1、Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Chapter 9: Operational Amplifiers9.1 General Considerations9.2 One-Stage Op Amps9.3 Two-Stage Op Amps9.4 Gain Boosting9.5 Comparison9.6 Output Swing9
2、.7 Common Feedback 9.8 Input Range Limitations9.9 Slew Rate9.10 High-Slew-Rate Op Amps9.11 Power Supply Rejection9.12 Noise in Op Amps Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 2Op Amp Defini
3、tion We loosely define an op amp as a “high-gain differential amplifier.” Usually employed in a feedback system when precision is a requirement. Applications ranging from DC generation, high-speed amplification or filtering. Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction
4、or distribution without the prior written consent of McGraw-Hill Education. 3Op Amp Design ChallengeThree decades ago General-purpose blocks as an “ideal” op amp Design effort is to satisfy an ideal op amp - infinite gain - infinite input impedance - zero output impedanceToday Design effort is to ma
5、ke trade-offs for a specific application, often sacrificing the unimportant aspects to improve the critical ones. E.g., gain error vs speed, open loop gain vs VDD Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hi
6、ll Education. 4Performance Parameter Gain(Precision), Bandwidth(Speed): 3-dB/fu Output Swing, Power dissipation Noise, Linearity, Supply Rejection, offset Input CM Range, Input/Output Impedance Large-Signal behavior (e.g. slew rate) Copyright 2017 McGraw-Hill Education. All rights reserved. No repro
7、duction or distribution without the prior written consent of McGraw-Hill Education. 5Example 9.1The circuit has a nominal gain of 10. i.e.,1+R1/R2=10.Determine the minimal value of A1 for a gain error 1%:Thus, A11000. Open-loop gain determines precision. Solution: Copyright 2017 McGraw-Hill Educatio
8、n. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 6Example 9.2Assume the op amp is a single-pole voltage amplifier. For a small step input, calculate the time required for theoutput to reach within 1% and its unity-gain bandwidth if 1
9、+R1/R2=10 and its settling time is less than 5ns.Speed vs. BandwidthSolution: Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 7Example 9.3Explain the circuit behavior if we swap the inverting and n
10、on-inverting inputs of the op amp.Solution: Positive feedback destabilizes the circuit.Output grows exponentially to non-linearity range. Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 8One-Stage
11、Op Amps Low-frequency gain: Bandwidth: usually proportional to 1/(CL*Rout) Output Swing (single-side): VDD-3Overdrive Mirror pole in single-ended circuit Power and noise: good, with four devices - input noise Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution
12、without the prior written consent of McGraw-Hill Education. 9Example 9.4Calculate the input common-mode voltage range and theclosed-loop output impedance of the unity-gain buffer.Solution:VinCascode_NInput_N Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution w
13、ithout the prior written consent of McGraw-Hill Education. 14Linear Scaling How to modify design if power budget is different while all the other specifications are the same? Only scale the widths of all the transistors while keeping the lengths constant.Example 9.6Explain what aspects of the perfor
14、mance degrade for a low-power op amp design when we scale down the transistor width.Solution:(1) The speed of the op amp in driving a capacitive load(2) The input-referred noise voltage rises by a square root factor of scale constant. (for input device) Copyright 2017 McGraw-Hill Education. All righ
15、ts reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Gate Bias Voltage Generation Ensure bias voltage to track the input CM level Choose Mb1 to be a narrow, long, “weak” device 15 Copyright 2017 McGraw-Hill Education. All rights reserved. No reprod
16、uction or distribution without the prior written consent of McGraw-Hill Education. 16Folded Cascode Op AmpsRecall Folded Cascode Not “stack” the cascode transistor on the input device Consume higher power Output Voltage Swing: VDD-4overdrive Output and input could short together Copyright 2017 McGra
17、w-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 17Folded Cascode Voltage Gain Since 2000 Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
18、McGraw-Hill Education. 26Gain Boosting Increase the output impedance without adding more cascode devices. But how? A transistor preceded by an ideal voltage amplifier exhibits a transconductance of gmA1 and a output resistance of ro. Copyright 2017 McGraw-Hill Education. All rights reserved. No repr
19、oduction or distribution without the prior written consent of McGraw-Hill Education. 27Gain Boosting Increase the output impedance without adding more cascade devices. But how? First Perspective: A degenerated transistor preceded by an ideal voltage amplifierIn fact, the output resistance is “booste
20、d. The headroom is similar to a simple degenerated transistor Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 28Example 9.11Determine the resistance seen at the source of M2 without considering bod
21、y effect.Solution: Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 29Basic gain-boosted stage Current-Voltage feedback increase the output impedance by a factor of A1+1, while the real gm raised by
22、 A1 is reduced by A1+1 when feedback is applied.- Rout:- Gm: gm1A1/(A1+1)gm1- Rp:(look above P, see example 9.11) (ro1, can be neglected)- Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 30 Regulat
23、ed CascodeSecond Perspective Loosely view the voltage change divided by Rs and gmroRs. Drain current response can be suppressed as - Vp is constant - Current through Rs is constant Vp is “pinned” to Vb by feedback regulation. Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction
24、 or distribution without the prior written consent of McGraw-Hill Education. 31Example 9.12 Determine the small-signal values of and . Assume is large.Solution: Current circulates M2 Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
25、consent of McGraw-Hill Education. 32 Gain boosting Key The amplifier boosts the gm of the cascode device The amplifier regulates the output current by monitoring and pinning the source voltage Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prio
26、r written consent of McGraw-Hill Education. 33 Gain Boosting Circuit Implementation Simplest a common-source stage Avoid headroom limitation, PMOS common-source stage is better, but M3 could go in triode Folded-cascode inserts one more stage Copyright 2017 McGraw-Hill Education. All rights reserved.
27、 No reproduction or distribution without the prior written consent of McGraw-Hill Education. 34Example 9.13Determine the allowable range for Vb.Solution: Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Educat
28、ion. 35 Gain Boosting with a Differential Pair One threshold higher than a simple differential circuit Merge two gain boosting blocks to differential one Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Educat
29、ion. 36 Differential Folded Cascode Gain Boosting The minimal allowable Vx,Vy is VOD12+VISS1 The output impedance of the circuit (Example 9.14) Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 37Gai
30、n Boosting in Signal Path and Load Gain boosting can be utilized in the load current source To allow maximum swings, A2 employs NMOS-input. Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 38Gain Bo
31、osting Frequency Response Zero: Dominant pole: Non-dominant pole: Above the original-3dB bandwidth Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 39Frequency Response Bode Plot Gain boosting frequ
32、ency response bode plot Two poles, non-dominant is below the original 3dB pole Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 40Example 9.15Is the dominant-pole approximation valid here.Solution:T
33、he second term is typically much greater than unity and the approximation is valid. Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 41Comparison Copyright 2017 McGraw-Hill Education. All rights res
34、erved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 42Output Swing Calculation Be careful about distortion and gain error The maximum output amplitude that yields an acceptable distortion or gain error Apply a growing sinusoid wave, monitor the resultin
35、g output, and calculate the maximum allowable gain Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 43Common-Mode Feed Back Vcm(in) and Vcm(out): Copyright 2017 McGraw-Hill Education. All rights res
36、erved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 44Basic Concepts In fully-differential op amps, the output CM level is usually not well defined. - Case 1: , Vx,Vy decreases, Iss triode; - Case 2: In reverse, Vx,Vy increases, M3,M4 triode. Copyright
37、2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 45Basic Concepts In high-gain amplifiers, CMFB balances the PMOS and NMOS current mismatches, thus avoid driving one of them into triode region. Differential f
38、eedback cannot define CM level In simulation, CM may be well-defined around half VDD, yet in real world, random mismatches and device variations would degrade CM easily without CMFB. Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
39、consent of McGraw-Hill Education. 46Example 9.16Consider the telescopic op amp below. Suppose M9 suffers from a 1% current mismatch with respect to M10, producing Iss = 2.97 mA rather than 3 mA. Assuming perfect matching for the others. Explain what happens in the circuit.Solution:Output voltage err
40、or: =3.99VVx, Vy must rise so much that M5, M6, M7, M8 go to triode,yielding ID7 = 1.485 mA.Current mismatch is largelydepended on different drain-source voltage. Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hi
41、ll Education. 47 Conceptual topology Measure output CM level; Compare with a reference; Apply the error to correct the level. Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 48 CM Sensing Technique
42、s Resistive sensing - large R1,R2 to avoid loading effect - large chip area and parasitic capacitance - reduce frequency performance Source follower sensing - lose one Vth in swing - large R1, I1 to avoid “starved” Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distrib
43、ution without the prior written consent of McGraw-Hill Education. 49 CM Sensing Techniques Capacitive sensing-Switched-capacitor Deep triode sensing- Rtot vout1+vout2- Rtot has no relationshipwith differential voltage- may go to saturation region Copyright 2017 McGraw-Hill Education. All rights rese
44、rved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 50Example 9.17A student simulates the step response of a closed-loop op amp circuit and observes the output waveforms shown in below. Explain why Vout1 and Vout2 do not change symmetrically.Solution:As
45、evident from waveforms, the output CM levels change from t1 to t2, indicating CM sensing mechanism is nonlinear. For example, if M7 or M8 in last slide does not indeep triode at t2, the CM level would change because now it is a function of differential output. Copyright 2017 McGraw-Hill Education. A
46、ll rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 51 CM Sensing Techniques Differential pair sensing - by small signal analysis - Under Large swings situation, sensing is not valid due to large non-linearity. Copyright 2017 McGraw-Hill Ed
47、ucation. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 52 CM Feedback Techniques Control cascade current source Control tail current source Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution wi
48、thout the prior written consent of McGraw-Hill Education. 53 CM Feedback Techniques Deep triode sensing feedback - Limited headroom - Large C - Device variation Deep triode folded-cascade sensing feedback Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution with
49、out the prior written consent of McGraw-Hill Education. 54Example 9.18Determine the sensitivity of Vout,CM to Vb, i.e, dVout,CM/dVb.Solution:CMFB small signal analysis Maximize Vds7,8 for Sensitivity Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without t
50、he prior written consent of McGraw-Hill Education. 55 CM Feedback Techniques Modification of deep triode sensing feedback The output level is relatively independent of device parameters and lowers sensitivity of Vb Copyright 2017 McGraw-Hill Education. All rights reserved. No reproduction or distrib
