Download Lecture I: Introduction to pattern recognition

Feedback
8 Feedback
Why Feedback?
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Desensitize the gain: make the value of the gain less sensitive
to variations in the value of circuit components, such as might
be caused by changes in temperature
Reduce nonlinear distortion: make the output proportional to
the input
Reduce the effect of noise: minimize the contribution to the
output of unwanted electric signals generated, either by the
circuit components themselves, or by extraneous interference
Control the input and output impedances: raise or lower the
input and output impedance by the selection of an appropriate
feedback topology
Extend the bandwidth of the amplifier
8 Feedback
8.1 The General Feedback Structure
xo  Axi
Af 
xo
?
xs
x f  xo
xi  xs  x f
Af 
xo
A

xs 1  A
8.2 Some Properties of Negative Feedback
8.2.1 Gain Desensitivity
Af 
xo
A

xs 1  A
Assume  is constant. Taking differentials of both sides results in
A f 
A f
Af

A
(1  A ) 2
1
A
(1  A ) A
desensitivity factor
8.2 Some Properties of Negative Feedback
8.2.2 Bandwidth Extension
A( s) 
AM
1  s / H
A( s)
1  A( s)
AM /(1  AM  )
Af ( s) 
1  s /  H (1  AM  )
Af ( s) 
Midband Gain:
AM 
AM
1  AM 
3-dB Frequency:
H  H (1  AM  )
8.2 Some Properties of Negative Feedback
8.2.3 Noise Reduction
Signal-to-Noise Ratio
S/N 
Vs
Vn
Vo  Vs
A1 A2
A1
 Vn
1  A1 A2 
1  A1 A2 
S/N 
Vs
A2
Vn
8.2 Some Properties of Negative Feedback
8.2.3 Reduction in Nonlinear Distortion
 = 0.01
1000
 90.0
1  1000  0.01
100

 50
1  100  0.01
Open Gain: 1000
Af 1 
Open Gain: 100
Af 2
8.3 The Four Basic Feedback Topologies
8.3.1 Voltage Amplifiers
Mix Feedback
Input: Voltage
Output: Voltage
Voltage-mixing voltage sampling
Series - shunt feedback
Sample Voltage
8.3 The Four Basic Feedback Topologies
8.3.2 Current Amplifiers
Mix Feedback
Input: Current
Output: Current
Current-mixing current sampling
Shunt - series feedback
Sample Current
8.3 The Four Basic Feedback Topologies
8.3.3 Transconductance Amplifiers
Mix Feedback
Input: Voltage
Output: Current
Voltage-mixing current sampling
Series - series feedback
Sample Current
8.3 The Four Basic Feedback Topologies
8.3.4 Transresistance Amplifiers
Mix Feedback
Input: Current
Output: Voltage
Current-mixing Voltage sampling
Shunt - shunt feedback
Sample Voltage
8.4 The Series-Shunt Feedback Amplifier
8.4.1 The Ideal Situation
Rif  ?
V
A
Af  o 
Vs 1  A
Rof  ?
8.4 The Series-Shunt Feedback Amplifier
8.4.1 The Ideal Situation (cont.)
Rif 
Vi  V f
Vs Vs
Vs
V
V  AVi
 
 Ri s  Ri
 Ri i
 Ri (1  A )
I s I i Vi / Ri
Vi
Vi
Vi
Z if ( s )  Z i ( s )(1  A( s )  ( s ))
Series mixing
8.4 The Series-Shunt Feedback Amplifier
8.4.1 The Ideal Situation (cont.)
Rof 
I
Shunt sampling
Vt Vt

It
I
Vt  AVi Vt  A(V f ) Vt  A( Vt ) Vt (1  A )



Ro
Ro
Ro
Ro
Rof 
Ro
1  A
Z of ( s) 
Z i ( s)
1  A( s)  ( s)
8.5 The Series-Series Feedback Amplifier
8.5.1 The Ideal Situation
Vs V f  Vi
Rif  
I i Vi / Ri
 Ri
I o  Vi
Vi
Rif  Ri (1  A )
Series mixing
 Ri
AVi  Vi
Vi
8.5 The Series-Series Feedback Amplifier
8.5.1 The Ideal Situation (cont.)
Rof 
V ( I t  AVi ) Ro

It
It
 Ro
( I t  AV f )
It
 Ro
Rof  Ro (1  A )
Series sampling
( I t  AI t )
It
8.6 The Shunt-Shunt and Shunt-Series Feedback Amplifier
8.6.1 The Shunt-Shunt Configuration
Rif 
Vi
IR
Ii
Ii
Ri
 i i  Ri
 Ri

I s Ii  I f
I i  Vo
I i  AI i 1  A
Rof 
Vo
Vo
Vo
Vo
Ro

 Ro
 Ro

I (Vo  AI i ) / Ro
Vo  AI f
Vo  AVo 1  A
8.6 The Shunt-Shunt and Shunt-Series Feedback Amplifier
8.6.3 The Shunt-Series Configuration
Rif 
Vi
IR
Ii
Ii
Ri
 i i  Ri
 Ri

I s Ii  I f
I i  I o
I i  AI i 1  A
Rof 
I o  AI f
Vo ( I o  AI i ) Ro
I  AI o

 Ro
 Ro o
 Ro (1  A )
Io
Io
Io
Io
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
Homework:
10.1, 10.3, 10.8, 10.16, 10.24, 10.26, 10.31, 10.32