Download Chap10part4

Shunt-Series Feedback Amplifier - Ideal Case
*
Current feedback
Current sampling
*
*
*
Feedback circuit does not load down the basic
amplifier A, i.e. doesn’t change its characteristics
 Doesn’t change gain A
 Doesn’t change pole frequencies of basic
amplifier A
 Doesn’t change Ri and Ro
For this configuration, the appropriate gain is the
CURRENT GAIN A = AIo = Io/Ii
For the feedback amplifier as a whole, feedback changes
midband current gain from AIo to AIfo
AIo
AIfo 
1   f AIo
Feedback changes input resistance from Ri to Rif
Rif 
*
Ri
1   f AIo 
Feedback changes output resistance from Ro to Rof

Rof  Ro 1   f AIo
*
Feedback changes low and high frequency 3dB
frequencies


 Hf  1   f AIo  H
ECE 352 Electronics II Winter 2003

Ch. 8 Feedback
 Lf 
L
1   f AIo


1
Shunt-Series Feedback Amplifier - Ideal Case
Gain
AIfo 
Io
A I
 Io i 
I s Ii  I f
AIo
AIo
AIo


If
 f I o 1   f AIo
1
1
Ii
Ii
Input Resistance
Rif 

Vs
Vs
Vs


I s Ii  I f
Ii   f Io
Vs

I 
I i 1   f o 
Ii 


Ri
1   f AIo 
Output Resistance
Is=0
Io ’

Vo ' Ro I o ' AIo I i 
I 

 Ro 1  AIo i 
Io '
Io '
Io ' 

But I s  0 so I i   I f
Rof 
Vo’
and I f   f I o ' so I i    f I o '
  f Io '
Ii

  f
Io '
Io '

Rof  Ro 1   f AIo
ECE 352 Electronics II Winter 2003
Ch. 8 Feedback

2
Equivalent Network for Feedback Network
*
*
*
*
*
*
*
*
ECE 352 Electronics II Winter 2003
Ch. 8 Feedback
Feedback network is a two port network
(input and output ports)
Can represent with g-parameter network
(This is the best for this feedback
amplifier configuration)
G-parameter equivalent network has
FOUR parameters
G-parameters relate input and output
currents and voltages
Two parameters chosen as independent
variables. For G-parameter network,
these are input voltages V1 and the
output current I2
Two equations relate other two quantities
(input current I1 and output V2) to these
independent variables
Knowing V1 and I2, can calculate I1 and
V2 if you know the G-parameter values
G-parameters have various units of ohms,
conductance (1/ohms=siemens) and no
units !
3
Shunt-Series Feedback Amplifier - Practical Case
*
*
*
Feedback network consists of a set of resistors
These resistors have loading effects on the basic
amplifier, i.e they change its characteristics, such as
the gain
Can use g-parameter equivalent circuit for feedback
network
 Feedback factor f given by g12 since
g12 
I1
I2

V1 0
If
f
Io
Feedforward factor given by g21 (neglected)
 g22 gives feedback network loading on output
 g11 gives feedback network loading on input
Can incorporate loading effects in a modified basic
amplifier. Gain AIo becomes a new, modified gain AIo’.
Can then use analysis from ideal case

I2
I1
g22
*
V1 g11
g12I2
g21V1
V2 *
AIo '
AIfo 
1   f AIo '
Rif 
 Hf  1   f AIo ' H
ECE 352 Electronics II Winter 2003
Ch. 8 Feedback
Ri
1  
 Lf 
f AIo '
Rof  Ro 1   f AIo '
L
1   f AIo '
4
Shunt-Series Feedback Amplifier - Practical Case
*
*
*
I2
I1
g22
V1
g11
g12I2
g21V1
ECE 352 Electronics II Winter 2003
*
V2
Ch. 8 Feedback
How do we determine the g-parameters
for the feedback network?
For the input loading term g11
 We turn off the feedback signal by
setting Io = I2 = 0.
 We then evaluate the resistance seen
looking into port 1 of the feedback
network.
For the output loading term g22
 We short circuit the connection to
the input so V1 = 0.
 We find the resistance seen looking
into port 2 of the feedback network.
To obtain the feedback factor f (also
called g12 )
 We apply a test signal Io’ to port 2 of
the feedback network and evaluate
the feedback current If (also called
I1 here) for V1 = 0.
 Find f from f = If/Io’
5
Example - Shunt-Series Feedback Amplifier
*
*
*
*
*
Two stage [CE+CE] amplifier
Transistor parameters Given:  =100, rx= 0
Input and output coupling and emitter bypass capacitors, but
direct coupling between stages
Capacitor in feedback connection removes Rf from DC bias
DC bias of two stages is coupled (bias of one affects the other)
ECE 352 Electronics II Winter 2003
Ch. 8 Feedback
6
DC Bias Analysis
Given :
1   2  100
VC1
VB2

I B1 
VB 2  VC1  VBE 2  I E 2 RE 2  0.7V    1I B 2 RE 2
RB 2
15K
12V 
12V  1.6V
RB1  RB 2
15K  100K
I B2 

I C1 0.87 m A

 34 m A/ V
VT 0.0256 V
r 1 
ECE 352 Electronics II Winter 2003

I C 2  I B 2  100 7.6 A  0.76 m A
I C1  I B1  100 8.7 A  0.87 m A (neglecting IB2 )
g m1 
3.3V  0.7V
2.6V

 7.6 A (<<IC1 =870 A)
  1RE 2 1013.4 K 

VTH 1  VBE1
1.6V  0.7V

 8.7 A
RTH 1    1RE1 13K  (101)0.87K


VC1  12 V  I C1RC1  12 V  0.87 m A10K  3.3 V
RTH 1  RB1 RB 2  100K 15K  13K
VTH 1 
rx1  rx 2  0
g m2 

100

 2.9 K
g m1 34m A/ V
r 2 
Ch. 8 Feedback
I C 2 0.76 m A

 30 m A/ V
VT
0.0256V

100

 3.3K
g m 2 30 m A/ V
7
Example - Shunt-Series Feedback Amplifier
*
Redraw circuit to show

Feedback circuit

Type of output sampling
(current in this case = Io)

Type of feedback signal to
input (current in this case = If)
Iout’
Io ’
ECE 352 Electronics II Winter 2003
Ch. 8 Feedback
Iout’
8
Example - Shunt-Series Feedback Amplifier
Iout’
Io ’
Input Loading Effects
Output Loading Effects
Io’= 0
R1
R2
R2  RF RE 2  10K 3.4 K  2.5K
R1  RF  R1  10 K  3.4 K  13.4 K
ECE 352 Electronics II Winter 2003
Ch. 8 Feedback
9
Example - Shunt-Series Feedback Amplifier
Amplifier with Loading Effects but Without Feedback
ECE 352 Electronics II Winter 2003
Ch. 8 Feedback
10
Example - Shunt-Series Feedback Amplifier
Midband Gain Analysis
Ri2
Is
IC’
Iout’
Vi2
R1
R2
I out '  I out '  I c '  V 2  Vi 2  V 1 





 
Is
I
'
V
V
V
I
 c   2  i 2   1  s 
I out '
RC 2
8K


 0.89
Ic '
RC 2  RL
8 K  1K
AIo 
Ic '
g V
 m 2  2  g m 2  30 mA / V
V 2
V 2
V 2
I  2 r 2
r
r 2
3.3K

 2 

 0.013
Vi 2
I  2 r 2  I  2 1  g m 2 r 2 R2
Ri 2
r 2  1  g m 2 r 2 R2
3.3K  1012.5 K 
Vi 2
  g m1 RC1 Ri 2   g m1 RC1 r 2  1  g m 2 r 2 R2   34 mA / V 10 K 3.3K  1012.5 K   327
V 1

 

V
 RS R1 r 1 RB1  10 K 13.4 K 2.9 K 13K  1.7 K
IS
AIo 
I out '
 0.89 30 mA / V 0.013 327 1.7 K   193
Is
ECE 352 Electronics II Winter 2003
Ch. 8 Feedback
11
Midband Gain with Feedback
*
Determine the feedback factor f
f 
*
Xf
Xo

If '
Io '

 RE 2
 3.4 K

RE 2  R f  3.4K  10K   0.25
-
Calculate gain with feedback AIfo
 f AIo  193(0.25)  48
AIfo 
VE 2   I f ' R f  I o ' I f 'RE 2
AIo
 193

 3.9
1   f AIo 1  48
 I f ' R f  RE 2   I o ' RE 2
AIfo dB  20 log 3.9  11.8 dB
*
If '
Note





f < 0 and AIo < 0
f AIo > 0 as necessary for negative feedback
and dimensionless
f AIo is large so there is significant feedback.
Can change f and the amount of feedback
by changing RF.
Gain is determined by feedback resistance
AIfo 
1
f
ECE 352 Electronics II Winter 2003

+
VE2
RE 2  R f
RE 2
Io '

 RE 2
R f ' RE 2
  4.0
Ch. 8 Feedback
12
Input and Output Resistances with Feedback
Ro
Ri
*
Determine input Ri and output Ro resistances with loading effects of feedback network.
Ri  RS R1 RB1 r1  10K 13.4K 13K 2.9K  1.7 K
*
Ro  RC 2 RL    
Calculate input Rif and output Rof resistances for the complete feedback amplifier.
Rif 

Ri
Rof  Ro (1   f AIo )  (49)  
1   f AIo 
1.7 K
 0.035K
49
ECE 352 Electronics II Winter 2003
Ch. 8 Feedback
13
Voltage Gain for Current Gain Feedback Amplifier
*
Can calculate voltage gain
 RL AIfo  1K
V 
  I 'R 
 RL  I out ' 

 
 4.2   0.42 V / V
AVfo   o    out L  

V
I
R
R
I
R
10
K
s 
s f
s
 s f  s s f
AVfo (dB)  20 log 0.42  7.5 dB
*
Note - can’t calculate the voltage gain as follows:
Assume AVfo 
Find AVo 
AVo
1   f AVo
Vo  I o RL  AIo RL  (193)1K 



 19.3 V / V
Vs
I s Rs
Rs
10 K
Calculate  f AVo   0.2519.3 V / V   4.8
AVfo 
Calculate voltage gain with feedback from
 19.3 V / V
AVo

 5.8 V / V
1   f AVo
1  4.8
Magnitude is off by nearly a factor of ten!
ECE 352 Electronics II Winter 2003
Ch. 8 Feedback
14
Equivalent Circuit for Shunt-Series Feedback Amplifier
*
*
*
Current gain amplifier A = Io/Is
Feedback modified gain, input and
output resistances
 Included loading effects of feedback
network
 Included feedback effects of
feedback network
Significant feedback, i.e.
f AIo is large and positive
 f AIo  193(0.25)  48
Rif
AIfoI i
Rof
AIfo 
AIo
1   f AIo

 193
 3.9
1  48
AIfo dB   20 log 3.9  11.8 dB
I
ARfo   o
 IS
Rif 
Ri
1  
f AIo 

AIo
 
  3.9
 f 1   f AIo
 0.035K
ECE 352 Electronics II Winter 2003
AIfo 
1
f

RE 2  R f
RE 2
  4.0
Rof  Ro (1   f AIo )  
Ch. 8 Feedback
15
Frequency Analysis
*
*
*
*
*
*
Hf  1   f ACo 'H
Lf 
ECE 352 Electronics II Winter 2003
Low frequency analysis of poles for
feedback amplifier follows Gray-Searle
(short circuit) technique as before.
Low frequency zeroes found as before.
Dominant pole used to find new low 3dB
frequency.
For high frequency poles and zeroes,
substitute hybrid-pi model with C and
C (transistor’s capacitors).
 Follow Gray-Searle (open circuit)
technique to find poles
High frequency zeroes found as before.
Dominant pole used to find new high 3dB
frequency.
L
1   f ACo '
Ch. 8 Feedback
16
Summary of Feedback Amplifier Analysis
*
Xs
Xi
Xo
Xf
f
• Calculate low frequency poles and zeroes.
• Determine dominant (highest)
low frequency pole L including loading
effects of feedback network
• Calculate new dominant low frequency
L
pole Lf .  
Lf
1   f Ao 
*
• Calculate high frequency poles and zeroes.
• Determine dominant (lowest)
high frequency pole H including loading
effects of feedback network
• Calculate new dominant high frequency
pole Hf .   1   A 
*
*
Hf

f
o
ECE 352 Electronics II Winter 2003

*
Identify the amplifier configuration by:
 Output sampling
 Io = series configuration
 Vo = shunt configuration
 Feedback to input
 Io = shunt configuration
 Vo = series configuration
Calculate loading effects of feedback
network
 On input
 On output
Calculate appropriate midband gain A’
(modified by loading effects of feedback
network)
Calculate feedback factor f.
Calculate midband gain with feedback
Af.
Afo 
Ao
1   f Ao
H
Ch. 8 Feedback
17
Summary of Feedback Amplifier Analysis
ECE 352 Electronics II Winter 2003
Ch. 8 Feedback
18