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Feedback
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8.4 The Series-Shunt Feedback Amplifier
AA
V
VA
s
of
1
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of
if
R
R
8.4.1 The Ideal Situation
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8.4 The Series-Shunt Feedback Amplifier
)1(/
AR
V
VAVR
V
VVR
V
VR
RV
V
I
V
I
VR i
i
iii
i
fii
i
si
ii
s
i
s
s
sif
))()(1)(()( ssAsZsZ iif
8.4.1 The Ideal Situation (cont.)
Series mixing
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8.4 The Series-Shunt Feedback Amplifier
A
RR
R
AV
R
VAV
R
VAV
R
AVVI
I
V
I
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o
t
o
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it
t
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1
)1()()(
)()(1
)()(
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of
8.4.1 The Ideal Situation (cont.)
Shunt sampling
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8.5 The Series-Series Feedback Amplifier
8.5.1 The Ideal Situation
i
iii
i
ioi
ii
if
i
sif
V
VAVR
V
VIR
RV
VV
I
VR
/
)1( ARR iif
Series mixing
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8.5 The Series-Series Feedback Amplifier
8.5.1 The Ideal Situation (cont.)
t
tto
t
fto
t
oit
tof
I
IAIR
I
AVIR
I
RAVI
I
VR
)()(
)(
)1( ARR oof
Series sampling
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8.6 The Shunt-Shunt and Shunt-Series Feedback Amplifier
8.6.1 The Shunt-Shunt Configuration
A
R
VAV
VR
AIV
VR
RAIV
V
I
VR
A
R
IAI
IR
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IR
II
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8.6 The Shunt-Shunt and Shunt-Series Feedback Amplifier
8.6.3 The Shunt-Series Configuration
)1()(
1
ARI
IAIR
I
AIIR
I
RAII
I
VR
A
R
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IR
II
RI
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8.6 The Shunt-Shunt and Shunt-Series Feedback Amplifier
8.6.3 Summary
Ri Rif: Mixing
Voltage (series) mixing always increases the input resistance.
Current (shunt) mixing always reduces it.
Ro Rof: Sampling
Voltage (shunt) sampling always reduces the output resistance
Current (series) sampling increases it
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8.8 The Stability Problem
8.8.1 Transfer Function of the Feedback Amplifier
Open-loop gain: A, A(s)
Loop gain: A, A(s)(s)
Close-loop gain: )()(1
)()(
1 ssA
sAsA
A
AA ff
)()(1
)()(
jjA
jAjAf
)()()( jjAjL 180For
)()()()()()( jejjAjjAjL
unstable Else
stable)()( then ,1)()( If
jAjAjjA f
Oscillator: =-1, zero input, infinite output
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8.8 The Stability Problem
8.8.2 The Nyquist Plot
unstable Else
stable)()( then ,1)()( If
jAjAjjA f
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8.9 Effect of Feedback on the Amplifier Poles
8.9.1 Stability and Pole Location
Figure 8.29 Relationship between pole location and transient response.
)cos(2)( 00 teeeetv nttjtjt nn
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8.9 Effect of Feedback on the Amplifier Poles
8.9.2 Poles of the feedback amplifier
)()(1
)()(
ssA
sAsAf
ps
AsA
/1)( 0
Simplified case
)1(/1
)1/()(
0
00
As
AAsA
pf
)1( 0 Apf
)()( 0 sAs
AsA p
f
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8.10 Stability Study Using Bode Plots
8.10.1 Gain and Phase Margin
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8.10 Stability Study Using Bode Plots
8.10.2 Effect of Phase Margin on Closed-loop Response
1
1
1
f
A
f AA
AA
margin phase180
where
1)(
thenunity, isgain loopwhen
1
jejA
jfj
j
f ejA
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e
jA
jAjA
1
)/1()(
1
)/1(
)(1
)()( 1
1
11
peaksgain ,margin Phase
1
3.1)(135 1 jAf
Zero margin?
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8.10 Stability Study Using Bode Plots
8.10.3 An Alternative Approach for Investigating Stability
|AB|<1 20log|A| < 20log(1/)
The closed-loop amplifier will be stable if the 20log(1/) line intersects the 20log|A| curve at a point on the -20-dB/decade segment.
)10/j1)(10/j1)(10/j1(
10765
5
fffA
)10/j1)(10/j1)(10/j1(
10765
5
fffA
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8.11 Frequency Compensation
8.11.1 Theory
Df
20
40
60
80
100
104 105 106 107 10810 103 103
'Df 1Pf 2Pf 3Pf
f(Hz)
dB
-20dB/decade
-40dB/decade
-60dB/decade
dB40)1
log(2010 2
A
A’
dB40)1
log(20 Y
Y’
'1:PoleShift
poles Three
Dp ff
• Four poles• Simplest• Reduced the bandwidth
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Homework: 8.37, 8.43, 8.47, Ex-8.14, 8.70, 8.76, 8.77, 8.79