1、Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter 6:Frequency Response of Amplifiers6.1 Basic Current Mirrors6.2 Common-Source Stage6.3 Source Followers6.4 Common-Gate Stage6.5 Cascode Stage6.6
2、Differential Pair6.7 Gain-Bandwidth Trade-Offs Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.2General Considerations In this chapter,we are primarily interested in the magnitude of the transfer func
3、tion.The magnitude of a complex number a+jb is given by.Zeros and poles are respectively defined as the roots of the numerator and denominator of the transfer function.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw
4、-Hill Education.3Miller effect If the circuit of Fig(a)can be converted to that of Fig(b),then Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.4Example A student needs a large Capacitor and decides to
5、 utilize the Miller multiplication What is the issues in this approach?Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.5 Millers theorem does not stipulate the conditions under which this conversion i
6、s valid.If the impedance Z forms the only signal path between X and Y,then the conversion is often invalid.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.6Example Calculate the input resistance of th
7、e circuit shown.Since Av is usually greater than unity,is a negative resistance.Av=Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.7Example The value of Av=VY/VX must be calculated at the frequency of
8、 interest.In the figure,the equivalent circuit reveals that at high frequencies.In many cases we use the low-frequency value of VY/VX to gain insight.We call this approach“Millers approximation.”Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prio
9、r written consent of McGraw-Hill Education.8Example Direct Calculation:Miller Aproximation:Millers approximation has eliminated the zero and predicted two poles for the circuit!Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent
10、of McGraw-Hill Education.9Example Actual Rout=r0 Millers approximation:(1)it may eliminate zeros(2)it may predict additional poles(3)it does not correctly compute the“output”impedance.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written c
11、onsent of McGraw-Hill Education.10Association of Poles with Nodes The overall transfer function can be written as Each node in the circuit contributes one pole to the transfer function.Not valid in general.Example:Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distributi
12、on without the prior written consent of McGraw-Hill Education.11Example At node X:At node Y:The overall transfer funtion:Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.12Common-Source Stage The magni
13、tude of the“input”pole At the output node Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.13Direct Analysis While the denominator appears rather complicated,it can yield intuitive expressions for the
14、two poles.“Dominant pole”approximation.The intuitive approach provides a rough estimate with much less effort.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.14Example One pole is at the origin becaus
15、e the dc gain is infinity.For a large CDB or load capacitance No miller multiplication.Why?Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.15Zero in Transfer Function The transfer function of exhibits
16、 a zero given by CGD provides a feedthrough path that conducts the input signal to the output at very high frequencies.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.16Calculating zero in a CS stage
17、The transfer function Vout(s)=Vin(s)must drop to zero for s=sz.Therefore,the currents through CGD and M1 are equal and opposite:That is Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.17Example Can th
18、is(the zero)occur if H1(s)and H2(s)are first-order low-pass circuits?H1=and H2=The overall transfer function contains a zero.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.18Example Since the corresp
19、onding terminals ofM1 and M2 are shorted to one another in the small-signal model,we merge the two transistors.The circuit thus has the same transfer function as the simple CS stage.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written con
20、sent of McGraw-Hill Education.19Millers Approximation With the aid of Millers approximation,But at high frequencies,the effect of the output node capacitance must be taken into account.Ignore CGS if CGD is large,it provides a low impedance path between the gate and drain of M1.Copyright 2017 McGraw-
21、Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.20Source Followers The strong interaction between nodesX and Y through CGS in makes it difficult to associate a pole with each node.Contains a zero in the left half plane.Why
22、?Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.21Example Transfer function if CL=0?CGS disappear In the absence of channel-length modulation and body effect,the voltage gain from the gate to the sou
23、rce is equal to unity.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.22Input impedance CGD simply shunts the input and can be ignored initially.If gmb=0 and CL=0,then Zin=CGS is entirely bootstrapped
24、 by the source follower and draws no current from the input.At Low frequency the overall input capacitance is equal to CGD plus a fraction of CGS.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.23Inpu
25、t Impedance At high frequencies,A source follower driving a load capacitance exhibits a negative input resistance,possibly causing instability.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.24Output
26、Impedance At low frequency:At very high frequencies,Because CGS shorts the gate and the source.Which one of these variations is more realistic?Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.25Output
27、Impedance Since the output impedance increases with frequency,we postulate that it contains an inductive component.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.26Example Can we construct a(two-term
28、inal)inductor from a source follower?Yes,but non-ideal.It also incurs a parallel resistance and a series resistance.The inductance can partially cancel the load capacitance,CL,at high frequencies,thus extending the bandwidth.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or
29、 distribution without the prior written consent of McGraw-Hill Education.27Common-Gate Stage A transfer function No Miller multiplication of capacitances.RD is typically maximized,so the dc level of the input signal must be quite low.As an amplifier in cases where a low input impedance is required I
30、n cascode stages.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.28Example Why Zin becomes independent of CL as this capacitance increases?As CL or s increases,Zin approaches 1/(gm+gmb)CL lowers the v
31、oltage gain of the circuit,thereby suppressing the effect of the negative resistance introduced by Miller effect through rO.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.29CG Stage The bias network
32、providing the gate voltage exhibits a finite impedance.Consider only CGS here.Lowering the pole magnitude.Output impedance of the circuit drops at high frequencies.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hil
33、l Education.30Cascode Stage Miller effect is less significant in cascode amplifiers than in common-source stages.But I is typically quite higher than the other two.What if RD is replaced by a current source?Pole at node X may be quite lower,but transfer function will not affect much by this.See exam
34、ple.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.31Example Compute the transfer function.For The magnitude of the pole at node X is still given by gm2/CX.Why?Copyright 2017 McGraw-Hill Education.Al
35、l rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.32Differential Pair For differential signals,the response is identical to that of a common-source stage.the common-mode rejection of the circuit degrades considerably at high frequencies.Chan
36、nel-length modulation,body effect,and other capacitances are neglected.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.33Differential Pair This transfer function contains a zero and a pole.The magnitu
37、de of the zero is much greater than the pole.Common-mode disturbance at node P translates to a differential noise component at the output,if the supply voltage contains high-frequency noise and the circuit exhibits mismatches.Trade-off between voltage headroom and CMRR.Copyright 2017 McGraw-Hill Edu
38、cation.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.34Diff Pair Frequency response of differential pairs with high-impedance loads.Fig(b)CGD3 and CGD4 conduct equal and opposite currents to node G,making this node an ac ground.The dif
39、ferential half circuit is depicted in Fig.(c).More on chapter 10 Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.35Differential Pair with Active Load How many poles does this circuit have?The severe t
40、rade-off between gm and CGS of PMOS devices results in a pole that impacts the performance of the circuit.The pole associated with node E is called a“mirror pole.”Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill
41、 Education.36Active Load Replacing Vin,M1,and M2 by a Thevenin equivalent.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.37Active Load A zero with a magnitude of in the left half plane.The appearance
42、 of such a zero can be understood by noting that the circuit consists of a“slow path”(M1,M3 and M4)in parallel with a“fast path”(M1 and M2)by and Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.38Exam
43、ple Not all fully differential circuits are free from mirror poles.Estimate the low-frequency gain and the transfer function of this circuit.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.39Example M
44、5 multiplies the drain current of M3 by K.Assume RDCL is relatively small so that the Miller multiplication of CGD5 can be approximated as The overall transfer function is then equal toVx/Vin1 multiplied by Vout1/Vx.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribu
45、tion without the prior written consent of McGraw-Hill Education.40Gain-Bandwidth Trade-Offs We wish to maximize both the gain and the bandwidth of amplifiers.we are interested in both the 3-dB bandwidth,and the“unity-gain”bandwidth,Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduc
46、tion or distribution without the prior written consent of McGraw-Hill Education.41One pole circuit Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.42Multi-Pole Circuits It is possible to increase the
47、GBW product by cascading two or more gain stages.Assume the two stages are identical and neglect other capacitances.While raising the GBW product,cascading reduces the bandwidth.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent
48、 of McGraw-Hill Education.43Appendix A:Extra Element Theorem Suppose the transfer function of a circuit is known and denoted by H(s).Add an extra impedance Z1 between two nodes of the circuit.New transfer function:Particularly useful for frequency response analysis.Copyright 2017 McGraw-Hill Educati
49、on.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.44Example 1 Find the transfer function.The negative sign of Zout,0 does not imply a negative impedance between A and B,since Copyright 2017 McGraw-Hill Education.All rights reserved.No r
50、eproduction or distribution without the prior written consent of McGraw-Hill Education.45Example 2 Include CB,from node B to ground.Copyright 2017 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.46Appendix B:Zero-Va
