Stability for Op Amps

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难军穆
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1 R ISO CF Tim Green Electrical Engineering R ISO CF CF Output Pin Compensation R ISO Tina SPICE Tina SPICE V OUT V IN AC Tina SPICE (Transient Real World Stability Test)23 R O /40V OPA452 (piezo actuator) 6.1 AC R O R O Analog & RF Models ( W. K. Sands SPICE Tina SPICE R O W. K. Sands SPICE OPA452 Supply: /10V to /40V Slew Rate: 7.2V/us, 10V/us Vout Saturation: Io=50mA, (V)5V, (V)5.5V Io=10mA, (V)2V, (V)2V 6.1OPA542 R O 6.2 OPA452 operating point R OUT R OUT = R O R O R OUT 3 R O Test Point R ISO CF Tim Green

4 AC VT U1 U2U1 U2 SPICE R O =28.67 6.3 R O OPA452 R O =28.7 R2 1M R12 1M VO1 = 17.22mV rms VO2 = 16.

2 6.2 R O OPA542 Aol Tina SPICE R O 6.3 SPICE 100AC C1 R3 R OUT R O R O R2 100k R1 1k U1 OPA452 V2 40 FLAG V1 40 R4 40k = 19.73mV rms C1 10u R3 1k A AM1 AM1 = uA RO = / AM1 RO = 19.73mV / uA RO = ohms VT 1MHz 1Vp 6.3Tina SPICE R O 1 3 R O R O R O 6.4 AC VT U1 U2U1 U2 SPICE R O = R O OPA452 R O =28.7 R2 1M R12 1M VO1 = 17.22mV rms VO2 = 16.74mV rms R1 10k V2 40 VOUT R11 10k V12 40 VOUTL U1 OPA452 FLAG U2 OPA452 FLAG RL 1k VT 1MHz 10mVp V1 40 R4 40k V11 40 R14 40k RO = [RL(VOUT VOUTL)] / VOUTL RO = [1k (17.22mV 16.74mV)] / 16.74mV RO = ohms R ISO CF Tim Green

3 Aol 6.4Tina SPICE R O 2 Aol 6.5 Aol R O CL R O Aol Aol 6.6 RI RF 100kΩ 100kΩ OPA452 R O Extra Pole in Aol Plot due to R O & CL: fpo1 = 1/(2 П R O CL) 28.7Ω Data Sheet Aol V OUT CL 1µF fpo1 = 1/(2 П 28.7Ω 1µF) fpo1 = 5.545kHz V IN Create a new Modified Aol Plot 6.5 CL Aol 6.6 Aol 1β Aol 40dBdecade OPA452 Aol STABLE fpo1 40dB/Decade RateOfClosure 1/β fcl Modified Aol due to CL R ISO CF Tim Green K 10K 100k 1M 10M

4 6.6 CL OPA452 Aol Tina SPICE 6.7 AC CL R O Aol RF 100k VFB RI 100k LT 1G CT 1G VT VM U1 OPA452 V2 40 FLAG V1 40 Aol = / VM Loop Gain = VFB / VM R4 40k CL 1u 6.7Tina SPICE CL Aol 6.8 Aol 5.6kHZ CL 5.45kHz Magnitude (db) Modified Aol Magnitude a Magnitude : Aol A:(5.6k; 50.47) Phase : Aol A:(5.6k; 45.01) Phase (Degrees) Modified Aol Phase R ISO CF Tim Green 18

5 6.8Tina SPICE CL Aol 6.9 fcl a Loop Gain 40 Magnitude fcl 18 b STABLE Phase [deg] Loop Gain Phase Gain : Phase : Loop A:(86.03k; 20.29m) B:(86.01k; 15.55m) Loop A:(86.03k; 1.43) B:(86.01k; 1.44) Tina SPICE CL 6.10 Tina SPICE RF 100k V2 40 VIN 1Vpk 1k Hz RI 100k U1 OPA452 FLAG V1 40 R4 40k CL 1u R ISO CF Tim Green 6.10Tina SPICE CL 6.11 Tina SPICE

6 1.00 VIN STABLE m u 10u 15u 20u Time (s) 6.11Tina SPICE CL R O CL Aol 6.12 RL R O R O RL CL decade RL 10R O RL R O CL 1 VO/ = CL * RO * RL {S 1/{CL[RO*RL/(RORL)]}} Implies that there is a single pole at: fp= 1 / {2*pi*CL*(RO//RL)} fp= 1 / {2*pi*100nF*(1k//100)} fp= 17.5kHz RO 1k RL 100 CL 100n VO If RL > 10*RO Dominant single pole at: fp= 1 / {2*pi*CL*RO} 6.12 RL R ISO CF Tim Green

7 6.13 R O RL CL R O RL CL a Gain : Phase : VO A:(17.45k; 23.83) VO A:(17.45k; 44.9) Phase [deg] R ISO CL Frequency (Hz) 6.13Tina SPICE R O RLCL 6.14 CL R ISO Aol R ISO V OUT V OA R ISO CF Tim Green

8 RI 100kΩ V IN RF R ISO Isolates CL 100kΩ from Op Amp Output OPA425 V R OA R ISO O V OUT 28.7Ω 4.99Ω CL 1µF Extra Pole in Aol Plot due to (RO RISO) & CL: fpo1 = 1/[2 П (R O R ISO ) CL] Extra Zero in Aol Plot due to R ISO & CL: fzo1 = 1/[2 П R ISO CL] Data Sheet Aol Check: V OUT error vs. V OA (point of feedback) depending on I OUT 6.14R ISO CL R ISO CL 6.15 fpo1 R O R ISO CL fzo1 R ISO CL 6dB 1β fcl 20dBdecade OPA452 Aol fpo1 = 1/[2 П (R O R ISO ) CL] fpo1 = 1/[2 П (28.7Ω 4.99Ω) 1µF] fpo1 = 4.724kHz /β fpo1 20dB/Decade RateOfClosure fzo1 = 1/[2 П R ISO CL] fzo1 = 1/[2 П 4.99Ω 1µF] fzo1 = 31.89kHz fzo fcl Modified Aol R ISO 10 CF 100 1K 10K 100k 1M 10M Tim Green

9 6.15R ISO CL Aol 6.16 Tina SPICE Aol 1β x2 6dB VFB RI 100k LT 1G CT 1G VM U1 OPA452 VT 6.16Tina SPICE R ISO CL 6.17 Aol fp01=4.724khz fz01 =31.89kHz V2 40 FLAG V1 40 RF 100k R4 40k Aol = / VM Loop Gain = VFB / VM RISO 4.99 CL 1u VO Modified Aol Magnitude Phase [deg] Modified Aol Phase R ISO CF Tim Green Tina SPICE R ISO CL Aol

10 6.18 R ISO CL DC fcl a Loop Gain Magnitude 6 fcl Phase [deg] Loop Gain Phase Tina SPICE R ISO CL 6.19 Tina SPICE AC V OUT V IN V IN RF 100k RI 100k U1 OPA452 VIN V2 40 FLAG V1 40 R4 40k RISO 4.99 CL 1u VOUT AC Analy sis: VIN = 1Vpk Transient Analy s is VIN = 100mVpk, 10kHz, 10nS ris e/f all time 6.19Tina SPICE R ISO CL V OUT V IN R ISO & CL V OUT V IN AC 6.20 V OA V IN AC V OUT V IN AC V OA 1β Aol V OA V IN R ISO CF Tim Green

11 fcl V OA V IN Aol V OUT V IN DC fzo1v OUT V IN R ISO CL R ISO CL fzo1 V OUT V IN 20db decade fcl Aol V OA 20dBdecade R ISO CL V OUT V IN fcl V OUT V IN 40dBdecade OPA452 Aol fpo1 40 Modified Aol 20 1/β 20dB/Decade RateOfClosure fzo1 fcl 0 V OA /V IN 20 V OUT /V IN K 10K 100k 1M 10M 6.20 AC R ISO CL V OUT V IN Tina SPICE V OUT V IN V OA V IN VOUT Phase [deg] VOUT R ISO CF Tim Green

12 6.21Tina SPICE R ISO CL V OUT V IN 6.22 V OA SPICE IC 10m VIN 10m m m m VOUT m CF 25.00u 5u 75.00u 10u Time (s) 6.22Tina SPICE R ISO CL V OUT V IN 6.23 R O CL Aol 1β 1/β 20dB/decade Aol CF 180pF RI RF 10kΩ 100kΩ R ISO CF Tim Green Extra Pole in Aol Plot due to R O & CL: fpo1 = 1/(2 П R O CL) Add Pole in 1/β Plot: fp1 = 1/(2 П RF CF) Note: 1/β before fp1 must be large enough for 1/β intersection with modified Aol at fcl to be 20dB/Decade with rolloff due to fp1 V IN OPA452 R O 28.7Ω Data Sheet Aol V OUT CL 1µF

13 6.23 CF fp β fp1 1β 20dBdecade CF 1β 1 (0dB) CF V OUT CL V OUT V IN CF RF V OUT V IN AC fp1 (8.84kHz) 20dBdecade fcl V OUT V IN OPA452 Aol fpo1 = 1/(2 П RO CL) fpo1 = 1/(2 П 28.7Ω 1µF) fpo1 = 5.545kHz 80 fp1 = 1/(2 П RF CF) fp1 = 1/(2 П 100kΩ 180pF) fp1 = 8.84kHz /β fpo1 20dB/Decade RateOfClosure fp1 fz1: Intersection of 1/β and 0dB. At high frequency CF=Short and 1/β=10dB. fcl 0 fz V OUT /V IN Modified Aol due to CL K 10K 100k 1M 10M CF Tina SPICE R ISO CF Tim Green

14 CF 180p RF 100k VFB RI 10k LT 1G Aol = / VM Loop Gain = VFB / VM 1/Beta = / VF B VM U1 OPA452 CT 1G VT V2 40 FLAG V1 40 R4 40k CL 1u 6.25Tina SPICE CF 1β 6.26 Aol fp 5.45kHz 1β fp1 8.84kHz1β 8.84kHz 20dBdecade 0dB 0dB 12 a 10 Modified Aol /Beta Tina SPICE CF Aol 1β R ISO CF Tim Green

15 6.27 DC fcl 45 fcl AC 10 8 a Loop Gain Magnitude b Phase [deg] Loop Gain Phase Gain : Phase : Loop A:(104.03k; 4.14m) B:(104.03k; 4.14m) Loop A:(104.03k; 38.53) B:(104.03k; 38.53) Tina SPICE CF 6.28 Tina SPICE V OUT V IN CF 180p RF 100k RI 10k VIN U1 OPA452 V2 40 FLAG V1 40 R4 40k CL 1u AC Analy sis: VIN = 1Vpk Trans ient Analy sis VIN = 10mVpk, 1kHz, 10nS rise/f all time R ISO CF Tim Green 6.28Tina SPICE CF V OUT V IN

16 V OUT V IN AC kHz V OUT V IN 40dBdecade 100Khz V OUT V IN 100kHz Aol 1Beta VOUT/VIN Magnitude Phase [deg] VOUT/VIN Phase Tina SPICE CF V OUT V IN Tina SPICE V OUT V IN 6.30 ringing 1m VIN 1m m m 25u 50u 75u Time (s) 6.30Tina SPICE CF R ISO CF Tim Green

17 6.31 R O CL Aol 1β 1β 1β fpn Rn Cn fzn fpn 20dBdecade DC 1β 1β (Inverting Noise Gain) V OUT V IN RFRICnRn 1β (NonInverting Noise Gain) Rs Rn 1β V OUT V IN = 1RFRI RI RF Cn 82nF Rn 1k Ω Inverting Noise Gain 10kΩ 100kΩ V IN RI 10kΩ RF 100kΩ OPA452 R O 28.7Ω Data Sheet Aol V OUT V IN CL 100nF Rn 1kΩ Cn 82nF Rs 100Ω Data Sheet Aol OPA452 R O 28.7Ω NonInverting Noise Gain: Rs < Rn/10 V OUT CL 100nF Extra Pole in Aol Plot due to R O & CL: fpo1 = 1/(2 П R O CL) Add Noise Gain Zero & Pole in 1/β Plot: 1/β DC = RF/RI 1/β Hif = RF/Rn (Must intersect Modified Aol at 20dB/Decade) fpn = 1/(2 П Rn Cn) fzn = Intersect of 20dB/decade slope from fpn down to 1/β DC value V OUT /V IN = RF/RI V OUT /V IN High Frequency Noise Gain increases to RF/Rn R ISO CF Tim Green V OUT V IN AC RnCn ZnSuperposition 4 V OUT V OUT V IN 1RFRI RnCn 1β V OUT V IN

18 RI RF 10kΩ 100kΩ Use Superposition: V OUT = 0V(RF/RI) V IN (RF/Zn) [1 RF/(Zn//RI)][V IN ] = V IN (RF/Zn) V IN [RF/(Zn//RI)] V IN [RF/(Zn//RI)] = RF/[ZnRI/(ZNRI)] = (RF ZN RI RF) / ZN RI = RF ZN/ ZN RI RI RF/RI Zn = RF/RI RF/Zn Zn Rn 1kΩ Cn 82nF V IN Data Sheet Aol OPA452 R O 28.7Ω V OUT CL 100nF V OUT = V IN (RF/Zn) V IN [RF/RI RF/Zn] V IN = V IN (RF/Zn) V IN V IN (RF/RI) V IN (RF/Zn) = V IN V IN (RF/RI) V OUT = V IN [1(RF/RI)] V OUT /V IN = 1(RF/RI) DC 1β 10 (20dB) 20dBdecade 1Beta 100 (40dB) RFRn fpn fcl Aol IC Aol ½ 40dBdecade fpn 20dBdecade 1β fzn 1β V OUT V IN DC fcl fcl V OUT V IN R ISO CF Tim Green

19 OPA452 Aol fpo1 = 1/(2 П R O CL) fpo1= 1/(2 П 28.7Ω 100nF) fpo1 = 55.45kHz dB/Decade RateOfClosure 1/β fzn fpn fcl fpo1 fpn = 1/(2 П Rn Cn) fpn = 1/(2 П 1kΩ 82nF) fpn = 1.94kHz fzn: Plot graphically from fpn to 1/β DC with 20dB/Decade slope /β DC = RF/RI 1/β DC = 100kΩ/10kΩ = 10 (20dB) 1/β Hif = RF/Rn 1/β Hif = 100kΩ/1kΩ = 100 (40dB) V OUT /V IN Modified Aol due to CL K 10K 100k 1M 10M Tina SPICE 1βAol Aol C1 82n R1 1k RF 100k RI 10k VFB LT 1G Aol = / VM Loop Gain = VFB / VM 1/Beta = / VF B VM U1 OPA452 CT 1G VT 6.34Tina SPICE Tina SPICE kHz 1β 20dB 40dB 1.94kHz 194Hz fcl 20kHz 20dBdecade V2 40 FLAG V1 40 R4 40k CL 100n R ISO CF Tim Green

20 Modified Aol /Beta Tina SPICE Aol 1β 6.36 fcl Hz 1kHz 45 a Loop Gain Magnitude Phase [deg] Loop Gain Phase Gain : Phase : loop A:(22.32k; 61.15m) loop A:(22.32k; 63.24) 18 R ISO CF Tim Green

21 6.36Tina SPICE 6.37 V OUT V IN AC C1 82n R1 1k RF 100k RI 10k VIN U1 OPA452 V2 40 FLAG V1 40 R4 40k VOUT CL 100n AC Analy sis VIN = 1Vp Transient Analy s is VIN = 10mVpk, 5kHz, 10ns rise/f all time 6.37Tina SPICE V OUT V IN 6.38 V OUT V IN AC 20kHz50kHzAol 40dBdecade 20dBdecade VOUT / VIN Magnitude 20dB/Decade 40dB/Decade k 1k 10k 1.00M 1M VOUT/VIN Phase Phase [deg] R ISO CF Tim Green

22 6.38Tina SPICE V OUT V IN 6.39 V OUT V IN m VIN 1m m VOUT m 5u 10u 15u 20u Time (s) 6.39Tina SPICE V OUT V IN R ISO CF 7 CF 8 R ISO (TI) BurrBrown Tina SPICE BurrBrown TI TinaTI SPICE FrederiksenThomas MMcGraw Hill 1988 BurrBrown TobeyGraemeHuelsman McGrawHill 1971 R ISO CF Tim Green

input commom-mode range) output swing (open loop gain) (GBW) ( phase margin) (gain margin)

input commom-mode range) output swing (open loop gain) (GBW) ( phase margin) (gain margin) OP AMP... 4 1. :... 4 2.... 5 2.1... 5 2.2... 6 3.... 6 3.1... 7 3.1.1... 7 3.1.2... 7 3.1.3... 7 3.1.4... 8 3.2 (Symbol)... 8 4.... 9 4.1... 9 4.1.1 Folded cascode... 9 4.1.2... 9 Fig 7... 10 4.1.3...