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Analog Electronics Lecture 6 Op amp Stability Analysis and Compensation Electronic Devices, 9th edition Thomas L. Floyd Muhammad Amir Yousaf © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Lecture: Stability analysis and compensation of op-amps Op-amps Three gains: Open Loop Gain Aol Closed Loop Gain Acl Loop Gain AolB Un-Stability Compensation Op-amp Circuits Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Open Loop Gain Op-amp’s gain is so high that even a slightest input signal would saturate the output. In most real op amps the open loop gain starts to decrease before 10 Hz, Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Negative Feedback Vin + Vf – Vout Internal inversion makes Vf 180° out of phase with Vin . Negative feedback circuit Rf + Vout – Vin Ri – Rf Vf Feedback circuit Vout Vin Ri + Negative feedback is used to control the gain Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Closed loop gain Acl Op-amp feedback systems Non-inverting amplifier + Vout – Vin Rf Vf Feedback circuit Ri Non-inverting amplifier R i ) Vout Aol.(VIN VOUT . R R i f Vout VIN Electronic Devices, 9th edition Thomas L. Floyd Aol R i 1 Aol R R i f © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Closed loop gain Acl Op-amp feedback systems Inverting amplifier Rf Ri – Vout Vin + Vout Aol.VA R R f i VA VIN . VOUT . R R R R i f i f R R VOUT f i VIN . VOUT . Aol R R R R i f i f Aol . R Aol . R VOUT f i VIN . VOUT . R R R R i f i f Electronic Devices, 9th edition Thomas L. Floyd f R R i f Aol . R i ) (1 R R i f VOUT VIN Aol . R Aol . R f R R VOUT i f VIN (1 Aol . B) © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Loop Gain for Op-amp feedback systems V Rf Ri R i V Re turn V R R i f V Vtest . Aol V R Re turn Aol . i V R R test i f Electronic Devices, 9th edition Thomas L. Floyd R i AolB Aol R R i f © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Loop Gain The term AolB is very important in stability analysis and is called ‘Loop Gain’ As the Loop Gain is identical in both inverting and non inverting amplifier circuits, hence the stability analysis is identical. Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Loop Gain and Stability analysis System output heads to infinity as fast as it can when 1+ AB approaches to zero. Or |AB| =1 and ∠AB = 180o If the output were not energy limited the system would explode the world. System is called unstable under these conditions: o It could lock to maximum supply rails. o It could oscillate. Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Loop gain plots are key to understanding Stability: AolB Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Bode plots and stability analysis. Bode plots of loop gain is a tool to understand Stability: Stability is determined by the loop gain, when AolB = -1 = |1| ∠180o instability or oscillation occurs Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Loop gain plot is a tool to understand Stability: f1 f2 oNotice that a single pole can only accumulate 90° phase shift, so when a transfer function passes through 0 dB with a one pole, it cannot oscillate. oA two-pole system can accumulate 180° phase shift, therefore a transfer function with a two or greater poles is capable of oscillation. Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Op-amp transfer function The open loop gain of even the simplest operational amplifiers will have at least two poles. At some frequency, the phase of the amplifier's output = -180° compared to the phase of its input signal. f1 f2 The amplifier will oscillate if it has a loop-gain of one at this frequency. Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Phase Margin, Gain Margin Phase Margin = ΦM Phase margin is a measure of the difference in the actual phase shift and the theoretical 180° at gain 1 or 0dB crossover point. Gain Margin = AM The gain margin is a measure of the difference of actual gain (dB) and 0dB at the 180° phase crossover point. f1 f2 For Stable operation of system: ΦM > 45o or AM > 2 (6dB) Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Phase Margin, Gain Margin The phase margin is very small, 20o f1 So the system is nearly stable f2 A designer probably doesn’t want a 20° phase margin because the system overshoots and rings badly. Increasing the loop gain to (K+C) shifts the magnitude plot up. If the pole locations are kept constant, the phase margin reduces to zero and the circuit will oscillate. Electronic Devices, 9th edition Thomas L. Floyd f1 f2 © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Compensation Techniques: Dominant Pole Compensation (Frequency Compensation) Gain Compensation Lead Compensation Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Dominant Pole Compensation A pole placed at an appropriate low frequency in the open-loop response reduces the gain of the amplifier to one (0 dB) for a frequency at or just below the location of the next highest frequency pole. Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Dominant Pole Compensation (Frequency Compensation) The lowest frequency pole is called the dominant pole because it dominates the effect of all of the higher frequency poles. Dominant-pole compensation can be implemented for general purpose operational amplifiers by adding an integrating capacitance. The result is a phase margin of ≈ 45°, depending on the proximity of still higher poles. Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Gain Compensation As loop gain is a product of open loop gain, Aol and feed back factor B, it can be manipulated by varying feedback factor. R i AolB Aol R R i f Feedback factor B is equal to inverse of Closed loop gain Acl so technique is called Gain compensation. Acl 1 B As long as the application can stand the higher gain, gain compensation is the best type of compensation to use. Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Gain Compensation Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Lead Compensation It consists of putting a zero (inverse of a pole) in the loop transfer function to cancel out one of the poles. The best place to locate the zero is on top of the second pole, since this cancels the negative phase shift caused by the second pole. Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. Lead Compensation Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved. References Slides by ‘Pearson Education’ for Electronic Devices by Floyd ‘Op.amp for every one’ by Ron Mancini ’Stability Analysis for volatge feedback op-amps’, Application Notes byTexas Instruments (TI) ’Feedback amplifiers analysis tool’ by TI ‘Feedback, Op Amps and Compensation’ Application Note 9415 by Intersil Modified by Muhammad Amir Yousaf Electronic Devices, 9th edition Thomas L. Floyd © 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.