chapter 8 - feedback 1 - desensitize the gain 2 - reduce nonlinear distortions 3 - reduce the effect...
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Chapter 8 - Feedback
1 - Desensitize The Gain
2 - Reduce Nonlinear Distortions
3 - Reduce The Effect of Noise
4 – Control The Input And Output Impedances
5 – Extend The Bandwidth Of The Amplifier
The General Feedback Structure
xs xi xf xo
A
xo A xi
xi xs xf
xf xo
Af
xo
xs
A
1 A
A 1 A
feedabck factor loop gain amount of feedabck
x fA
1 A x s
The General Feedback Structure
MATLAB / SIMULINK
Anyone interested to put together an Introduction to MATLAB / Simulink PowerPoint Presentation plus some examples?
The General Feedback Structure
Exercise 8.1
Af 10 A 104
a ) R1
R1 R2
b ) AfA
1 A
1
given
AfA
1 A
Find 0.1
R1
R1 R20.1
R2
R19
Amount_Feedback 20 log 1 A c )
Amount_Feedback 60
Vs 1 Vo Af Vs Vo 10d )
Vf Vo Vf 0.999
Vi Vs Vf Vi 10 104
e ) A 0.8 104
AfA
1 A Af 9.998
10 9.99810
100 0.02
The General Feedback Structure
Exercise 8.1
Some Properties of Negative Feedback
Gain Desensitivity
AfA
1 A
deriving
dAfdA
1 A ( )2
dividing by AfA
1 A
dAf
Af
1
1 A ( )
dA
A
The percentage change in Af (due to variations in some circuit parameter) is smaller than the pecentage cahnge in A by the amount of feedback. For this reason the amount of feedback
1 A
is also known as the desensitivity factor.
Some Properties of Negative Feedback
Bandwidth Extension
High frequency response with a single pole
A s( )AM
1s
H
AM denotes the midband gain and H the upper 3-dB frequency
Af s( )A s( )
1 A s( )
Af s( )
AM
1 AM
1s
H 1 AM
Hf H 1 AM Lf
L
1 AM
Some Properties of Negative Feedback
Noise Reduction, Reduction of Nonlinear Distortion
Read and discuss in class
The Four Basic Feedback Topologies
Voltage Amplifiers (V/V)
Current Amplifiers (I/I)
Transconductance Amplifiers (I/V)
Transresistance Amplifiers (V/I)
The four basic feedback topologies:
(a) voltage-sampling series-mixing (series-shunt) topology;
(b) current-sampling shunt-mixing (shunt-series) topology;
(c) current-sampling series-mixing (series-series) topology;
(d) voltage-sampling shunt-mixing (shunt-shunt) topology.
The Four Basic Feedback Topologies
The Four Basic Feedback Topologies
Voltage AmplifiersVCVSInput Resistance HighOutput Resistance LowFeedback sample the output voltageVoltage-sampling series-mixing
Current Amplifiers
Transconductance Amplifiers
Transresistance Amplifiers
The Shunt-Series Feedback Amplifier
The Ideal Situation
The series-shunt feedback amplifier:
(a) ideal structure; (b) equivalent circuit.
AfVo
Vs
A
1 A
RifVs
Ii
Vs
Vi
Ri
RiVs
Vi Ri
Vi A Vi
Vi
Rif Ri 1 A
Zif s( ) Zi s( ) 1 A s( ) s( )
Z of s( )Z o s( )
1 A s( ) s( )
The Shunt-Series Feedback Amplifier
The Practical Situation
Derivation of the A circuit and circuit for the series-shunt feedback amplifier.
(a) Block diagram of a practical series-shunt feedback amplifier.
(b) The circuit in (a) with the feedback network represented by its h parameters.
(c) (c) The circuit in (b) after neglecting h21.
The Shunt-Series Feedback Amplifier
Summary
For Finding the A Circuit for a given series-shunt feedback amplifier.
The Shunt-Series Feedback Amplifier
Example 8.1
AVo'
Vi'
RL R1 R2( )[ ]
RL R1 R2
RL R1 R2( )[ ]
RL R1 R2ro
Rid
Rid RsR1 R2
R1 R2
Rif Ri 1 A Vf
Vo''
R1
R1 R2Ri Rs Rid
R1 R2R1 R2
Rin Rif RsAf
Vo
Vf
A
1 A
RofRo
1 A
Ro
roRL R1 R2( )RL R1 R2
roRL R1 R2( )RL R1 R2
The Shunt-Series Feedback Amplifier
Exercise 8.4
The Series-Series Feedback Amplifier
The Ideal Case
The Series-Series Feedback Amplifier
The Ideal Practical Case
The Series-Series Feedback Amplifier
For Finding the A Circuit for a given series-series feedback amplifier
The Series-Series Feedback Amplifier
Example 8.2
The Series-Series Feedback Amplifier
Example 8.2
The Series-Series Feedback Amplifier
Example 8.2Gain of the first stage
Vc1
Vi1
1RC1 r2
RC1 r2
re1
RE1 RF RE2
RE1 RF RE2
Since Q1 is biased at 0.6mA, re1=41.7ohms
Q2 is biased at 1mA
r2
hfe
gm2
100
402.5kohms
substituting
1 0.99 RC1 9kohms RE1 100ohms
RF 640ohms RE2 100ohms
Vc1
Vi114.92
V
V
The Series-Series Feedback Amplifier
Example 8.2
The Shunt-Shunt and Shunt-Series Feedback Amplifiers
Shunt Configuration
The Shunt-Shunt and Shunt-Series Feedback Amplifiers
The Shunt-Shunt and Shunt-Series Feedback Amplifiers
Example 8.3
The Shunt-Series Feedback Amplifier
The Shunt-Series Feedback Amplifier
The Shunt-Series Feedback Amplifier
Example 8.4
The Shunt-Series Feedback Amplifier
Example 8.4
Determining Loop Gain
The Stability Problem and Margins
Closed-LoopTransfer Function
Nyquist
Root-Locus
Bode
Polar Plot
Af s( )A s( )
1 A s( ) s( )The Nyquist Plot intersects the negative real axis at 180. If this intersection occurs to the left of the point (-1, 0), we know that the magnitude of the loop gain at this frequency is greater than the unity and the system will be unstable. If the intersection occurs to the right of the point (-1,0) the system will be stable.It follows that if the Nyquist encircles the point (-1,0) the amplifier will be unstable.
The Stability Problem and Margins
Closed-LoopTransfer Function
Nyquist
Root-Locus
BodeMagnitude and Phase
Gain MarginPhase Margin - If at the frequency of unity loop-gain magnitude, the phase lag is in excess of 180 degrees, the amplifier is unstable.
The Nyquist Plot
w 100 99.9 100 j 1 s w( ) j w f w( ) 1
G w( )50 4.6
s w( )3
9 s w( )2 30 s w( ) 40
2 1 0 1 2 3 4 5 65
0
5
Im G w( )( )
0
Re G w( )( )
Effect of Feedback On The Amplifier Poles
Stability Study Using Bode Plots
w .1 .11 2 K 2 j 1
G w( )K
j w j w 1( ) j w 2( )
Bode1 w( ) 20 log G w( )
0 0.5 1 1.5 220
0
20
Bode1 w( )
w
Open Loop Bode Diagram
T w( )G w( )
1 G w( )
0 0.5 1 1.5 220
0
20
Bode1 w( )
w
T w( )G w( )
1 G w( )
Bode2 w( ) 20 log T w( )
0.5 1 1.5 220
10
0
10
Bode2 w( )
w
Closed-Loop Bode Diagram
Frequency Compensation
Spice Simulation Examples