Lecture 6

Report
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.

similar documents