© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
Analog Electronics
Lecture 6
Muhammad Amir Yousaf
Op amp Stability Analysis and Compensation
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
Lecture:
Op-amp Circuits
Stability analysis and compensation of op-amps
Op-ampsThree gains:
Open Loop Gain Aol
Closed Loop Gain Acl
Loop Gain AolBUn-StabilityCompensation
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
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,
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
Vout
+
–
Vin
Vf
Internal inversion makes Vf
180° out of phase with Vin.
Negativefeedbackcircuit
Negative Feedback
Negative feedback is used to control the gain
Rf
Ri
Vf
Vin
+
–
Feedbackcircuit
Vout
–
+
Rf
Vout
Ri
Vin
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
Non-inverting amplifier
Closed loop gain Acl Op-amp feedback systems
Rf
Ri
Vf
Vin
+
–
Feedbackcircuit
Vout
Non-inverting amplifier
).(f
Ri
Ri
RVVAV OUTINol.out
fR
iR
iR
A
A
V
V
ol
ol
IN
out
1
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
Closed loop gain Acl Op-amp feedback systems
Inverting amplifier
–
+
Rf
Vout
Ri
Vin
fR
iR
iR
Vf
Ri
Rf
RVV
VAV
OUTINA
Aol.out
..
fR
iR
iRA
Vf
Ri
Rf
RAV
V
fR
iR
iR
Vf
Ri
Rf
RV
A
V
ol
OUT
ol
INOUT
OUTINol
OUT
..
..
..
)1(.
.
fR
iR
iRA
fR
iR
fRA
V
Vol
ol
IN
OUT
)1( .
.
BAf
Ri
Rf
RA
V
V
ol
ol
IN
OUT
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
Loop Gain for Op-amp feedback systems
Rf
Ri
fR
iR
iR
VV turn
Re
oltest AVV .
fR
iR
iR
Atest
Vturn
Vol
.
Re
fR
iR
iR
ABA olol
V
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
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.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
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.
Loop Gain and Stability analysis
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
Loop gain plots are key to understanding Stability:
AolB
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
Bode plots of loop gain is a tool to understand Stability:
Stability is determined by the loop gain, when AolB = -1 = |1| 180∠ o instability or oscillation occurs
Bode plots and stability analysis.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
Loop gain plot is a tool to understand Stability:
o Notice 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.
o A two-pole system can accumulate 180° phase shift, therefore a transfer function with a two or greater poles is capable of oscillation.
f1
f2
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas 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 loop-gain of one at this frequency.
f1
f2
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
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.
Phase Margin, Gain Margin
Gain Margin = AM
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:ΦM > 45o or AM > 2 (6dB)
Safe Margin
f1
f2
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
The phase margin is very small, 20o
So the system is nearly stable
A designer probably doesn’t 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.
f1
f2
f1
f2
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
Dominant Pole Compensation (Frequency Compensation)
Gain Compensation
Lead Compensation
Compensation Techniques:
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
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.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas 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.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
As loop gain is a product of open loop gain, Aol and feed back factor B, it can be manipulated by varying feedback factor.
Gain Compensation
As long as the application can stand the higher gain, gaincompensation is the best type of compensation to use.
fR
iR
iR
ABA olol
Feedback factor B is equal to inverse of Closed loop gain Acl so technique is called Gain compensation.
BAcl
1
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
Gain Compensation
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
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.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas L. Floyd
Lead Compensation
© 2012 Pearson Education. Upper Saddle River, NJ, 07458. All rights reserved.
Electronic Devices, 9th editionThomas 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