework April 17th, 2008 7.1; 7.2; 7.7; 7.10 Microelectronic Circuits SJTU Yang Hua 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 Microelectronic Circuits SJTU Yang Hua Internal Capacitances of the BJT and High Frequency Model Internal capacitance The base-charging or diffusion capacitance Junction capacitances The base-emitter junction capacitance The collector-base junction capacitance High frequency small signal model Cutoff frequency and unity-gain frequency Microelectronic Circuits SJTU Yang Hua The Base-Charging or Diffusion Capacitance Diffusion capacitance almost entirely exists in forward-biased pn junction Expression of the small-signal diffusion capacitance IC Cde F g m F VT F : forward base - transit ti me, represents the average time a charge carrier spends in crossing the base10ps - 100ps Proportional to the biased current Microelectronic Circuits SJTU Yang Hua Junction Capacitances The Base-Emitter Junction Capacitanc C je C je0 2C je0 VBE m (1 ) Voe C je0 : is the value of Cje at zero voltage Voe : is the build in voltage (tipically , 0.9v) The collector-base junction capacitance C 0 C V (1 CB ) m Voc C 0 :is the value of C at zero voltage Voc : is the CBJ bulid in voltage (typically , 0.75v) Microelectronic Circuits SJTU Yang Hua The High-Frequency Hybrid- Model C Cde C je Two capacitances Cπ and Cμ , where One resistance rx . Accurate value is obtained from high frequency measurement. rx r Microelectronic Circuits SJTU Yang Hua The Cutoff and Unity-Gain Frequency IC h fe ( s ) Circuit for deriving an expression for IB vCE 0 According to the definition, output port is short circuit Microelectronic Circuits SJTU Yang Hua The Cutoff and Unity-Gain Frequency Expression of the short-circuit current transfer function h fe ( s) 0 1 s(C C )r Characteristic is similar to the one of firstorder low-pass filter Microelectronic Circuits SJTU Yang Hua The Cutoff and Unity-Gain Frequency 1 (C C )r gm T 0 C C r Microelectronic Circuits SJTU Yang Hua The MOSFET Internal Capacitance and High-Frequency Model Internal capacitances The gate capacitive effect Triode region Saturation region Cutoff region Overlap capacitance The junction capacitances Source-body depletion-layer capacitance drain-body depletion-layer capacitance High-frequency model Microelectronic Circuits SJTU Yang Hua The Gate Capacitive Effect MOSFET operates at triode region C gs C gd 12 WLCox MOSFET operates at saturation region C gs 23 WLC ox C gd 0 MOSFET operates at cutoff region C gs C gd 0 C gb WLCox Microelectronic Circuits SJTU Yang Hua Overlap Capacitance Overlap capacitance results from the fact that the source and drain diffusions extend slightly under the gate oxide. The expression for overlap capacitance Cov WLovCox Typical value This additional component should be added to Cgs and Cgd in all preceding formulas. Lov 0.05 0.1L Microelectronic Circuits SJTU Yang Hua The Junction Capacitances • Source-body depletion-layer capacitance C sb • C sb0 VSB 1+ Vo drain-body depletion-layer capacitance C db Microelectronic Circuits C db 0 VDB 1+ Vo SJTU Yang Hua High-Frequency MOSFET Model Microelectronic Circuits SJTU Yang Hua High-Frequency Model (b) The equivalent circuit for the case in which the source is connected to the substrate (body). (c) The equivalent circuit model of (b) with Cdb neglected (to simplify analysis). Microelectronic Circuits SJTU Yang Hua The MOSFET Unity-Gain Frequency Current gain Io gm I i s(Cgs Cgd ) Unity-gain frequency Microelectronic Circuits gm fT 2 (Cgs Cgd ) SJTU Yang Hua 7.3 Low-frequency response of the CS and CE amplifiers Microelectronic Circuits SJTU Yang Hua Low-frequency response of the CS Microelectronic Circuits SJTU Yang Hua The procedure to find quickly the time constant: 1. Reduce Vsig to zero 2. Consider each capacitor separately; that is , assume that the other Capacitors are as perfect short circuits 3. For each capacitor, find the total resistance seen between its terminals Microelectronic Circuits SJTU Yang Hua Analysis of Common-emitter amplifier Low frequency small signal analysis: 1) Eliminate the DC source 2) Ignore Cπ and Cμ and ro 3) Ignore rx, which is much smaller than rπ Microelectronic Circuits SJTU Yang Hua (b) the effect of CC1 is determined with CE and CC2 assumed to be acting as perfect short circuits; Microelectronic Circuits SJTU Yang Hua (c) the effect of CE is determined with CC1 and CC2 assumed to be acting as perfect short circuits Microelectronic Circuits SJTU Yang Hua (d) the effect of CC2 is determined with CC1 and CE assumed to be acting as perfect short circuits; Microelectronic Circuits SJTU Yang Hua (e) sketch of the low-frequency gain under the assumptions that CC1, CE, and CC2 do not interact and that their break (or pole) frequencies are widely separated. Microelectronic Circuits SJTU Yang Hua Homework: April 15th, 2008 7.29; 7.35; 7.39 Microelectronic Circuits SJTU Yang Hua 7.4 High-frequency response of the CS and CE amplifiers • Miller’s theorem. • Analysis of the high frequency response. Using Miller’s theorem. Using open-circuit time constants. Microelectronic Circuits SJTU Yang Hua High-Frequency Equivalent-Circuit Model of the CS Amplifier Fig. 7.16 (a) Equivalent circuit for analyzing the high-frequency response of the amplifier circuit of Fig. 7.15(a). Note that the MOSFET is replaced with its high-frequency equivalent-circuit. (b) A slightly simplified version of (a) by combining RL and ro into a single resistance R’L = RL//ro. Microelectronic Circuits SJTU Yang Hua High-Frequency Equivalent-Circuit Model of the CE Amplifier Vs' Vs r Rs rs r Rs' Rs rx // r RL' RL // ro Fig. . 7.17 (a) Equivalent circuit for the analysis of the high-frequency response of the common-emitter amplifier of Fig. 7.15(b). Note that the BJT is replaced with its hybrid- high-frequency equivalent circuit. (b) An equivalent but simpler version of the circuit in (a), Microelectronic Circuits SJTU Yang Hua Miller’s Theorem Impedance Z can be replaced by two impedances: Z1 connected between node 1 and ground Z2 connected between node 2 and ground Microelectronic Circuits SJTU Yang Hua Miller’s Theorem The miller equivalent circuit is valid as long as the conditions that existed in the network when K was determined are not changed. Miller theorem can be used to determining the input impedance and the gain of an amplifier; it cannot be applied to determine the output impedance. Microelectronic Circuits SJTU Yang Hua Analysis Using Miller’s Theorem Vo g mVgs RL' Neglecting the current through Cgd Ceq C gd (1 g m RL' ) CT C gs C gd (1 g m RL' ) Approximate equivalent circuit obtained by applying Miller’s theorem. This model works reasonably well when Rsig is large. The high-frequency response is dominated by the pole formed by Rsig and CT. Microelectronic Circuits SJTU Yang Hua Analysis Using Miller’s Theorem Using miller’s theorem the bridge capacitance Cgd can be replaced by two capacitances which connected between node G and ground, node D and ground. The upper 3dB frequency is only determined by this pole. CT C gs C gd (1 g m RL ) ' 1 fH 2CT Rsig Microelectronic Circuits SJTU Yang Hua Analysis Using Open-Circuit Time Constants Rgs Rsig Microelectronic Circuits Rgd Rsig (1 g m RL ) RL ' ' SJTU Yang Hua Analysis Using Open-Circuit Time Constants RCL RL Microelectronic Circuits ' SJTU Yang Hua High-Frequency Equivalent Circuit of the CE Amplifier Thevenin theorem: Microelectronic Circuits SJTU Yang Hua Equivalent Circuit with Thévenin Theorem Employed Microelectronic Circuits SJTU Yang Hua The Situation When Rsig Is Low High-frequency equivalent circuit of a CS amplifier fed with a signal source having a very low (effectively zero) resistance. Microelectronic Circuits SJTU Yang Hua The Situation When Rsig Is Low fT, which is equal to the gain-bandwidth product Bode plot for the gain of the circuit in (a). Microelectronic Circuits SJTU Yang Hua The Situation When Rsig Is Low The high frequency gain will no longer be limited by the interaction of the source resistance and the input capacitance. The high frequency limitation happens at the amplifier output. To improve the 3-dB frequency, we shall reduce the equivalent resistance seen through G(B) and D(C) terminals. Microelectronic Circuits SJTU Yang Hua 7.5 Frequency Response of the CG and CB Amplifier High-frequency response of the CS and CE Amplifiers is limited by the Miller effect Introduced by feedback Ceq. To extend the upper frequency limit of a transistor amplifier stage one has to reduce or eliminate the Miller C multiplication. Microelectronic Circuits SJTU Yang Hua 1 1 I e V sC g mV Ve g m sC r r Ie 1 1 g m sC sC Ve r re 1 1 p1 for CG amplifier : p1 CB amplifier has a C re // Rs C gs 1 / g m // Rs 1 1 p2 for CG amplifier : p 2 C RL C gd RL Microelectronic Circuits much higher uppercutoff frequency than that of CE amplifier SJTU Yang Hua Comparisons between CG(CB) and CS(CE) Open-circuit voltage gain for CG(CB) almost equals to the one for CS(CE) Much smaller input resistance and much larger output resistance CG(CB) amplifier is not desirable in voltage amplifier but suitable as current buffer. Superior high frequency response because of the absence of Miller’s effects Cascode amplifier is the significant application for CG(CB) circuit Microelectronic Circuits SJTU Yang Hua Frequency Response of the BJT Cascode Microelectronic Circuits SJTU Yang Hua Frequency Response of the BJT Cascode The cascode configuration combines the advantages of the CE and CB circuits 1 1 ' H RS C 1 2C 1 2 1 C 2 re 2 1 3 C 2 RL Vo r AM g m RL VS r rx RS Microelectronic Circuits SJTU Yang Hua The Source (Emitter) Follower • Self-study • Read the textbook from pp626-629 Microelectronic Circuits SJTU Yang Hua Homework: May 6th,2008 7.44; 7.45; 7.46; 7.57 Microelectronic Circuits SJTU Yang Hua Test: (1)the reason for gain decreasing of high-frequency response , the reason for gain decreasing of low-frequency response 。 A. coupling capacitors and bypass capacitors B. diffusion capacitors and junction capacitors C. linear characteristics of semiconductors D. the quiescent point is not proper (2)when signal frequency is equal to fL or fH,the gain of of amplifier decreases compare to that of midband frequency。 A.0.5times B.0.7times C.0.9times that is decreasing 。 A.3dB B.4dB C.5dB (3)The CE amplifier circuit,when f = fL,the phase is 。 A.+45˚ B.-90˚ C.-135˚ when f = fH, the phase is 。 A.-45˚ B.-135˚ C.-225˚ Microelectronic Circuits SJTU Yang Hua