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Feedback
Section 8.1
Topics
• General Feedback
• Examples of Feedback Circuits
– Bandwidth Extension
– Gain Sensitivity
– Input and Output Impedance
• Types of Amplifiers
General Feedback System
H(s)=Feedforward network, represents an amplifier,
“Open-loop” transfer function, a.k.a. A
G(s)=Feedback network, usually frequency independent, a.k.a, β.
Y(s)/X(s)=“Closed-loop” transfer function
Behavior of a well-designed
Negative Feedback System
The error term is minimized!
An accurate copy of the input.
The input of H(s) is a virtual ground because
the error term is minimized!
Elements of Feedback System
•
•
•
•
Feed forward amplifier
Means of Sensing the Output
Feedback network
Means of Generating Feedback Error
C2 senses the output voltage, converts it to a current feedback
signal, which is added tot eh current produced by Vin through C1.
Common-Source Stage
Poor definition of the gain (gmro):
Both gm and ro depend vary with process and temperature.
Gain Desensitization Example
Assumption:
1. The frequency is low enough that C2 does
not load the output node and CGS behaves as an open circuit.
2. gmro is sufficiently large
3. Bias of the gate is not shown!
Results:
1. If C1 and C2 are made of the same material, then
Process and temperature variations do not change C1/C2.
Gain Desensitization
(Taylor series expansion)
The closed loop gain is approximately, 1/β.
If Aβ is sufficiently large, Y/X is relatively insensitive to variations
of A. Aβ is called the loop gain.
Calculation of Loop Gain
The input is set to 0.
The negative of the transfer function is the loop gain.
VF=-βAVt
Calculation of Loop Gain
Use Feedback to Desensitive
Gain
Loop Gain Calculation Example
The loading of C2
is neglected!
Common Gate Loop Gain
Example
Feed forward: M1 and RD
Feedback: R1 and R2
R1+R2>>RD
M1 operates as a subtractor.
(Loop gain)
Bandwidth Modification
Gain is reduced by 1+βAo.
Bandwidth is increased by 1+βAo
Bandwidth Modification as a
Result of Feedback
Achieving High gain and High
Bandwidth
1. Apply feedback to
Improve speed of each amplifier
2. Cascade to improve gain!
Input Impedance Modification
Example
Loop is opened!
Calculation of Loop Gain
(loop gain)
Closed Loop Input Impedance
Feedback Mechanism
(Feed forward amplifier)
Subtraction occurs in the current domain at the
Input terminal.
Output Impedance
Modification
Senses Vout
Return a current
Calculation of Output
Resistance at Low Frequencies
(Loop gain)
Linearity Improvement
Types of Amplifiers
Ideal Amplifier Models
Realistic Model
(Voltage)
Transimpedance
Transimpedance
Transconductance
More than one model is possible.
Current amplifier
Examples of Four Types of
Amplifiers
(Suffers from large output impedacne)
Amplifiers with Improved
Performance
Voltage Sensing
How do you measure voltage across a port?
1. Place a voltmeter in parallel
2. Use a voltmeter of high input impedance so
It does not disturb the circuit.
R1+R2 must be large
enough so that A1
does feel the effect
of the resistive divider.
Example: Voltage Sensing
Current Sensing
(Current Meter resistance)
Current is sensed by
measuring voltage
across r.
(Implementation)
RS is ideally small.
Return Voltage to the Input
(Differential pair implementation)
(Single-ended Implementation)
Example: Voltage Subtraction
Return Current to the Input
(KCL)
(KCL)
(Use RF large enough
to approximate current
Source)
Example
(Sensing
Achieves via
R1 and R2)
Differential pair
performs voltage subtraction.
Voltage Sensing/Current
Feedback
Input Impedance of Ideal
Feedback Networks
(Voltage Sensing)
(Current Sensing)
Output Impedance of Ideal
Feedback Networks
(Return Voltage)
(Return Current)
Polarity of Feedback
1. Assume the input signal goes up or
down
2. Follow the change through the
forward amplifier and the feedback
network
3. Determine whether the returned
quantity opposes or enhances the
original effect produced by the input
change.
Example 1
Example 2