Analog Electronics - Miunapachepersonal.miun.se/~amiyou/AE/Lecture6.pdf · Electronic Devices, 9th...
Transcript of Analog Electronics - Miunapachepersonal.miun.se/~amiyou/AE/Lecture6.pdf · Electronic Devices, 9th...
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Analog Electronics
Lecture 6
Muhammad Amir Yousaf
Op amp Stability Analysis and Op-
amp Circuits
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Lecture:
Stability analysis and compensation of op-amps
Op-amp Circuits
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Stability analysis and compensation of op-amps
Op-amp’s gain is so high that even a slightest input signal
would saturate the output.
Negative feedback is used to control the gain.
A classic form of feedback equation
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Feedback equation:
Loop Gain
The term AolB( or AB for simplicity) is called ‘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.
When loop gain is higher i.e. AB >> 1
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
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 = 180o
If the output were not energy limited the system
would explode the world.
System is called unstable under these conditions
Stability analysis and compensation of op-amps
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Non-inverting amplifier
Feedback equation for Op-amp feedback systems
Rf
Ri
Vf
Vin
+
–
Feedbackcircuit
Vout
Non-inverting amplifier
fR
iR
iR
AAB
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Inverting amplifier
Feedback equation for Op-amp feedback systems
–
+
Rf
Vout
Ri
Vin
Replace ZF with Rf and ZG with Ri
Loop Gain for both inverting and non inverting amplifier
circuits are identical, hence the stability analysis is identical.
fR
iR
iR
AAB
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
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 AB = -1 = |1| ∠180o
instability or oscillation occurs
Bode plot analysis of Feedback circuits
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Loop gain plots are key to understanding Stability:
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.
A two-slope system can accumulate 180° phase shift, therefore a
transfer function with a two or greater poles is capable of oscillation.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Op-amp transfer function
The transfer function of even the
simplest operational amplifiers will
have at least two poles.
At some critical 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 critical
frequency.
This is because:
(a) the feedback is implemented through the use of an inverting input that adds
an additional -180° to the output phase making the total phase shift -360°
(b) the gain is sufficient to induce oscillation.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas 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)
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas 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.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas 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 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.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
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.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
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 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.
fR
iR
iR
AAB
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Gain Compensation
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
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.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Lead Compensation
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Lecture:
Stability analysis and compensation of op-amps
Op-amp Circuits
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Comparators
A comparator is a specialized nonlinear op-amp circuit that
compares two input voltages and produces an output state that
indicates which one is greater.
Comparators are designed to be fast and frequently have other
capabilities to optimize the comparison function.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Comparator with Hysteresis
Noise contaminated signal may cause an unstable output.
To avoid this, hysteresis can be used.
Hysteresis is incorporated by adding regenerative (positive) feedback, which
creates two switching points:
The upper trigger point (UTP) and the lower trigger point (LTP).
After one trigger point is crossed, it becomes inactive and the other one
becomes active.
Vin 0 t
VUTP
VLTP
+Vout(max)
–Vout(max)
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Schmitt Trigger
A comparator with hysteresis is also called a Schmitt trigger. The
trigger points are found by applying the voltage-divider rule:
2UTP ( )
1 2
out max
RV V
R R
and 2LTP ( )
1 2
out max
RV V
R R
What are the trigger points for the circuit
if the maximum output is ±13 V?
2UTP ( )
1 2
10 k+13 V
47 k + 10 kout max
RV V
R R
R1
47 k
–
+
R2
10 k
Vout
Vin
= 2.28 V
By symmetry, the lower trigger point = 2.28 V.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Output Bounding
Some applications require a limit to the output of the
comparator (such as a digital circuit). The output can be
limited by using one or two Zener diodes in the feedback
circuit.
The circuit shown here is bounded as a positive value equal to
the zener breakdown voltage.
+VZ
Ri
–
+
Vin
0 V0
–0.7 V
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Comparator Applications
Simultaneous or flash analog-to-digital
converters use 2n-1 comparators to
convert an analog input to a digital
value for processing. Flash ADCs are a
series of comparators, each with a
slightly different reference voltage.
The priority encoder produces an
output equal to the highest value input.
In IC flash converters, the priority
encoder usually includes a latch that
holds the converter data constant for a
period of time after the conversion.
Vin
(analog)
R
R
R
R
R
R
R
R
VREF
Op-ampcomparators
Binary
output
D2
D1
D0
(7)
Priorityencoder
(6)
(5)
(4)
(3)
(2)
(1)
(0)
Enableinput
+
–
+
–
+
–
+
–
+
–
+
–
+
–
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Comparator Applications
Over temperature sensing circuit:
o R1 is temperature sensing resistor with a negative temperature
coefficient.
o R2 value is set equal to the resistance of R1 at critical temperature
oAt normal conditions R1 > R2 driving op-amp to low
An over
temperature
sensing circuit
At R1=R2, balance bridge
creates high op-amp output,
energizes relay, activates
alarm.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Summing Amplifier
A summing amplifier has two or more inputs; normally all inputs have
unity gain. The output is proportional to the negative of the algebraic sum
of the inputs.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Summing Amplifier
VOUT = (VIN1 + VIN2 + VIN3)
= (+5.0 V 3.5 V + 4.2 V)
–
+
VIN1
VIN2
VIN3
VOUT
R
R
1
3
Rf
R2
What is VOUT if the input voltages are +5.0 V, 3.5 V and +4.2 V and all
resistors = 10 k?
= 5.7 V
10 k
Example
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Averaging Amplifier
An averaging amplifier is basically a summing amplifier with the gain
set to Rf /R = 1/n (n is the number of inputs). The output is the negative
average of the inputs.
VOUT = ⅓(VIN1 + VIN2 + VIN3)
= ⅓(+5.0 V 3.5 V + 4.2 V)
–
+
VIN1
VIN2
VIN3
VOUT
R
R
1
3
Rf
R2
What is VOUT if the input voltages are +5.0 V, 3.5 V and +4.2 V? Assume
R1 = R2 = R3 = 10 k and Rf = 3.3 k?
= 1.9 V
3.3 k
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Scaling Adder
A scaling adder has two or more inputs with each input having a different
gain.
It is useful when one input has higher weight than the other.
The output represents the negative scaled sum of the inputs.
Assume you need to sum the inputs from three microphones. The first two
microphones require a gain of 2, but the third microphone requires a gain
of 3. What are the values of the
input R’s if Rf = 10 k?
5.0 k –
+
VIN1
VIN2
VIN3
VOUT
R
R
1
3
Rf
R2
10 k
1 2
1
10 k
2
f
v
RR R
A
3
3
10 k
3
f
v
RR
A
3.3 k
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
Scaling Adder: D/A Converter
An application of a scaling adder is the D/A converter circuit shown
here. The resistors are inversely proportional to the binary column
weights. Because of the precision required of resistors, the method is
useful only for small DACs.
–
+
8R
VOUT
R
20
23
Rf
4R
21
2R
22
+V
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
R/2R Ladder DAC
A more widely used method for D/A conversion is the R/2R ladder. The
gain for D3 is 1. Each successive input has a gain that is half of previous
one. The output represents a weighted sum of all of the inputs (similar to
the scaling adder).
–
+Vout
Inputs
D0 D1 D2 D3
Rf = 2 R
R8
R
R6
R
R4
R
R2
2R
R1
2R
R3
2R
R5
2R
R7
2R
An advantage of the
R/2R ladder is that
only two values of
resistors are required
to implement the
circuit.
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
The Integrator
The ideal integrator is an inverting amplifier
that has a capacitor in the feedback path. The
output voltage is proportional to the negative
integral (running sum) of the input voltage.
–
+
Vin
R
Vout
C
Ideal
Integrator
An op-amp integrator simulates mathematical
integration, a summing process that determines
total area under curve.
Ii
IC
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
The Integrator
Capacitor in the ideal integrator’s feedback is
open to dc.
This implies open loop gain with dc offset.
That would lead to saturation.
The practical integrator overcomes these
issues– the simplest method is to add a
relatively large feedback resistor.
Rf should be large enough
–
+
Vin
R
R
Vout
C
f
Practical
Integrator
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
The Integrator
If a constant level is the input, the current is constant. The capacitor
charges from a constant current and produces a ramp. The slope of the
output is given by the equation:
Example
out in
i
V V
t R C
220 k
–
+
Vin
R
R
Vout
C
f
i
10 k
0.1mF
Sketch the output wave:
Vin
2 V
2 V/ms10 k 0.1 μF
out in
i
V V
t R C
+1.0 V
1.0 V
0 V0.5 1.0 1.5 2.0
t (ms)0.0
Vout
+2.0 V
2.0 V
0 V0.5 1.0 1.5 2.0
t (ms)0.0
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
The Differentiator
The ideal differentiator is an inverting amplifier that has a capacitor in
the input path. The output voltage is proportional to the negative rate of
change of the input voltage.
–
+
C
Vout
Vin
R
An op-amp differentiator simulates
mathematical differentiation, a process to
determine instantaneous rate of change of a
function.
Ideal
Differentiator
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
All rights reserved. Electronic Devices, 9th edition
Thomas L. Floyd
The Differentiator
Example
The output voltage is given by
–
+
C
Vout
Vin
R
R
R
in
c
f
Cout f
VV R C
t
Sketch the output wave: Vin
+1.0 V
1.0 V
0 V0.5 1.0 1.5 2.0
t (ms)0.0
Vout
220
10 k
0.1mF
10 k
C
1 V10 k 0.1 μF 2 V
0.5 ms
out f
VV R C
t
+2.0 V
2.0 V
0 V0.5 1.0 1.5 2.0
t (ms)0.0
© 2012 Pearson Education. Upper Saddle River, NJ, 07458.
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