Presentation on theme: "Op amp Stability Analysis"— Presentation transcript:
1 Op amp Stability Analysis Analog ElectronicsLecture 6Op amp Stability AnalysisMuhammad Amir Yousaf
2 Stability analysis and compensation of op-amps Lecture:Stability analysis and compensation of op-ampsOp-ampsThree gains:Open Loop Gain AolClosed Loop Gain AclLoop Gain AolBUn-StabilityCompensationOp-amp Circuits
3 Open Loop GainOp-amp’s gain is so high that even a slightest input signal would saturate the output.
4 Negative Feedback Negative feedback is used to control the gain. A classic form of feedback equation
5 Closed Loop Gain Feedback equation: For AolB >> 1 The system gain with feed back is Vout/Vin and is called Closed Loop Gain Acl.It is determined by only feedback factor B.
6 Closed Loop GainThe system gain is determined by only feedback factor B.Feedback factor is implemented by stable passive components .Thus in ideal conditions the closed loop gain is predictable and stable because B is predictable and stable.
7 Feedback equation for Op-amp feedback systems Non-inverting amplifierNon-inverting amplifier
8 Feedback equation for Op-amp feedback systems Inverting amplifierReplace ZF with Rf and ZG with RiThe factor AolB is identical in both inverting and non inverting amplifier circuits.
9 Loop GainThe 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.
10 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 = 180oIf the output were not energy limited the system would explode the world.System is called unstable under these conditions
11 Bode plots and stability analysis. Bode plots of loop gain are key to understanding Stability:Stability is determined by the loop gain,when AolB = -1 = |1| ∠180o instability or oscillation occurs
12 Loop gain plots are key to understanding Stability: f1f2Notice 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.A two-pole system can accumulate 180° phase shift, therefore a transfer function with a two or greater poles is capable of oscillation.
13 Loop gain plots are key to understanding Stability: AolB
14 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.f1f2The amplifier will oscillate if it has a gain of one or more at this frequency.
15 Phase Margin, Gain Margin Phase Margin = ΦMPhase margin is a measure of the difference in the actual phase shift and the theoretical 180° at gain 1 or 0dB crossover point.f1Gain Margin = AMThe 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:ΦM > 45o or AM > 2 (6dB)f2Safe Margin
16 Phase Margin, Gain Margin The phase margin is very small, 20oSo the system is nearly stableA designer probably doesn’t want a 20° phase margin because the system overshoots and rings badly.f1f2Increasing 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.f1f2
17 Compensation Techniques: Dominant Pole Compensation (Frequency Compensation)Gain CompensationLead Compensation
18 Dominant Pole Compensation (Frequency Compensation) 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.f1f2 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.
19 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.
20 Gain CompensationThe 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 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, gaincompensation is the best type of compensation to use.
22 Lead CompensationIt 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.
24 ReferencesSlides 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 IntersilModified by Muhammad Amir Yousaf