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Ref:080130HKN EE3110 Feedback Amplifiers 1
Lecture 2 Feedback Amplifier
• Introduction of Two-Port Network
• Negative Feedback (Uni-lateral Case)
• Feedback Topology
• Analysis of feedback applications– Close-Loop Gain– Input/Output resistances
Ref:080130HKN EE3110 Feedback Amplifiers 2
Two-Port Network (z-parameters)(Open-Circuit Impedance)
2121111 IzIzV
2221212 IzIzV
021
111
II
Vz
012
112
II
Vz
Open-circuit input impedance
At port 1
Open-circuit reverse transimpedance 012
222
II
Vz
021
221
II
Vz
At port 2
Open-circuit forwardtransimpedance
Open-circuit output impedance
V1
+
I1
V2
+
I2
z11z22
z12I2 z21I1+ +
2
1
2221
1211
2
1
I
I
zz
zz
V
V
Ref:080130HKN EE3110 Feedback Amplifiers 3
Two-Port Network (y-parameters)(Short-Circuit Admittance)
2121111 VyVyI
2221212 VyVyI
021
111
VV
Iy
012
112
VV
Iy
Short-circuit input admittance
At port 1
Short-circuit reverse transadmittance 012
222
VV
Iy
021
221
VV
Iy
At port 2
Short-circuit forwardtransadmittance
Short-circuit output admittance
V1
+
V2
+
I1 I2
1/y11 1/y22
y12V2 y21V1
2
1
2221
1211
2
1
V
V
yy
yy
I
I
Ref:080130HKN EE3110 Feedback Amplifiers 4
Two-Port Network (h-parameters)(hybrid)
2121111 VhIhV
2221212 VhIhI
021
111
VI
Vh
012
112
IV
Vh
Short-circuit input impedance
At port 1
Open-circuit reverse voltage gain 012
222
IV
Ih
021
221
VI
Ih
At port 2
Short-circuit forwardcurrent gain
Open-circuit output admittance
V2
+
I2
1/h22
h21I1
V1
+
I1
h11
h12V2 +
2
1
2221
1211
2
1
V
I
hh
hh
I
V
Ref:080130HKN EE3110 Feedback Amplifiers 5
Two-Port Network (g-parameters)(inverse-hybrid)
2121111 IgVgI
2221212 IgVgV
021
111
IV
Ig
012
112
VI
Ig
Open-circuit input admittance
At port 1
Short-circuit reverse current gain 012
222
VI
Vg
021
221
IV
Vg
At port 2
Open-circuit forwardcurrent gain
Short-circuit output impedance
V2
+
I2
g22
g21V1
V1
+
I1
1/g11
g12I2 +
2
1
2221
1211
2
1
I
V
gg
gg
V
I
Ref:080130HKN EE3110 Feedback Amplifiers 6
z-parameter exampleI1 I2
V1
+ V2
+6
I1 I2
V2
+V1
+
12
3V2
+V1
+
I1 I2312
6
30
012
00
00
312
21
221
12
112
2211
Z
II
VZ
II
VZ
ZZ
66
66
60
60
66
21
221
12
112
2211
Z
II
VZ
II
VZ
ZZ
96
618
66
0
66
0
918
1
1
21
221
2
2
12
112
2211
Z
I
I
II
VZ
I
I
II
VZ
ZZ
Note: (1) z-matrix in the last circuit = sum of two former z-matrices
(2) z-parameters is normally used in analysis of series-series circuits
(3) Z12 = Z21 (reciprocal circuit)
(4) Z12 = Z21 and Z11 = Z22 (symmetrical and reciprocal circuit)
Ref:080130HKN EE3110 Feedback Amplifiers 7
y-parameter exampleI1 I2
V1
+ V2
+
0.05S
V2
+V1
+
I1 I20.2S0.1S
0.025S
05.005.0
05.005.0
05.005.0
0
05.005.0
0
05.005.0
1
1
21
221
2
2
12
112
2211
y
V
V
VV
Iy
V
V
VV
Iy
ySy
S
S
S
0769.00615.0
0615.00692.0
S0615.0 ,reciprocalBy
S0615.0
0615.08.0025.01.0
0769.0But
0
S0769.0025.01.0
1
2.0
1
S0692.0025.02.0
1
1.0
1
1221
12
221
121
22222
12
112
1
22
1
11
y
yy
y
VII
III
VVyI
VV
Iy
y
y
Ref:080130HKN EE3110 Feedback Amplifiers 8
y-parameter example (Cont’)
V2
+V1
+
I1 I20.2S0.1S
0.025S
0.05S
1269.01115.0
1115.01192.0
1115.0
1115.005.00615.0
0615.00769.0025.01.0
1.0
0769.0
05.01269.0
05.0
1269.0
0
1269.0769.005.0
1192.0692.005.0
2112
2221
221.0
205.022.0
2205.0
22222
12
11221
22
11
Y
yy
VVVI
VVI
VIII
VII
VVyI
VV
Iyy
y
y
S
SS
S
Note: the y-matrix is equal to the sum of two former ones.Therefore, y-parameters is normally used in analysis of shunt-shunt circuits
What connection should be for h- or g- parameters?
Ref:080130HKN EE3110 Feedback Amplifiers 9
General Feedback Structure
A
Source Load+
-
Vs
Vf
V V A : Open Loop Gain A = Vo / V
: feedback factor = Vf / Vo
VAV
VVV
VV
VVV
o
oS
of
fs
1 :Note
1 :feedback ofAmount
:Gain Loop
)1
(1
1 :gain loop Close
ACL
s
oCL
A
A
AT
T
T
A
A
V
VA
Ref:080130HKN EE3110 Feedback Amplifiers 10
Negative Feedback Properties • Negative feedback takes a sample of the output signal and applies
it to the input to get several desirable properties. In amplifiers, negative feedback can be applied to get the following properties
– Desensitized gain : gain less sensitive to circuit component variations
– Reduce nonlinear distortion : output proportional to input (constant gain independent of signal level)
– Reduce effect of noise
– Control input and output impedances by applying appropriate feedback topologies
– Extend bandwidth of amplifier
• All of these properties can be achieved by trading off gain
Ref:080130HKN EE3110 Feedback Amplifiers 11
Gain De-sensitivity • Feedback can be used to desensitize the closed-loop gain to variations in the
basic amplifiler.
• Assume is constant. Take differentials of the closed loop gain equation gives,
• Divided by Av, the close loop gain sensitivity is equal to,
• This result shows the effects of variations in A on ACL is mitigated by the feed
back amount.
• (1+A) is also called the desensitivity amount.
22 )1(or
)1(
1
1 A
dAdA
AdA
dA
A
AA CL
CLCL
Differential respected with A
A
dA
AA
A
A
dA
A
dA
CL
CL
1
1)1(
)1( 2
Ref:080130HKN EE3110 Feedback Amplifiers 12
Basic Feedback TopologiesDepending on the input signal (voltage or current) to be amplified and form of the output (voltage or current), amplifiers can be classified into four categories. Depending on the amplifier category, one of four types of feedback structures should be used.
(Type of Feedback) (Type of Sensing)
(1) Series (Voltage) Shunt (Voltage)
(2) Series (Voltage) Series (Current)
(3) Shunt (Current) Shunt (Voltage)
(4) Shunt (Current) Series (Current)
Ref:080130HKN EE3110 Feedback Amplifiers 13
Feedback Structure (Series-Shunt)
Voltage amplifier voltage-controlled voltage source
Requires high input impedance, low output impedance
Voltage-voltage feedback
Voltage Gain Calculation:
)1(
1
get weAnd,
where
)1
(1
Gain) Voltage Loop (Close
AVV
A
AVV
AT
T
T
V
VA
VA
VVVV
VV
VAV
i
io
i
oCL
oo
fi
of
o
+
+
+
Basic amplifier
Feedback network
Ii +
+
Vori
ro
AV
Vf=Vo
Vi
V
Ref:080130HKN EE3110 Feedback Amplifiers 14
Input/Output Resistance (Series-Shunt)
Input Resistance:
ii
i
i
i
ii
i
i
i
rTI
VR
rT
V
r
VI
VTV
I
VR
)1(
)1(
)1(
in
in
Output Resistance (Closed loop output resistance with zero input voltage)
+AV
ro
Vo
Io
+
T
r
A
r
I
VR
r
VAVI
VV
VVV
r
VAVI
I
VR
oo
o
o
o
ooo
o
io
o
oo
o
oVi
11
0
|
out
0out
Ref:080130HKN EE3110 Feedback Amplifiers 15
h-parameter Modeling
Only uni-lateral case
will be considered :
(1) NO reverse dependent signal found in the amplifier network. |h12a| = 0
(2) NO reverse dependent signal found in the feedback network. |h21f| = 0
+
+
V1
+
zs +
V2
1/yL1/h22a
h11a
h11f
1/h22f
h12aV2
h12f V2
h21aI1
h21f I1
I1
Ref:080130HKN EE3110 Feedback Amplifiers 16
Uni-lateral
faoi
a
oi
fa
oi
a
CL
f
Lfaosfai
oi
a
Lfasfa
a
f
Lfa
a
aLfa
fsfa
hhyz
h
yz
hhyz
h
A
AA
hf
YhhyZhhz
yz
h
YhhZhh
h
V
VA
h
Yhh
IhV
IhVYhh
VhIZhhV
1221
21
1221
21
12
22221111
21
22221111
21
1
2
12
2222
1212
12122222
212111111
11
isGain Loop Closed the,feedback With the
and where
))((
Gain, LoopOpen the,0For
equation,first back to )(
Put
0)( :port output From
)( :port Input From
V21/yL1/h22a
1/h22fh21aI1
V1
zs
h11a
h11f
h12f V2
I1
+
+
Ref:080130HKN EE3110 Feedback Amplifiers 17
Series-Shunt Example
+
VVi
Vf
R1
R2
Vo
Equivalent circuit
+
AV
V
Vi
r r
+Vo
Vf Vo
R1 R2
Amplifier
Feedback
It is observed that:(1) Series connection in input ports(2) Shunt connection in output ports Series-Shunt connection h-parameter should be used.
40 and M10 ,9 ,1 ,10 :Given 215
orrkRkRA
Ref:080130HKN EE3110 Feedback Amplifiers 18
h-parameter analysis
+
h11f
h22f
h12fV2
R1
R2
V1 V2
I1
kRRRRI
I
IV
Ih
RR
R
RRI
RI
IV
Vh
RR
RRRR
VI
Vh
f
f
f
10
11
)(0
1.0)(0
9.0//0
21212
2
12
222
21
1
212
12
12
112
21
2121
21
111
1
Ref:080130HKN EE3110 Feedback Amplifiers 19
10~)1.0)(10(1
10
1A
gain, voltageloop close theAnd
10~)(
A
isgain voltageloopopen theTherefore,
11
get we,1
and puttingby
0
port,output from
~V
port,input thefrom
andcircuit loopopen for 0set Firstly,
5
5
CL
5
210
21
1
2OP
12
21
21221
2222
111
1
12
OP
OP
oo
fε
fo
f
f
A
A
ARRr
RRA
V
V
r
AVV
RRr
RRhVV
Vhr
AVV
Vhr
rV
h
01
)/1//(
))(1(
22
11
OP
fo
fOP
A
hr
rhA
out
in
R
impedance,output The
R
impedance,input The
V21/h22f
AV
V1
r
h11f
h12f V2
I1
+
+V
+
+
+
r
Ref:080130HKN EE3110 Feedback Amplifiers 20
Feedback Structure (Series-Series)
+
Basic amplifier
Feedback network
Ii
+
V ri
Vf=Io
ro
AV
I
Vi
V+
)1(
1
get weAnd,
where
)1
(1
Gain) tanceTransadmit Loop (Close
:nCalculatioGain
AVV
A
AVI
AT
T
T
V
IA
IA
IVVV
IV
VAI
i
io
i
oCL
oo
fi
of
o
Ref:080130HKN EE3110 Feedback Amplifiers 21
Input/Output Resistance (Series-Series)
Input Resistance:
i
i
i
i
rT
I
VT
I
VR
)1(
)1(
in
Output Resistance (Closed loop output resistance with zero input voltage)
oo
o
o
oo
o
oo
of
o
oV
rTI
VR
r
VIT
r
VAVI
IVV
I
VR
i
)1(
port,output from
port,input from
|
out
0out
Ref:080130HKN EE3110 Feedback Amplifiers 22
Series-Series Example
CE amplifier with an un-bypassed emitter ac small signal equivalent circuit
R1
R2 RE
RC
vs
vo
+VCC
vs vo
B
E
C
R1//R2 RC
RE
Feedback network
r+
+
r
Ref:080130HKN EE3110 Feedback Amplifiers 23
Feedback Network with z-parameter
REV1 V2
I1 I2
Ef
Ef
Ef
Rii
vZ
Rii
vZ
Rii
vz
0
0
0
12
222
12
112
21
111
Reduce equivalent circuit
+
r v
+z12fio
vo
+
rogv
io
z11f
z22f
+vs
ii
Ref:080130HKN EE3110 Feedback Amplifiers 24
Close loop analysis
)]1)([(R
:is impedanceOutput
)(
)(1)()1)((R
:is impedanceInput
11 isgain ttance transadmiloop close The
Therefore,
isgain ttance transadmiloopopen Then
and
22out
11in
11
OLf
EE
E
EEOLf
EE
E
E
E
op
opCL
Es
oop
osf
Az
RgrRr
Rr
gRrRrAzr
gRrRr
gr
Rr
gRrRr
gr
A
AA
Rr
gr
v
iA
gvivZr
rv
Ref:080130HKN EE3110 Feedback Amplifiers 25
Final Rin and Rout
+
r v
+z12fio
vo
+
rogv
io
z11f
z22f
+vs
ii
R1//R2RC
RinR'in Rout R'out
21
21inin
////])[(
////RR'
RRRgrRr
RR
EE
COPf
C
RAz
R
//)]1)([(
//RR'
22
outout
Ref:080130HKN EE3110 Feedback Amplifiers 26
Feedback Structure (Shunt-Shunt)
)1(
1
get weAnd,
where
)1
(1
Gain) anceTransimped Loop (Close
)1(
)(
)(
:nCalculatioGain
AII
A
AIV
AT
T
T
I
VA
VTAI
VVIA
VI
IIAIAV
i
io
i
oCL
oi
ooi
of
fio
Feedback network
Ii ri
If= Vo
Vi
+
I
Basic amplifier
+
Vo
ro
AI+
Ref:080130HKN EE3110 Feedback Amplifiers 27
Input/Output Resistance (Shunt-Shunt)
Input Resistance:
)1(
)1(
in
T
r
TI
rI
I
VR
i
i
i
i
Output Resistance (Closed loop output resistance with zero input voltage)
)1(
port,output from
port,input from
|
out
0out
T
r
I
VR
r
TVV
r
AIVI
VII
I
VR
o
o
o
o
oo
o
oo
of
o
oVi
Ref:080130HKN EE3110 Feedback Amplifiers 28
Shunt-Shunt Example
+
RS
RL
RC
vS
C1
C2
Vcc
RF
CE amplifier
+
Rs
r
+
V
gVRc RLVs Vo
RF
ac small signal equivalent circuit
Shunt-Shunt connection found! y-parameter
Ref:080130HKN EE3110 Feedback Amplifiers 29
F
F
F
RVV
Iy
RV
I
VV
Iy
RVV
Iy
VyVyI
VyVyI
1
0
1
0
1
0
12
222
2
2
12
112
21
111
2221212
2121111
I1 I2
V1 V2RF
V1
I1 I2
RFRF
1/RFVo
Feedback Network
y-parameter modeling
Ref:080130HKN EE3110 Feedback Amplifiers 30
OP
OPCL
F
FLCFOP
S
o
LCFo
LCF
o
FS
FS
A
AA
R
rRRRRgVA
I
V
RRRgVV
gVRRR
V
rR
VI
rRIV
1
:gain dance transimpeloop close the
,1
factor feedback With
)//)(////(
:gain ance tranimpedloopOpen
)////(
0////
port,output from And
)//(
)//(
port,input From
)( :Gain Voltage
)1(
)////(
)1(
)1(
)//(
)1(
out
in
inss
o
s
o
OP
LCF
OP
o
OP
F
OP
i
RRI
V
V
V
A
RRR
A
rR
A
rR
A
rR
Is
RF
1/RF¡ EVo
r
+
V gV
RF RC//RL
Vo
Ref:080130HKN EE3110 Feedback Amplifiers 31
Feedback Structure (Shunt-Series)
)1(
1
get weAnd,
where
)1
(1
Gain)Current Loop (Close
)1(
)(
)(
:nCalculatioGain
AII
A
AII
AT
T
T
I
IA
ITAI
IIIA
II
IIAIAI
i
io
i
oCL
oi
ooi
of
fio
Feedback network
If= Io
+
I
AI
IBasic amplifier
Ii Vi ri ro
Ref:080130HKN EE3110 Feedback Amplifiers 32
Input/Output Resistance (Shunt-Series)
Input Resistance:
)1(
)1(
in
T
r
I
rT
I
I
rI
I
VR
i
i
ii
i
i
i
i
Output Resistance (Closed loop output resistance with zero input voltage)
oo
o
oooo
ooo
ooo
of
o
oV
rTI
VR
rITIV
rAIIV
AIrVI
III
I
VR
i
)1(
)(
)(
/ port,output from
port,input from
|
out
0out
Ref:080130HKN EE3110 Feedback Amplifiers 33
SummaryFeedback Structure
Close loop gain
Input impedance
Output impedance
Parameter used
Series-Shunt
h-parameter
Series-Series
z-parameter
Shunt-Shun
y-parameter
Shunt-Series
g-parameter
)1
(1
T
T
V
V
i
o
)1
(1
T
T
V
I
i
o
)1
(1
T
T
I
V
i
o
)1
(1
T
T
I
I
i
o
irTR )1(in
irTR )1(in
T
rR i
1in
T
rR i
1in
T
rR o
1out
T
rR o
1out
orTR )1(out
orTR )1(out
Ref:080130HKN EE3110 Feedback Amplifiers 34
Supplementary
R1
RE
RC
vs
vo
+VCC
kr
kR
kR
R
E
C
10
200
2
1
1001
Find the input and output resistance from - Two port network, and - Circuit theory
Ref:080130HKN EE3110 Feedback Amplifiers 35
Circuit Theory
kRR
ivR
RrRR
Rrivriv
iR
v
r
vvi
i
vRRRR
Cout
bsout
Ein
EbEbs
bE
EEsb
b
sin
1
00 , find To
100~])1(//[
])1([
)1( and but
where//
1
1
R1
RE
RC
vs vo ib
ib
rvE
Ref:080130HKN EE3110 Feedback Amplifiers 36
Two Port Network
RE
vs vo ib
ib
r
RE RE
+RE i2
RE
Ef
Ef
Ef
Rii
vZ
Rii
vZ
Rii
vz
0
0
0
12
222
12
112
21
111
Ref:080130HKN EE3110 Feedback Amplifiers 37
kRRRR
RRRR
RRr
RR
RRr
RrR
RrRri
i
v
iA
ii
Rriv
CCoutout
inin
EE
Eout
EE
Ein
EEb
b
s
oOL
bo
Ebs
1~//
100~//
)(1
)(1)(
)()(
)(
0 signalfeedback settingby found isGain tanceTransadmit LoopOpen The
11
+
r
RE
RE io
RE
vs vo
ib
ib
RinR'in Rout R'out
R1 RC
Recommended