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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Analog Electronics Lecture 6 Muhammad Amir Yousaf Op amp Stability Analysis

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Lecture: Op-amp Circuits Stability analysis and compensation of op-amps Op-amps Three gains: Open Loop Gain A ol Closed Loop Gain A cl Loop Gain A ol B Un-Stability Compensation

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Open Loop Gain Op-amps gain is so high that even a slightest input signal would saturate the output.

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Negative Feedback Negative feedback is used to control the gain. A classic form of feedback equation

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Feedback equation: Closed Loop Gain o The system gain with feed back is V out /V in and is called Closed Loop Gain A cl. o It is determined by only feedback factor B. For A ol B >> 1

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Closed Loop Gain o The system gain is determined by only feedback factor B. o Feedback factor is implemented by stable passive components. o Thus in ideal conditions the closed loop gain is predictable and stable because B is predictable and stable.

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Non-inverting amplifier Feedback equation for Op-amp feedback systems Non-inverting amplifier

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Inverting amplifier Feedback equation for Op-amp feedback systems Replace Z F with R f and Z G with R i The factor A ol B is identical in both inverting and non inverting amplifier circuits.

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Loop Gain The term A ol B 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.

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd System output heads to infinity as fast as it can when 1+ AB approaches to zero. Or |AB| =1 and AB = 180 o If the output were not energy limited the system would explode the world. System is called unstable under these conditions Loop Gain and Stability analysis

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Bode plots of loop gain are key to understanding Stability: Stability is determined by the loop gain, when A ol B = -1 = |1| 180 o instability or oscillation occurs Bode plots and stability analysis.

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Loop gain plots are key to understanding Stability: o Notice that a one pole can only accumulate 90° phase shift, so when a transfer function passes through 0 dB with a one pole, it cannot oscillate. o A two-pole system can accumulate 180° phase shift, therefore a transfer function with a two or greater poles is capable of oscillation. f1f1 f2f2

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Loop gain plots are key to understanding Stability: A ol B

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd 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. The amplifier will oscillate if it has a gain of one or more at this frequency. f1f1 f2f2

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Phase Margin = Φ M Phase margin is a measure of the difference in the actual phase shift and the theoretical 180° at gain 1 or 0dB crossover point. Phase Margin, Gain Margin Gain Margin = A M The gain margin is a measure of the difference of actual gain (dB) and 0dB at the 180° phase crossover point. For Stable operation of system: Φ M > 45 o or A M > 2 (6dB) f1f1 f2f2

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd The phase margin is very small, 20 o So the system is nearly stable A designer probably doesnt want a 20° phase margin because the system overshoots and rings badly. Phase Margin, Gain Margin 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. f1f1 f2f2 f1f1 f2f2

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Dominant Pole Compensation (Frequency Compensation) Gain Compensation Lead Compensation Compensation Techniques:

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Dominant Pole Compensation is implemented by modifying the gain and phase characteristics of the amplifier's open loop output or of its feedback network, or both, in such a way as to avoid the conditions leading to oscillation. This is usually done by the internal or external use of resistance-capacitance networks. Dominant Pole Compensation (Frequency 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. f1f1 f2f2

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd The lowest frequency pole is called the dominant pole because it dominates the effect of all of the higher frequency poles. Dominant Pole Compensation (Frequency Compensation) 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.

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd The closed-loop gain of an op-amp circuit is related to the loop gain. So the closed-loop gain can be used to stabilize the circuit. Gain Compensation Gain compensation works for both inverting and non-inverting op-amp circuits because the loop gain equation contains the closed-loop gain parameters in both cases. As long as the application can stand the higher gain, gain compensation is the best type of compensation to use.

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Gain Compensation

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Lead Compensation It consists of putting a zero 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.

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd Lead Compensation

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© 2012 Pearson Education. Upper Saddle River, NJ, All rights reserved. Electronic Devices, 9th edition Thomas L. Floyd 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

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