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Microelectric Circuits by Meiling CHEN
1
Lecture 14Lecture 14
FeedbackFeedback
National United University Department of Electrical Engineering ~ Meiling CHEN
topicstopics
• The series-shunt feedback• The series-series feedback• The shunt-shunt feedback• The shunt-series feedback
National United University Department of Electrical Engineering ~ Meiling CHEN
Two port networks
Two port Network
1v
2v
1i 2i
Type I: Impedance z-parameters
222121212
212111211
),(
),(
iziziifv
iziziifv
2
1
2221
1211
2
1
i
i
zz
zz
v
v
1i 2i
11z 22z
212iz 121iz
1v
2v
National United University Department of Electrical Engineering ~ Meiling CHEN
Type II: Admittance y-parameters
222121212
212111211
),(
),(
vyvyvvfi
vyvyvvfi
2
1
2221
1211
2
1
v
v
yy
yy
i
i
Type III: hybrid h-parameters
222121212
212111211
),(
),(
vhihvifi
vhihvifv
2
1
2221
1211
2
1
v
i
hh
hh
i
v
2i
22
1
h
121ih
2v1i
11h
212vh
1v
ce
b
oefe
reie
c
be
v
i
hh
hh
i
v
1i 2i
212vy 121vy
1v
2v22
1
y11
1
y
National United University Department of Electrical Engineering ~ Meiling CHEN
Type IV: Inverse-hybrid g-parameters
222121212
212111211
),(
),(
igvgivfv
igvgivfi
2
1
2221
1211
2
1
i
v
gg
gg
v
i
1i
11
1
g
212ig
1v 2i
22g
121vg
2v
Type V: transmission ABCD parameters
)(),(
)(),(
22221
22221
iDCvivfi
iBAvivfv
2
2
1
1
i
v
DC
BA
i
v
National United University Department of Electrical Engineering ~ Meiling CHEN
Type VI: Inverse transmission parameters
)(),(
)(),(
11112
11112
iDvCivfi
iBvAivfv
1
1
2
2
i
v
DC
BA
i
v
Two port Network combination: I. Cascade : ABCD parameters
1v
32 vv
11
11
DC
BA1i 32 ii
4v
22
22
DC
BA3i 4i
2
2
11
11
1
1
i
v
DC
BA
i
v
4
4
22
22
3
3
i
v
DC
BA
i
v
4
4
22
22
11
11
1
1
i
v
DC
BA
DC
BA
i
v
National United University Department of Electrical Engineering ~ Meiling CHEN
II: series-shunt
1v
2v
1i 2i
1v
2v
1i 2i
2
1
2221
1211
2
1
v
i
hh
hh
i
v
222
222
111
111
vvv
iii
vvv
iii
2
1
2221
1211
2
1
v
i
hh
hh
i
v
2221
1211
hh
hh
2221
1211
hh
hh
2
1
2221
1211
2221
1211
2
1
2
1
2
1 }{v
i
hh
hh
hh
hh
i
v
i
v
i
v
1i 2i
1v
2v
National United University Department of Electrical Engineering ~ Meiling CHEN
n
A2
1i
1v
2i
2v
1
1
1
1
2
Ex:
31
12h
Find v2=?
1
1
1
1i
1v
2i
2v
21212
212122
2
211211
1
2
3
2
12
211
2
1
2
1
11
vivvi
vvivvv
i
vivvvv
i
23
21
21
21
h
29
21
23
25
totalh
212
211
2
9
2
12
3
2
5
vii
viv
9
2
0,2
2
21
v
ii
National United University Department of Electrical Engineering ~ Meiling CHEN
III: series-series
1v
2v
1i 2i
222
222
111
111
vvv
iii
vvv
iii
2
1
2221
1211
2
1
i
i
zz
zz
v
v
2
1
2221
1211
2
1
i
i
zz
zz
v
v
2221
1211
zz
zz
2221
1211
zz
zz
2
1
2221
1211
2221
1211
2
1
2
1
2
1 }{i
i
zz
zz
zz
zz
v
v
v
v
v
v
1v
2v
1i 2i
1i 2i
1v
2v
National United University Department of Electrical Engineering ~ Meiling CHEN
IV: Shunt-shunt
222
222
111
111
vvv
iii
vvv
iii
2
1
2221
1211
2
1
v
v
yy
yy
i
i
2
1
2221
1211
2
1
v
v
yy
yy
i
i
2
1
2221
1211
2221
1211
2
1
2
1
2
1 }{v
v
yy
yy
yy
yy
i
i
i
i
i
i
1i 2i
1v
2v
1v
2v
1i 2i
1v
2v
1i 2i
2221
1211
yy
yy
2221
1211
yy
yy
National United University Department of Electrical Engineering ~ Meiling CHEN
V: shunt-series
1i 2i
1v
2v
1i 2i
1v
2v
1i 2i
1v
2v
222
222
111
111
vvv
iii
vvv
iii
2
1
2221
1211
2
1
i
v
gg
gg
v
i
2
1
2221
1211
2
1
i
v
gg
gg
v
i
2221
1211
gg
gg
2221
1211
gg
gg
2
1
2221
1211
2221
1211
2
1
2
1
2
1 }{i
v
gg
gg
gg
gg
v
i
v
i
v
i
National United University Department of Electrical Engineering ~ Meiling CHEN
General feedback structure
A
A
x
xA
xxx
xx
Axx
s
of
fsi
of
io
1
Open loop gain
ALoop gain
Closed-loop gain
Mixer networkVoltage seriesCurrent shunt
Sampling networkVoltage shuntCurrent Series
National United University Department of Electrical Engineering ~ Meiling CHEN
Negative feedback Negative feedback propertiesproperties
• Gain desensitivity • Bandwidth extension• Noise reduction• Nonlinear distortion reduction
National United University Department of Electrical Engineering ~ Meiling CHEN
1.Gain desensitivity
A
dA
AA
dA
A
dAdA
A
A
x
xA
f
f
f
s
of
1
1
)1(
1
2
2.Bandwidth extension
A
dA
A
dA
f
f
)1(
)1(/1
)1/(
)(1
)()(
/1)(
MHHf
MH
MMf
H
M
H
HM
A
As
AA
sA
sAsA
s
A
s
AsA
)1/(
)(1
)()(
/1)(
MLLf
f
L
M
L
M
A
sA
sAsA
s
A
s
sAsA
LfHfBW
National United University Department of Electrical Engineering ~ Meiling CHEN
3.Noise reduction
)Ratio Noise toS( ignalN
SSNR
N
S
V
V
N
S
VVV
n
s
nso
1010
100
10)10(
National United University Department of Electrical Engineering ~ Meiling CHEN
N
S1000
N
S
100V0.1V 1001
10000
1001
10
sn
sno VVV
N
S1
N
S
100100
)01.0(10000
nso
noso
VVV
VVVV
National United University Department of Electrical Engineering ~ Meiling CHEN
Figure 8.3 Illustrating the application of negative feedback to reduce the nonlinear distortion in amplifiers. Curve (a) shows the amplifier transfer characteristic without feedback. Curve (b) shows the characteristic with negative feedback ( 0.01) applied.
4.Nonlinear distortion reduction
9.901
A
A
1000A
(a) without feedback
(b) with feedback 01.0100A
501
A
A
National United University Department of Electrical Engineering ~ Meiling CHEN
Mixer network: Voltage series Current shunt
Sampling
Feedback Topology
National United University Department of Electrical Engineering ~ Meiling CHEN
Sampling network : Voltage shunt Current Series
National United University Department of Electrical Engineering ~ Meiling CHEN
series
series
shunt voltage
current
voltage
voltage
shunt
National United University Department of Electrical Engineering ~ Meiling CHEN
voltage
shunt
series
current
series
voltage
National United University Department of Electrical Engineering ~ Meiling CHEN
shunt
current
Shunt series
National United University Department of Electrical Engineering ~ Meiling CHEN
Series- shunt
National United University Department of Electrical Engineering ~ Meiling CHEN
voltage-mixing voltage-sampling (series–shunt) topology
National United University Department of Electrical Engineering ~ Meiling CHEN
current-mixing current-sampling (shunt–series) topology
National United University Department of Electrical Engineering ~ Meiling CHEN
voltage-mixing current-sampling (series–series) topology
National United University Department of Electrical Engineering ~ Meiling CHEN
current-mixing voltage-sampling (shunt–shunt) topology
National United University Department of Electrical Engineering ~ Meiling CHEN
The series–shunt feedback amplifier
A
RR
R
AVVI
VV
R
AVVI
I
VR
ARR
AR
RV
AVV
RV
VV
I
VR
A
A
V
VA
oof
o
oo
oVi
o
ioo
Vo
oof
iif
i
i
i
ii
i
i
oi
i
sif
s
of
s
s
1
)1(
)1(
1
0
0
National United University Department of Electrical Engineering ~ Meiling CHEN
2
1
2221
1211
2
1
2221212
2121111
V
I
hh
hh
I
V
VhIhI
VhIhV
Passive network h21 tends to zero
National United University Department of Electrical Engineering ~ Meiling CHEN
National United University Department of Electrical Engineering ~ Meiling CHEN
Louto
of
insiif
RRA
RR
RRRAR
//)1(
)1(
vA
sv
sR outR
inR
iv
ovif vA
LR
Series -Shunt
National United University Department of Electrical Engineering ~ Meiling CHEN
The series–series feedback amplifier
oof
oooooiooVo
oof
i
i
i
ii
i
i
oiVif
RAR
IRARIAIRAVIVI
VR
AR
RV
AvV
RV
IV
I
VR
S
o
)1(
)1()]([)(
)1(
0
0
National United University Department of Electrical Engineering ~ Meiling CHEN
2
1
2221
1211
2
1
2221212
2121111
I
I
zz
zz
V
V
IzIzV
IzIzV
National United University Department of Electrical Engineering ~ Meiling CHEN
Figure 8.15 (Continued) (c) A redrawing of the circuit in (b) with z21 neglected.
A
AA
RRzRRAR
RRzRRAR
f
LoutoLof
insisif
1
))(1(
))(1(
22
11
2211 zRR
R
zRR
RAA
Lo
o
is
iB
sv
sR
outRinR
iv
ovif iA
LR
Loutof
insif
RRR
RRR
Series -Series
National United University Department of Electrical Engineering ~ Meiling CHEN
National United University Department of Electrical Engineering ~ Meiling CHEN
the shunt–shunt feedback amplifier
A
RR
AII
RI
AII
V
VI
V
I
VR
I
VRA
iif
ii
ii
ii
s
oi
s
s
sif
i
om
1A
RA
AR
IARI
ARI
I
VR
A
RII
AIRIVI
I
AIRI
I
VR
oo
o
oooo
o
oof
ooi
ioooIi
o
ioo
o
oof
s
1
1)
11(
1
1
)(0
National United University Department of Electrical Engineering ~ Meiling CHEN
2
1
2221
1211
2
1
v
v
yy
yy
i
i
1i 2i
11y 22y
212vy 121vy
ivv1
ovv2
National United University Department of Electrical Engineering ~ Meiling CHEN
outR
ovif iA
LRsR inRsI
ii
LRsR
11
1
y 22
1
y
A
AA
RRA
RRR
RRA
yRR
R
f
LoutLyo
of
ins
is
if
1
//)1(
////
//)1(
)1
////(
22
1
11
)//(2211
11
11
1
yLo
o
yis
ysB RR
R
RR
RAA
Shunt -Shunt
National United University Department of Electrical Engineering ~ Meiling CHEN
National United University Department of Electrical Engineering ~ Meiling CHEN
The shunt–series feedback amplifier
A
RR
R
VA
R
VAI
R
VIAII
IR
VI
iif
i
s
i
si
i
ssiVo
oi
ss
o
1
0
oIo
oof
oo
ooooioo
Io
oof
RAI
VR
IRA
RIAIRAIIV
I
VR
s
s
)1(
)1(
)]([)(
0
0
National United University Department of Electrical Engineering ~ Meiling CHEN
2
1
2221
1211
2
1
i
v
gg
gg
v
i
1i
11g
212ig
ivv1 oii 2
22g
121vg
2v
National United University Department of Electrical Engineering ~ Meiling CHEN
LRsR
11
1
g
22g
A
AA
RRRgRAR
RRA
yRR
R
f
LoutLoof
ins
is
if
1
))(1(
//)1(
)1
////(
22
11
221
1
11
11
gRR
R
RR
RAA
Lo
o
gis
gSB
outRinR
ovif iA LRsR
sI
ii
Shunt -Series
National United University Department of Electrical Engineering ~ Meiling CHEN
National United University Department of Electrical Engineering ~ Meiling CHEN
Type Amplifier Feedback parameter
Series-Shunt(voltage-voltage)
Series-Series(voltage-current)
Shunt-Shunt(current-voltage)
shunt-series(current-current)
)1()1(1 12
ARRARRGz
GG oofiif
m
mmf
ifR ofR
i
ov v
vA
i
om v
iG
i
om i
vR
i
oI i
iA
hi
v
2
1
zv
v
2
1
yi
i
2
1
gv
i
2
1
A
RRRAR
Ah
AA o
ofiifv
vf
1
)1(1 12
)1()1(1 12 A
RR
A
RR
Ry
RR o
ofi
ifm
mmf
oofi
ifI
IIf RAR
A
RR
Ag
AA )1(
11 12
A
AAf
1
insif RRR
insif RRR
insif RRR //
insif RRR //
outLof RRR //
outLof RRR //
outLof RRR
outLof RRR
National United University Department of Electrical Engineering ~ Meiling CHEN
Example 8.1
Step 0 : Series-shunt feedback amplifier
Step 1 : Amplifier analysis
oo
idi
rR
RR
Amplifier Voltage amplifierFeedback h parameters
1122
22
)//(
)//(
hRR
R
rhR
hR
V
VA
sid
id
oL
L
i
o
BA
National United University Department of Electrical Engineering ~ Meiling CHEN
Step 2 : Feedback network analysis
2221212
2121111
VhIhI
VhIhV
21
10
2
112
2102
122
2101
111
1
1
2//
RR
R
V
Vh
RRV
Ih
RRI
Vh
I
I
V
National United University Department of Electrical Engineering ~ Meiling CHEN
Step 3 : Amp+Feedback analysis
A
AA
findR
RRA
RRRr
A
RRR
RRR
RRRRRRAhRRAR
f
out
LoutLoLho
of
ifsin
insidsisif
1
//)1(
//)//(
)1(
////
))//()(1())(1(
211
2111
22 Feedback AMP
National United University Department of Electrical Engineering ~ Meiling CHEN
Example 8.2
Step 0 : Series-series feedback amplifier
Amplifier Transconductance amplifierFeedback z parameters
National United University Department of Electrical Engineering ~ Meiling CHEN
Step 1 : Amplifier analysis
National United University Department of Electrical Engineering ~ Meiling CHEN
)//(
)//(
21322
32111
RRRZ
RRRZ
Step 2 : Analysis feedback Amp
The equivalent circuit
iV
oV
1ei3ei
11Z
1er
1cR
22Z
Vgm
V r 2cR 3er
3cRAV
oI
iR
oR1ei
National United University Department of Electrical Engineering ~ Meiling CHEN
Step 3 : Amp+Feedback analysis
m
mf
i
om
ec
ic
e
e
efecm
e
Ao
efecmA
eei
G
GA
V
IGA
ZrrR
vV
rR
vi
Zr
ZrhRvg
Zr
VI
ZrhRvgV
ZriV
1
)()//(//
)])(1//([
)])(1//([
)(
11111
1
222
2232
222
2232
1111
oof
iif
fe
ceo
feei
RAR
RAR
h
RZrR
hZrR
)1(
)1(
1
)1)((
2223
111
National United University Department of Electrical Engineering ~ Meiling CHEN
Example 8.3
Shunt-shunt: Rm amplifier + y parameter
2
1
2221
1211
2
1
v
v
yy
yy
i
i
National United University Department of Electrical Engineering ~ Meiling CHEN
02
2220
1
111 12 vv v
iy
v
iy
National United University Department of Electrical Engineering ~ Meiling CHEN
fv
o
f
cfo
sfi
sf
cfm
i
om
Rv
iy
kRRR
krRRR
k
rRRv
RRvg
i
vR
s
1
27.4//
4.1////
7.358
)////(
)//(
012
4951
//2.1621
6.411
12
12
12
m
oof
insm
iif
m
mmf
s
of
Ry
RR
RRRy
RR
kRy
RR
i
vA
National United University Department of Electrical Engineering ~ Meiling CHEN
Example 8.4
1.DC analysis
mAk
I
VkV
mAI
mAI
IIkkVkk
k
E
C
C
B
BB
765.04.3
7.03.3
3.31087.012
87.0
0087.0
87.0)1(7.0)15//100(1210015
15
2
1
1
1
11
22
12
2
22
75
030.0
Co
B
T
T
Cm
Ir
rI
Vr
V
Ig
11
11
11
75
9.2
0344.0
Co
B
T
T
Cm
Ir
kI
Vr
V
Ig
National United University Department of Electrical Engineering ~ Meiling CHEN
Shunt-seriescurrent Mixing – current samplingAmplifier: Current Amplifier Feedback network: hybrid parameters
02
222
01
111
2
1
2221
1211
2
1
1
2
v
i
i
vg
v
ig
i
v
gg
gg
v
i
LRsR
11
1
g
22g
National United University Department of Electrical Engineering ~ Meiling CHEN
1
1
111
//4.13//13//
)10//4.3(
)]10//4.3)(1//(//10[
)10//4.3(
rkkR
vi
kkr
kkrhrkvg
kkr
vi
i
iA
si
e
efeom
e
co
i
o
fE
E
o
fv RR
R
i
i
i
ig
2
20
2
112 1
1cv
National United University Department of Electrical Engineering ~ Meiling CHEN
oof
fe
oeo
iif
si
RAR
h
krkkrR
A
RR
rkkRR
)1(
1
10//)10//4.3(
1
)//4.13//13//(
12
1
neglect