feedback. 8.4 the series-shunt feedback amplifier 8.4.1 the ideal situation
TRANSCRIPT
Feedback
8.4 The Series-Shunt Feedback Amplifier
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R
8.4.1 The Ideal Situation
8.4 The Series-Shunt Feedback Amplifier
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VAVR
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VVR
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VR
RV
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8.4.1 The Ideal Situation (cont.)
Series mixing
8.4 The Series-Shunt Feedback Amplifier
A
RR
R
AV
R
VAV
R
VAV
R
AVVI
I
V
I
VR
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1
)1()()(
)()(1
)()(
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of
8.4.1 The Ideal Situation (cont.)
Shunt sampling
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
8.5 The Series-Series Feedback Amplifier
8.5.1 The Ideal Situation (cont.)
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t
fto
t
oit
tof
I
IAIR
I
AVIR
I
RAVI
I
VR
)()(
)(
)1( ARR oof
Series sampling
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
VI
IR
II
RI
I
VR
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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
IAI
IR
II
IR
II
RI
I
VR
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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
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
8.8 The Stability Problem
8.8.2 The Nyquist Plot
unstable Else
stable)()( then ,1)()( If
jAjAjjA f
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
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
8.10 Stability Study Using Bode Plots
8.10.1 Gain and Phase Margin
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
e
e
jA
jAjA
1
)/1()(
1
)/1(
)(1
)()( 1
1
11
peaksgain ,margin Phase
1
3.1)(135 1 jAf
Zero margin?
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
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
Homework: 8.37, 8.43, 8.47, Ex-8.14, 8.70, 8.76, 8.77, 8.79