Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-1 LECTURE 250 – SIMULATION AND MEASUREMENT OF OP AMPS LECTURE ORGANIZATION Outline • Introduction • Open Loop Gain • CMRR and PSRR • A general method of measuring Avd, CMRR, and PSRR • Other op amp measurements • Simulation of a Two-Stage Op Amp • Op amp macromodels • Summary CMOS Analog Circuit Design, 2nd Edition Reference Pages 310-341 CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-2 INTRODUCTION Simulation and Measurement Considerations Objectives: • The objective of simulation is to verify and optimize the design. • The objective of measurement is to experimentally confirm the specifications. Similarity between Simulation and Measurement: • Same goals • Same approach or technique Differences between Simulation and Measurement: • Simulation can idealize a circuit - All transistor electrical parameters are ideally matched - Ideal stimuli • Measurement must consider all nonidealities - Physical and electrical parameter mismatches - Nonideal stimuli - Parasistics CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-3 OPEN LOOP GAIN Simulating or Measuring the Open-Loop Transfer Function of the Op Amp Circuit (Darkened op amp identifies the op amp under test): Simulation: VDD vIN +VOS vOUT This circuit will give the voltage transfer function curve. This curve should identify: 1.) The linear range of operation RL CL VSS 2.) The gain in the linear range 3.) The output limits Fig. 240-01 4.) The systematic input offset voltage 5.) DC operating conditions, power dissipation 6.) When biased in the linear range, the small-signal frequency response can be obtained 7.) From the open-loop frequency response, the phase margin can be obtained (F = 1) Measurement: This circuit probably will not work unless the op amp gain is very low. CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-4 A More Robust Method of Measuring the Open-Loop Frequency Response Circuit: vOUT vIN C CL R RL VDD VSS Fig. 240-02 Resulting Closed-Loop Frequency Response: dB Op Amp Open Loop Frequency Response Av(0) 0dB 1 RC Av(0) RC log10(w) Fig. 240-03 Make the RC product as large as possible. CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-5 CMRR AND PSRR Simulation of the Common-Mode Voltage Gain V + OS- VDD vout + vcm - CL VSS RL Fig. 6.6-5 Make sure that the output voltage of the op amp is in the linear region. Divide (subtract dB) the result into the open-loop gain to get CMRR. CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-6 Simulation of CMRR of an Op Amp None of the above methods are really suitable for simulation of CMRR. Consider the following: Vcm V2 Vcm VDD V2 - Vout V1 V1 + VSS Vcm Av(V1-V2) Vcm Vout ±AcVcm Fig. 6.6-7 cm V 1+V2 V out = Av (V1-V 2) ±A 2 = -AvV out ± AcmV cm ±Acm ±Acm V out = 1+Av Vcm Av Vcm Av V cm |CMRR|=Acm=V out CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-7 Direct Simulation of PSRR Circuit: Vdd V2 V2 - V1 + Av(V1-V2) VDD V1 VSS Vss Vout Vss = 0 ±AddVdd Fig. 6.6-9 V out = Av (V1-V 2) ±AddV dd = -AvV out ± AddV dd ±Add ±Add V out = 1+Av Vdd Av Vdd Av V dd Av V ss PSRR+=Add=V out and PSRR-=Ass=V out Works well as long as CMRR is much greater than 1. CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-8 A GENERAL METHOD OF MEASURING AVD, CMRR, AND PSRR General Principle of the Measurement Circuit: 100kΩ vOS 100kΩ vSET 100kΩ 10kΩ 100kΩ - vOUT VDD + 10Ω "Op Amp" + "Op Amp" vI - vSET vOUT = -vSET CL RL VSS 070429-01 The amplifier under test is shown as the darkened op amp. Principle: Apply the stimulus to the output of the op amp under test and see how the input responds. Note that: vOS vOUT = - vSET and vI 1000 CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-9 Measurement of Open-Loop Gain Measurement configuration: + - Vos 100kΩ 100kΩ Vout 10kΩ Vout VDD + 10Ω V i V out V out CL RL VSS Avd = V id = V i 060701-01 V os 1000Vi 1000Vout Therefore, Avd = V os Sweep Vout as a function of frequency, invert the result and multiply by 1000 to get Avd(j). CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) 100kΩ + - Measurement of CMRR Measurement Configuration: Note that the whole amplifier is stimulated by vos V icm while the input responds to this change. The definition of the common-mode rejection 10kΩ ratio is (vout/vid) Avd CMRR = Acm = (vout/vicm) + 10Ω vi However, in the above circuit the value of vout is the same so that we get vicm CMRR = vid vos But vid = vi and vos 1000vi = 1000vid vid = 1000 Page 250-10 vicm 100kΩ vOUT VDD vicm CL RL VSS Fig. 240-08 vicm 1000vicm CMRR = vos = vos 1000 Make a frequency sweep of Vicm, invert the result and multiply by 1000 to get CMRR. Substituting in the previous expression gives, CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-11 Measurement of PSRR Measurement Configuration: The definition of the positive power supply rejection ratio is (Vout/V id) Avd + PSRR = Acm = (Vout/V dd) However, in the above circuit the value of Vout is the same so that we get V dd PSRR+ = V id But Vid = Vi and Vos 1000Vi = 1000Vid V id = V os 1000 Substituting in the previous expression gives, 100kΩ Vos 100kΩ Vdd 10kΩ Vout VDD + 10Ω Vi CL - RL Vss VSS 070429-02 V dd 1000Vdd PSRR+ = V = V os os 1000 Make a frequency sweep of Vdd, invert the result and multiply by 1000 to get PSRR+. (Same procedure holds for PSRR-.) CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-12 OTHER OP AMP MEASUREMENTS Simulation or Measurement of ICMR vOUT IDD vOUT VDD 1 1 vIN + vIN - ISS CL RL VSS ICMR Also, monitor IDD or ISS. Fig.240-11 Initial jump in sweep is due to the turn-on of M5. Should also plot the current in the input stage (or the power supply current). CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-13 Measurement or Simulation of Slew Rate and Settling Time Volts Peak Overshoot vin IDD vout Settling Error Tolerance VDD +SR -SR + vin - CL RL 1 VSS vout 1 t Settling Time Feedthrough Fig. 240-14 If the slew rate influences the small signal response, then make the input step size small enough to avoid slew rate (i.e. less than 0.5V for MOS). CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-14 Phase Margin and Peak Overshoot Relationship It can be shown (Appendix C of the text) that: 100 20 60 10 50 5 Phase Margin 40 Overshoot 30 Overshoot (%) For example, a 5% overshoot corresponds to a phase margin of approximately 64°. Phase Margin (Degrees) Phase Margin (Degrees) = 57.2958cos-1[ 44+1 - 22] Overshoot (%) 80 - = 100 exp 70 1-2 1.0 20 10 0 CMOS Analog Circuit Design 0 0.2 0.4 ζ= 1 2Q 0.6 0.8 1 0.1 070429-03 © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-15 SIMULATION OF A TWO-STAGE CMOS OP AMP Example 250-1 Simulation of a Two-Stage CMOS Op Amp An op amp designed using the procedure described in Lecture 230 is to be simulated by SPICE. The device parameters to be used are those of Tables 3.1-2 and 3.2-1 of the textbook CMOS Analog Circuit Design. 15μm 1μm M3 VDD = 2.5V M4 15μm 1μm M6 Cc = 3pF 30μA 4.5μm 1μm M1 vin + 3μm 1μm 3μm 1μm vout M2 95μA 30μA M8 4.5μm M5 1μm VSS = -2.5V 94μm 1μm M7 CL = 10pF 14μm 1μm Fig. 240-16 The specifications of this op amp are as follows where the channel length is to be 1μm and the load capacitor is CL = 10pF: Av > 3000V/V V DD = 2.5V V SS = -2.5V GB = 5MHz SR > 10V/μs 60° phase margin V out range = ±2V ICMR = -1 to 2V Pdiss 2mW CMOS Analog Circuit Design Lecture 250 – Measurement and Simulation of Op amps (3/28/10) © P.E. Allen - 2010 Page 250-16 Example 250-1 – Continued Bulk Capacitance Calculation: If the values of the area and perimeter of the drain and source of each transistor are known, then the simulator will calculate the values of CBD and C Bs. Since there is no layout yet, we estimate the values of the area and perimeter of the drain and source of each transistor as: AS = AD W[L1 + L2 + L3] PS = PD 2W + 2[L1 + L2 + L3] where L1 is the minimum allowable distance between the polysilicon and a contact in the moat (2μm), L2 is the length of a minimum-size square contact to moat (2μm), and L3 is the minimum allowable distance between a contact to moat and the edge of the moat (2μm). (These values will be found from the physical design rules for the technology). For example consider M1: AS = AD = (3μm)x(2μm+2μm+2μm) = 18μm2 PS = PD = 2x3μm + 2x6μm = 19μm CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-17 Example 250-1 - Continued Op Amp Subcircuit: - 2 vin + 1 - 8 VDD 6 vout + 9 VSS Fig. 240-17 .SUBCKT OPAMP 1 2 6 8 9 M1 4 2 3 3 NMOS1 W=3U L=1U AD=18P AS=18P PD=18U PS=18U M2 5 1 3 3 NMOS1 W=3U L=1U AD=18P AS=18P PD=18U PS=18U M3 4 4 8 8 PMOS1 W=15U L=1U AD=90P AS=90P PD=42U PS=42U M4 5 4 8 8 PMOS1 W=15U L=1U AD=90P AS=90P PD=42U PS=42U M5 3 7 9 9 NMOS1 W=4.5U L=1U AD=27P AS=27P PD=21U PS=21U M6 6 5 8 8 PMOS1 W=94U L=1U AD=564P AS=564P PD=200U PS=200U M7 6 7 9 9 NMOS1 W=14U L=1U AD=84P AS=84P PD=40U PS=40U M8 7 7 9 9 NMOS1 W=4.5U L=1U AD=27P AS=27P PD=21U PS=21U CC 5 6 3.0P .MODEL NMOS1 NMOS VTO=0.70 KP=110U GAMMA=0.4 LAMBDA=0.04 PHI=0.7 +MJ=0.5 MJSW=0.38 CGBO=700P CGSO=220P CGDO=220P CJ=770U CJSW=380P +LD=0.016U TOX=14N .MODEL PMOS1 PMOS VTO=-0.7 KP=50U GAMMA=0..57 LAMBDA=0.05 PHI=0.8 +MJ=0.5 MJSW=.35 CGBO=700P CGSO=220P CGDO=220P CJ=560U CJSW=350P +LD=0.014U TOX=14N IBIAS 8 7 30U .ENDS CMOS Analog Circuit Design Lecture 250 – Measurement and Simulation of Op amps (3/28/10) © P.E. Allen - 2010 Page 250-18 Example 250-1 - Continued PSPICE Input File for the Open-Loop Configuration: EXAMPLE 250-1 OPEN LOOP CONFIGURATION .OPTION LIMPTS=1000 VIN+ 1 0 DC 0 AC 1.0 VDD 4 0 DC 2.5 VSS 0 5 DC 2.5 VIN - 2 0 DC 0 CL 3 0 10P X1 1 2 3 4 5 OPAMP .. . (Subcircuit of previous slide) .. . .OP .TF V(3) VIN+ .DC VIN+ -0.005 0.005 100U .PRINT DC V(3) .AC DEC 10 1 10MEG .PRINT AC VDB(3) VP(3) .PROBE (This entry is unique to PSPICE) .END CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-19 Example 250-1 - Continued Open-loop transfer characteristic: 2.5 2 VOS vOUT(V) 1 0 -1 -2 -2.5 -2 -1.5 -1.0 -0.5 0 0.5 vIN(mV) 1 1.5 2 Fig. 240-18 CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-20 Example 250-1 - Continued Open-loop transfer frequency response: 200 80 150 Phase Shift (Degrees) Magnitude (dB) 60 40 20 0 100 50 0 -50 -100 -20 -150 GB -40 Phase Margin GB -200 10 100 1000 CMOS Analog Circuit Design 105 106 104 Frequency (Hz) 107 108 10 100 1000 104 105 106 Frequency (Hz) 107 108 Fig. 6.6-16 © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-21 Example 250-1 - Continued Input common mode range: - 3 Subckt. + 1 3 vout 5 vin VSS Fig. 6.6-16A 40 ID(M5) 30 20 Input CMR vOUT (V) -3 Note the usefulness of monitoring the current in the input stage to determine the lower limit of the ICMR. VDD 10 ID(M5) μA EXAMPLE 250-1 UNITY GAIN CONFIGURATION. .OPTION LIMPTS=501 VIN+ 1 0 PWL(0 -2 10N -2 20N 2 2U 2 2.01U -2 4U -2 4.01U + -.1 6U -.1 6.0 1U .1 8U .1 8.01U -.1 10U -.1) VDD 4 0 DC 2.5 AC 1.0 VSS 0 5 DC 2.5 CL 3 0 20P X1 1 3 3 4 5 OPAMP 4 .. . 3 (Subcircuit of Table 6.6-1) .. . 2 .DC VIN+ -2.5 2.5 0.1 .PRINT DC V(3) 1 .TRAN 0.05U 10U 0 10N .PRINT TRAN V(3) V(1) 0 .AC DEC 10 1 10MEG -1 .PRINT AC VDB(3) VP(3) .PROBE (This entry is unique to PSPICE) -2 .END 4 0 -3 -2 -1 0 vIN(V) CMOS Analog Circuit Design 1 2 3 Fig. 240-21 © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-22 Example 250-1 - Continued Positive PSRR: 100 100 Arg[PSRR+(jω)] (Degrees) |PSRR+(jω)| dB 80 60 40 20 0 -20 10 100 1000 104 105 106 Frequency (Hz) 107 108 50 0 -50 -100 10 100 1000 104 105 106 Frequency (Hz) 107 10 Fig. 240-22 This PSRR+ is poor because of the Miller capacitor. The degree of PSRR+ deterioration will be better shown when compared with the PSRR-. CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-23 Example 250-1 - Continued Negative PSRR: 200 120 Arg[PSRR-(jω)] (Degrees) 150 |PSRR-(jω)| dB 100 80 60 PSRR+ 40 20 10 100 50 0 -50 -100 -150 -200 100 1000 104 105 106 Frequency (Hz) 107 108 10 100 1000 104 105 106 Frequency (Hz) CMOS Analog Circuit Design 107 108 Fig. 240-23 © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-24 Example 250-1 - Continued Large-signal and small-signal transient response: 1.5 0.15 1 0.1 0.05 vout(t) Volts Volts 0.5 vin(t) 0 -0.5 vout(t) 0 -0.05 vin(t) -1 -0.1 -1.5 -0.15 0 1 2 3 Time (Microseconds) 4 5 2.5 3.0 Why the negative overshoot on the slew rate? If M7 cannot sink sufficient current then the output stage slews and only responds to changes at the output via the feedback path which involves a delay. Note that -dvout/dt -2V/0.3μs = -6.67V/μs. For a 10pF capacitor this requires 66.7μA and only 95μA-66.7μA = 28μA is available for Cc. For the positive slew rate, M6 can provide whatever current is required by the capacitors and can immediately respond to changes at the output. CMOS Analog Circuit Design 3.5 4.0 Time (Microseconds) 4.5 Fig. 240-24 VDD M6 Cc iCc iCL dvout dt CL 95μA + VBias - vout M7 VSS Fig. 240-25 © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-25 Example 250-1 - Continued Comparison of the Simulation Results with the Specifications of Example 250-1: Specification (Power supply = ±2.5V) Open Loop Gain GB (MHz) Input CMR (Volts) Slew Rate (V/μsec) Pdiss (mW) Vout range (V) PSRR+ (0) (dB) PSRR- (0) (dB) Phase margin (degrees) Output Resistance (k) Design Simulation >5000 5 MHz -1V to 2V >10 (V/μsec) < 2mW ±2V 60° - 10,000 5 MHz -1.2 V to 2.4 V, +10, -7(V/μsec) 0.625mW +2.3V, -2.2V 87 106 65° 122.5k CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Relative Overshoots of Ex. 250-1 Why is the negative-going overshoot larger than the positive-going overshoot on the small-signal transient response of the last slide? Consider the following circuit and waveform: Page 250-26 VDD = 2.5V 94/1 M6 i6 iCc iCL 0.1V t vout Cc 95μA CL -0.1V VBias M7 0.1μs 0.1μs Fig. 240-26 VSS = -2.5V During the rise time, iCL = CL(dvout/dt )= 10pF(0.2V/0.1μs) = 20μA and iCc = 3pf(2V/μs) = 6μA i6 = 95μA + 20μA + 6μA = 121μA gm6 = 1066μS (nominal was 942.5μS) During the fall time, iCL = CL(-dvout/dt) = 10pF(-0.2V/0.1μs) = -20μA and iCc = -3pf(2V/μs) = -6μA i6 = 95μA - 20μA - 6μA = 69μA gm6 = 805μS The dominant pole is p1 (RIgm6RIICc)-1 but the GB is gmI/Cc = 94.25μS/3pF = 31.42x106 rads/sec and stays constant. Thus we must look elsewhere for the reason. Recall that p2 gm6/CL which explains the difference. p2(95μA) = 94.25x106 rads/sec, p2(121μA) = 106.6 x106 rads/sec, and p2(69μA) = 80.05 x106 rads/sec. Thus, the phase margin is less during the fall time than the rise time. CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-27 OP AMP MACROMODELS What is a Macromodel? A macromodel uses resistors, capacitors, inductors, controlled sources, and some active devices (mostly diodes) to capture the essence of the performance of a complex circuit like an op amp without modeling every internal component of the op amp. Small Signal, Frequency Independent Op Amp Macromodel v1 v1 1 vo A 3 v1 Ro v o 1 4 R id Avd (v 1 -v 2 ) 2 2 v2 (a.) Avd (v -v ) 1 2 Ro R id v2 v2 3 (b.) (c.) vo Ro Fig. 010-01 Figure 1 - (a.) Op amp symbol. (b.) Thevenin form. (c.) Norton form. 1 Ric1 3 Rid Avd(v1 -v2 ) Ro 2 Avc v1 2Ro + Avc v2 2Ro Ro vo - Ric2 Linear Op Amp Macromodel Fig. 010-03 Figure 2 - Simple op amp model including differential and common mode behavior. CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-28 Small Signal, Frequency Dependent Op Amp Macromodel Avd(0) 1 Avd(s) = (s/1)+1 where 1= R1C1 (dominant pole) Model Using Passive Components: v1 3 1 vo Rid v2 2 Avd(0) (v1 -v2 ) R1 R1 C1 Fig. 010-04 Figure 3 - Macromodel for the op amp including the frequency response of Avd. Model Using Passive Components with Constant Output Resistance: v1 1 3 Rid v2 2 Avd(0) (v1 -v2 ) R1 R1 4 C1 v3 Ro vo Ro Fig. 010-05 Figure 4 - Frequency dependent model with constant output resistance. CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-29 Large Signal, Frequency Independent Op Amp Macromodel RLIM 1 Ric1 VIH1 Ric2 + 6 VIL1 - 7 + D4 8 - VIL2 + 9 3 Rid Avc v4 2Ro 5 D3 + VIH2 Nonlinear Op Amp Macromodel D2 D1 RLIM 2 4 Avc v5 2Ro + D5 Ro Avd (v -v ) Ro 4 5 VOH D6 + 10 + 11 vo VOL - Fig. 010-10 Figure 5 - Op amp macromodel that limits the input and output voltages. Io ILimit 2 v1 Io 2 Io 2 D1 D3 D2 ILimit D4 1 Io Rid 2 ILimit 2 Io 2 D3 4 v2 Io 2 Fig. 010-12 D4 Ro Avd (v -v ) Ro 1 2 5 D1 3 D5 + D2 VOH ILimit 6 D6 7 - VOL + vo 8 - Fig. 010-13 Figure 6 – Technique for current limiting and a macromodel for output voltage and current limiting. CMOS Analog Circuit Design © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-30 Large Signal, Frequency Dependent Op Amp Macromodel Slew Rate: dvo ±ISR dt = C1 = Slew Rate v1 6 1 v2 2 Avd(0) (v1 -v2 ) R1 3 5 C1 R1 D1 D3 4 Rid v4 -v5 Ro D2 D4 ISR 7 vo Ro Fig. 010-15 Figure 7 – Slew rate macromodel for an op amp. Results for a unity gain op amp in slew: 10V 5V Output Voltage 0V -5V -10V 0μs CMOS Analog Circuit Design Input Voltage 2μs 4μs Time 6μs 8μs 10μs Fig. 010-16 © P.E. Allen - 2010 Lecture 250 – Measurement and Simulation of Op amps (3/28/10) Page 250-31 SUMMARY • Simulation and measurement of op amps has both similarities and differences • Measurement of open loop gain is very challenging – the key is to keep the quiescent point output of the op amp well defined • The method of stimulating the output of the op amp or power supplies and letting the input respond results in a robust method of measuring open loop gain, CMRR, and PSRR • Carefully investigate any deviations or aberrations from expected behavior in the simulation and experimental results • Macromodels are useful for modeling the op amp without including every individual transistor CMOS Analog Circuit Design © P.E. Allen - 2010