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Chapter 10
Feedback
EE 3120 Microelectronics II
Suketu Naik
Operational Amplifier Circuit Components
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1. Ch 7: Current Mirrors and Biasing
2. Ch 9: Frequency Response
3. Ch 8: Active-Loaded Differential Pair
4. Ch 10: Feedback
5. Ch 11: Output Stages
EE 3120 Microelectronics II
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Feedback
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Two Stage
Op Amp
(MOSFET)
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Stability
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10.10 The Stability Problem
 In a feedback amplifier, the open loop gain (A) is generally
a function of frequency.
 It is called open-loop transfer function A(s).
 Question: What happens to gain at higher frequencies?
 This has huge implications on stability of the amplifier.
EE 3120 Microelectronics II
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10.4.1 The Ideal Case
A  s
(10.81) closed-loop gain t-function: A f  s  
1  A  s β  s 
A  j 
(10.82) closed-loop gain t-function: A f  j  
1  A  j  β  j 
(10.83) loop-gain: L  j   A  j  β  j   A  j  β  j  e



angle

j φ w 
magnitude of gain
EE 3120 Microelectronics II
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10.4.2 Nyquist Plot (Loop Gain with Varying Freq)
Figure 10.34: The Nyquist plot of an
unstable amplifier
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1) At ω=ω180 , the feedback
becomes positive
2) If the loop gain at ω=ω180
crosses the x-axis to the left of (1,0), the amplifier will be unstable
because Aβ < -1: oscillations will
grow with nonlinearity
3) If the loop gain at ω=ω180
crosses the x-axis exactly at (-1,0),
the amplifier will be unstable
because Aβ = -1: sustained
oscillations
4) If the loop gain at ω=ω180
crosses the x-axis to the right of (1,0), the amplifier will be stable
5) If the Nyquist plot encircles (1,0), then the amplifier will be
unstable
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Suketu Naik
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10.4.1 The Ideal Case
(10.84) instantaneous voltage: v  t   e 0t ent  ent   2e 0t cos nt 
(10.85) feedback-ampflier pole constraint: 1  A  s  β  s   0
A0
(10.86) open-loop transfer function: A  s  
1  s / P
(10.87) closed-loop transfer function: A f  s  
A0 / 1  A0  
1  s / P 1  A0  
(10.88) pole: Pf  P 1  A0  
A0P
(10.89) closed-loop transfer function: A f  s  
 A  s
s
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10.11. Effect of Feedback on the Amplifier Poles
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Figure 10.35: Relationship
between pole location and
transient response.
EE 3120 Microelectronics II
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10.11 Effect of Feedback on the Amplifier Poles
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Figure 10.36: Effect of feedback on (a) the pole location and (b) the frequency
response of an amplifier having a single-pole, open-loop response.
EE 3120 Microelectronics II
Suketu Naik
10.12 Stability Study Using Bode Plots
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Since the open-loop gain A(s)*β = 1
at low frequencies, we define
A(s)*β= 1ejθ, where
1)β= feedback factor at low
frequencies
2) θ=180-phase margin (PM)
At low frequencies closed-loop
gain=(1/β)
At phase margin=45, closed-loop
gain=1.3(1/β)
At phase margin=70, closed-loop
gain=0.87(1/β)
1
PM 
BW
The stability of the feedback
amplifier reduces as the phase
margin reduces
EE 3120 Microelectronics II
Suketu Naik
10.12 Stability Study Using Bode Plots
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The stability of the feedback
amplifier can be determined
directly from the plot of A(s)
(open-loop gain frequency
response)
After plotting A(s), we look at
the phase at 1/β
phase margin (PM) = 180-phase
If the phase < -180deg:
amplifier will be unstable
If the phase is very small:
amplifier will be stable but the
BW will be small
If the phase is about 110-120
deg: stable with acceptable BW
EE 3120 Microelectronics II
Suketu Naik
10.13 Miller Compensation and Pole Spitting
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Problem: open-loop response
A(s) shows instabilty
Solution: shift the response to
the left so that the phase
angle is positive and lies
between 110-120 deg
-While shifting, we end up
reducing the BW and desired
DC gain.
-We can shift the pole at the
intersection of 1/β and A(s)
curves to the right by
introducing compensation
capacitor.
EE 3120 Microelectronics II
Suketu Naik
10.13 Miller Compensation and Pole Spitting
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C1 and C2 include the Miller component due to Cμ
R1 and C1 = total resistance and capacitance at the input
R2 and C2 = total resistance and capacitance at the output
Cf = compensation capacitor
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Compensation Capacitor in Two-stage BJT Op-amp
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Suketu Naik
Compensation Capacitor in Two-stage CMOS Op-amp
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Suketu Naik
List of Problems
Feedback and Stability
p10.82: stability of op amp with feedback
p10.92: phase margin of op amp
p10.99: Miller capacitance compensation
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Suketu Naik
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Summary
 Negative feedback is employed to make the amplifier gain less
sensitive to component variations; to control input and output
impedances; to extend bandwidth; to reduce nonlinear distortion;
and to enhance signal-to-interference ratio
 The advantages above are obtained at the expense of a reduction in
gain and at the risk of the amplifier becoming unstable (that is,
oscillating). The latter problem is solved by careful design
 For each of the four basic types of amplifier, there is an appropriate
feedback topology. The four topologies, together with their
analysis procedures, are summarized in Table 10.1.
EE 3120 Microelectronics II
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Summary
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 The key feedback parameter are the loop gain (A), which for
negative feedback must be a positive dimensionless number, and the
amount of feedback (1+A). The latter directly determines gain
reduction, gain desensitivity, bandwidth extension, and changes in
input and output resistances
 Since A and  are in general frequency dependent, the poles of the
feedback amplifier are obtained by solving the characteristic equation
1+A(s)(s) = 0
 For the feedback amplifier to be stable, its poles must all be in the lefthand side of the s-plane.
EE 3120 Microelectronics II
Suketu Naik
Summary
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 Stability is guaranteed if at the frequency for which the phase angle
of A is 180O, |A| is less than unity; the amount by which it is less
than unity, expressed in decibels, is the gain margin. Alternatively,
the amplifier is stable if, at the frequency at which |A| = 1, the phase
angle is less than 180O, the difference ifs the phase margin
 The stability of a feedback amplifier can be analyzed by constructing
a Bode plot for |A| and superimposing it on a plot for 1/||. Stability
is guaranteed if the two plots intersect with a difference in slope no
greater than 6dB/decade.
EE 3120 Microelectronics II
Suketu Naik
Summary
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 To make a given amplifier stable for a given feedback factor, the
open-loop frequency response is suitably modified by a process
known as frequency compensation.
 A popular method for frequency compensation involves connecting
a feedback capacitor across an inverting stage in the amplifier.
This causes the pole formed at the input of the amplifier stage to
shift to a lower frequency and thus become dominant, while the
pole formed at the output of the amplifier stage is moved to a very
high frequency and thus becomes unimportant. This process is
known as pole splitting.
EE 3120 Microelectronics II
Suketu Naik