模拟集成电路的分析与设计：Chapter 9-Operational Amplifier.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,Operational Amplifier,Performance Parameters-gain(1),A,1,Question:,If the nominal,（标称）,gain(R,1,+R,2,)/R,2,=10,Determine the minimum value of A,1,for a gain error of 1%?,Operational Amplifier,Performance Parameters-gain(2),Solution:,Gain error:,Means that once the open-loop gain(A,1,)larger than 1000,the closed-loop gain always keeps constant value of 10,and with the error within 1%,Operational Amplifier,Performance Parameters-gain(3),If not use feedback system,Fig.9.3 can also obtain a gain of 10 by using a simple common-source stage.However,the typical gain error will be larger than 10%very easily because of the fabrication error.,Operational Amplifier,Performance Parameters-small-signal bandwidth(1),Small-signal Bandwidth:unity-gain frequency,f,u,f,3-dB,:3-dB frequency=dominant pole frequency f,0,(,bandwidth,),In a one-pole system(dominant pole of,0,),:,or,So,in a one-pole system,f,u,=GBW(gain-bandwidth),Although in multi-poles systems,f,u,GBW,GBW is still used to design the circuit.,Operational Amplifier,Performance Parameters-small-signal bandwidth(2),Question:,Assume the op amp is a single-pole voltage amplifier.If V,in,is a small step,calculate the time required for the output voltages to reach within 1%of its final value.What unity-gain bandwidth must the op amp provide if 1+R,1,/R,2,10 and the settling time is to be less than 5ns?For simplicity,assume the low-frequency gain is much greater than unity.,Operational Amplifier,Performance Parameters-small-signal bandwidth(3),Refer to Fig.8.9 in P.253:,Where:,If,A,0,1,then low frequency gain equal to,And the time constant,Back,Operational Amplifier,Performance Parameters-small-signal bandwidth(4),For a step input V,in,=a,u(t):,When t,the final output value,:,For 1%settling,V,out,=0.99V,F,and hence,For a 1%settling of 5ns,Unity gain-bandwidth,Operational Amplifier,Performance Parameters-Large-signal bandwidth,C,L,If C,L,is large,when V,in,change from 0 to 1V,V,out,cannot change instantaneously and still keep 0V,the signal feedback to negative input of A(s)is also 0V;,Therefore the differential input signal of A(s)will reach to 1V,if the gain of A(s)larger than 1000,then the output of A(s)will be larger than 1000V;,Large-signal,system non-linear,need to simulate carefully.,Operational Amplifier,Performance Parameters-others,Output swing;,Linearity;,Noise and offset;,Supply Rejection.,Operational Amplifier,One-stage Op Amps(1),Fig.9.6(a):Single-ended differential pair with active current mirror as load,this topology adds one mirror pole;,Fig 9.6(b):Fully differential pair;,For deep sub-micron technology,the gain usually hard to exceed 20.,Operational Amplifier,One-stage Op Amps(2),“Telescopic”cascode op amps can achieve high gain;,Output swing problem;,More severe when connected as unity gain(output-input shorting).,Operational Amplifier-,One-stage Op Amps(3),M,4,in saturation,V,out,V,b,-V,TH4,M,2,in saturation,Vout V,b,-V,GS4,+V,TH2,;,Output swing(,V,b,-V,GS4,+V,TH2,)-(V,b,-V,TH4,)=V,TH4,-(V,GS4,-V,TH2,),very small,so not suitable for unity-gain connection!,.,Overdrive voltage,Operational Amplifier,Telescopic cascode op amps design example(1),Specifications:,V,DD,=3V,Differential output swing=3 V,Power dissipation=10 mW,Voltage gain=2000,Other parameters(effective channel length=0.5,m):,n,C,ox,=60,A/V,2,p,C,ox,=30,A/V2,n,=0.1V,-1,p,=0.2V,-1,Voltage gain=2000,=0,V,THN,=|V,THP,|=0.7V,Operational Amplifier,Telescopic cascode op amps design example(2),First consider power P=10 mW,therefore the total current:,I=P/V,DD,=3.33mA,Allocating 3mA to M,9,and 330,A to M,b1,and M,b2,Second consider output swing:,Swing V,XY,=3V,SwingV,X,=SwingV,Y,=1.5V,V,DD,=3V,|V,OD7,|+|V,OD5,|+V,OD3,+V,OD1,+V,OD9,=1.5V,I,D9,largest,allocate V,OD9,=0.5V,P,n,V,ODP,should be larger than V,ODN,|V,OD7,|=|V,OD5,|=0.3V and V,OD3,=V,OD1,=0.2V,Operational Amplifier,Telescopic cascode op amps design example(3),Use initial bias guess,the W/L of all transistors can be calculated as:,(W/L),1-4,=1250,(W/L),5-8,=1111,(W/L),9,=400,Assuming all transistors minimum length of 0.5,m,Less than the required value of 2000,what shell we do?,Operational Amplifier,Telescopic cascode op amps design example(4),Since M,1,M,4,are in signal path,keep sizes unchanged first,therefore double the length of M,5,M,8,while keep their W/L unchanged:,(W/L),1-4,=1250(L,eff,=0.5,m),(W/L),5-8,=1111(L,eff,=1.0m),(W/L),9,=400,The gain can be re-calculated as,Operational Amplifier,Telescopic cascode op amps design example(5),The minimum input CM level equals:,V,GS1,+V,OD9,=V,OD1,+V,TH1,+V,OD9,=1.4V,The minimum value of V,b1,equals:,V,GS3,+V,OD1,+V,OD9,=1.6V,The maximum value of V,b2,equals:,V,DD,-(|V,GS5,|+|V,OD7,|)=1.7V,Some margin must be included in the value of V,b1,and V,b2,to allow for process variations,Body effect will increase the V,TH,Operational Amplifier,Folded cascode(1),Input transistor is replaced by the opposite type;,For small-signal,I,2,in Fig9.11(a),(suppose ideal current)can be seen as open,therefore M,1,and M,2,are still“stacked”,the circuit keeps high gain;,But for bias current,M,1,and M,2,are not“stacked”,solve the output swing problem and output-input shorting problem.,Operational Amplifier,Folded cascode(2),When used in differential pair,only replace NMOS input pair with PMOS input pair;,First drawback,:Additional currents are added for bias requirement,therefore the power is increased;,Operational Amplifier,Folded cascode(3),Use transistor to replace the current source in Fig9.12;,Output swing=,V,DD,-(V,OD3,+V,OD5,+|V,OD7,|+|V,OD9,|);,Less one overdrive voltage compare to Fig.9.10,Operational Amplifier,Folded cascode(4),Use half-circuit to calculate the gain of folded cascode op amp;,|A,v,|=G,m,R,out,Operational Amplifier,Folded cascode(5),The circuit of calculating G,m,;,i,D1,=I,out,+i,2,;,i,D1,i,2,(g,m3,+g,mb3,),-1,Operational Amplifier,Folded cascode(6),The circuit of calculating R,out,;,Where R,op,(g,m7,+g,mb7,)r,o7,r,o9,;,Therefore the gain can be obtained:,g,mp,g,mN,r,o1,r,o5,in parallel,Second drawback:,Gain of folded op amp is two to three times lower than that of telescopic cascode.,Operational Amplifier,Folded cascode(7),Third drawback,:the capacitance at the“folding point”(source of M,3,in Fig.9.13)is larger than that of telescopic cascode(also source of M,3,in Fig.9.10),and hence the pole at the“folding point”is quite closer to the origin than that of telescopic cascode,.,C,tot,=C,S3,+C,D1,C,tot,=C,S3,+C,D1,+C,D5,I,D5,is large,C,D5,is quite large!,Operational Amplifier,Folded cascode(8)-NMOS input pair,Use NMOS pair as input pair can increase the g,m1,and hence the gain of the folded-cascode,advantage!,;,But,since,N,fold-point,=1/(g,m3,p,+g,mb3,p,)(C,S3,+C,D1,+C,D5,P,);,While in,Fig.9.13,P,fold-point,=1/(g,m3,N,+g,mb3,N,)(C,S3,+C,D1,+C,D5,N,);,At same bias current,p,n,g,m,P,(W/L),N,C,D5,P,C,D5,N,Therefore,N,fold-point,P,fold-point,and hence f,N,fold-point,f,P,fold-point,drawback!,Operational Amplifier,Folded cascode(9)-Summary,The overall voltage swing of a folded-cascode op amp is only slightly higher than that of a telescopic cascode;,While many disadvantages:,Higher power dissipation;,Lower voltage gain;,Lower pole frequencies;,Higher noise.,But folded-cascode op amps are more popular than telescopic topologies,Why?,Because folded-cascode op amps got two other important advantages:,Input and output can be shorted together;,Choice of the input common-mode level is easier,can be close to one of the supply rails,for example NMOS input pair in Fig.9.16,V,in,(bias)can be high to V,DD,Operational Amplifier,Folded cascode(10)-Unity-gain connection,V,out,V,THN,+V,OD2,+V,OD11,V,out,I,D1,2,then M,3,and M,4,will enter into triode region in order to produce smaller current equal to I,D1,2,this will increase the CM level of output point(X or Y);,And if I,D3,4,I,D1,2,than M,5,will enter into triode region in order to produce smaller current equal to 2I,D3,4,this will decrease the CM level of output point(X or Y),Operational Amplifier,Common-Mode Feedback(2),As designed by example 9.5(page300),if M,10,and M,9,wholly match,then I,D9,=3 mA and I,D10,=300,A;,Now suppose M,9,suffers from a 1%current mismatch with respect to M,10,producing I,SS,=2.97 mA;,Assuming perfect matching for other transistors,what will happen in the circuit?,Operational Amplifier,Common-Mode Feedback(3),As calculated by example 9.5,the output impedance equals 266 k,;,I,D5,-I,D3,=30A/2=15 A;,Output voltage error would be 266,k,15 A=3.99 V;,Since this large error cannot be produced,V,X,and V,Y,must rise so much that M,5,M,8,enter the triode region in order to yield I,D7,8,=1.485 mA.,Operational Amplifier,Common-Mode Feedback(4),If some transistors enter triode region,then the gain of op amps is reduced and also distortion happens,;,CMFB is needed to keep the current of NMOS current source same as that of PMOS current source,in order to stabilize the output CM level,and hence the op amp gain.,Operational Amplifier,Common-Mode Feedback(5),How to perform the common-mode feedback?,Sensing the output CM level;,Comparing with a reference;,Returning error to the bias network of op amp.,Operational Amplifier,Common-Mode Feedback(6),Common-mode feedback control cascode load current source;,If R,1,=R,2,then V,out,CM,=(V,out1,CM,+V,out2,CM,)/2;,If V,out1,CM,and V,out2,CM,V,out,CM,V,E,I,D3,and I,D4,I,D5,I,D6,V,GS5,6,V,S5,6,V,out1,CM,and V,out2,CM,M,5,M,6,Operational Amplifier,Common-Mode Feedback(7),Common-mode feedback error control input pair tail current source;,If V,out1,CM,and V,out2,CM,V,out,CM,I,D1,and I,D2,I,D5,and I,D6,V,SG5,6,V,S5,6,V,out1,CM,and V,out2,CM,Operational Amplifier,Input Range Limitations(1),When the folded-cascode differential pair op amp is connected as unity-gain buffer,just as Fig.9.47 shown,the minimum input and output CM voltage V,in,min,V,out,min,=V,GS2,+V,ISS,approximately one V,TH,higher than the allowable minimum provided by M,5,M,8,;,Therefore,extending input range is very important!,Operational Amplifier,Input Range Limitations(2),When V,in,CM,is low,then PMOS pair work;,When V,in,CM,is high,then NMOS pair work;,Therefore,input range can be from 0V to V,DD,also called this,rail-to-rail,input.,Operational Amplifier,Input Range Limitations(3),The problem:G,m,tot,is not constant,and will affect the circuit gain stability;,How to improve?,Operational Amplifier,Input Range Limitations(4),Operational Amplifier,Input Range Limitations(5),Operational Amplifier,Input Range Limitations(6),Operational Amplifier,Input Range Limitations(7),Operational Amplifier,Input Range Limitations(8),G,m,tot,is equalized for all V,in,CM,range!,Operational Amplifier,Slew rate(1),A linear system:,Means that the slope of the step response is proportional to the final value of output;,If the input amplitude is doubled while other parameters remain constant,the output signal level must double at every point.,Operational Amplifier,Slew rate(2),In a linear op amp feedback system:,For small input step,the system acts like a linear system:,where,The slope is proportional to the final value,called“linear settling”.,Why?,Operational Amplifier,Slew rate(3),When input step is large enough,the output will ramp with a constant slope;,Under this condition,we say the op amp experiences slewing and call the slope of the ramp the“slew rate”(sometimes denoted as SR);,It is interesting that the“slew rate”is independent on the input step value.,Operational Amplifier,Slew rate(4),M,2,off,ignore the current flow into R,1,and R,2,Current I,SS,charge the load capacitance C,L,Slew rate of simple differential pair op amp during low-to-high transition;,Independent on input step!,Operational Amplifier,Slew rate(5),M,1,off,ignore the current flow into R,1,and R,2,discharge the load capacitance C,L,with current I,SS,.,Slew rate of simple differential pair op amp during high-to-low transition;,Operational Amplifier,Slew rate(6),Slew rate of cascode fully-differential pair op amp;,Operational Amplifier,Slew rate(7),Slew rate of folded-cascode differential pair op amp during low-to-high transition:,If I,P,I,SS,then:,Usually take I,P,I,SS.,Operational Amplifier,Slew rate(8),Slew rate of folded-cascode differential pair op amp during high-to-low transition:,If I,P,I,SS,then:,Usually take I,P,I,SS.,Operational Amplifier,Slew rate(9),If I,P,I,SS,then M,1,will enter triode and V,X,decreases,when M,2,turn on,V,X,experiences a swing and slow down the settling time.,Operational Amplifier,Slew rate(10),Two ways to improve:“clamp(,钳位,)”transistors are added to clamp voltage levels of V,X,and V,Y,.,clamped to each other,.,clamped to V,DD,.,Questions for Chap.9(1),(1)What are f,0,f,3-dB,f,u,?Tell us the relationship among them in a one-pole system.,(2)What will happen,when the op amp in Figure 9.9 connected as unity gain,.,Questions for Chap.9(2),(3)Describe the disadvantages and advantages of folded-cascode op amp comparing to telescopic op amp.,(4)Why do we use two-stage op amp?,(5)Write the gain of the circuit in Figure 9.25.What are the advantages and disadvantages of gain boosting technique as shown in Figure 9.25?,Questions for Chap.9(3),(6)Compare the performance of various op amps in short telescopic,folded-cascode,two-stage,gain-boosting.,(7)Describe the principle of the CMFB circuit shown in Figure 9.39.,Questions for Chap.9(4),(8)What is the circuit in Figure 9.48 used for?How does it work?,Questions for Chap.9(5),(9)Explain the“,Slew rate,”.,(10)Write,SR,of the circuit in Figure 9.55.,Questions for Chap.9(6),(11)Q 9.3;,(12)Example 9.10(page 329);,(13)Q9.4(a)(d),not do(e);,(14)Q9.8;,(15)Q9.14;,