Lecture 25
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• Reminder: Prof. Liu’s office hour is cancelled on Tuesday 12/4
OUTLINE
• Feedback
– General considerations
– Benefits of negative feedback
– Sense and return techniques
– Voltage-voltage feedback
Reading: Chapter 12.1-12.2,12.4,12.6.1
EE105 Fall 2007
Lecture 25, Slide 1
Prof. Liu, UC Berkeley
Negative Feedback System
• A negative feedback system consists of four components:
1) feedforward system, 2) sense mechanism, 3) feedback
network, and 4) comparison mechanism.
VY
A1
• Closed loop transfer function:

V X 1  KA1
EE105 Fall 2007
Lecture 25, Slide 2
Prof. Liu, UC Berkeley
Negative Feedback Example
• The amplifier is the feedforward system, R1 and R2 provide the
sensing and feedback capabilities, and comparison is provided
by differential input to the amplifier.
VY

VX 1 
EE105 Fall 2007
Lecture 25, Slide 3
A1
R2
A1
R1  R2
Prof. Liu, UC Berkeley
Comparison Error
• As A1K increases, the difference between the input and fed
back signal decreases, i.e. the fed back signal becomes a good
replica of the input.
VX
E
1 A1 K
E
EE105 Fall 2007
Lecture 25, Slide 4
Prof. Liu, UC Berkeley
Comparison Error Example
VY
R1
 1
VX
R2
EE105 Fall 2007
Lecture 25, Slide 5
Prof. Liu, UC Berkeley
Loop Gain
• The loop gain is the product of the gain of the feedforward
system (A1) and the feedback factor (K). It can be interpreted
to be the gain if a signal “goes around the loop,” i.e. if we
break the loop at an arbitrary location, then apply a test
voltage at one end and determine the voltage that comes out
at the other end, with the input grounded:
VX  0
EE105 Fall 2007
VN
KA1  
Vtest
Lecture 25, Slide 6
Prof. Liu, UC Berkeley
Benefit #1: Gain Desensitization
• A large loop gain is needed to achieve a precise gain, one that
does not depend on A1, which can vary by ±20%.
A1 K  1
EE105 Fall 2007
VY
1

VX K
Lecture 25, Slide 7
Prof. Liu, UC Berkeley
Ratio of Resistor Values
• If two resistors are built using the same unit resistor, then the
ratio of their resistances does not change with variations in
the fabrication process and the circuit operating temperature.
Thus, the ratio of two resistances can be more precisely
controlled than the open loop gain (A1) of an amplifier.
EE105 Fall 2007
Lecture 25, Slide 8
Prof. Liu, UC Berkeley
Example
Open Loop Gain
A1  g m RD
EE105 Fall 2007
Closed Loop Gain
vout

vin
Lecture 25, Slide 9
g m RD
R2
1
g m RD
R1  R2
Prof. Liu, UC Berkeley
Desensitization to Load Variation
w/o Feedback
with Feedback
Large Difference
Small Difference
g m RD  g m RD / 3
EE105 Fall 2007
g m RD
g m RD

R2
R2
1
g m RD
3
g m RD
R1  R2
R1  R2
Lecture 25, Slide 10
Prof. Liu, UC Berkeley
Benefit #2: Bandwidth Enhancement
• Although negative feedback lowers the gain by (1+KA1), it
increases the bandwidth by the same factor.
Open Loop
A1  j  
A0
j
1
0
EE105 Fall 2007
Closed Loop
Negative
Feedback
A0
1  KA0
VY
 j  
j
VX
1
1  KA0 0
Lecture 25, Slide 11
Prof. Liu, UC Berkeley
Bandwidth Enhancement Example
• As the loop gain increases, the low-frequency gain decreases
and the bandwidth increases.
EE105 Fall 2007
Lecture 25, Slide 12
Prof. Liu, UC Berkeley
Benefit #3: Modification of I/O Impedances
Open Loop
1
Rin 
gm
EE105 Fall 2007
Closed Loop

R2
1 
1 
Rin 
g m RD 
g m  R1  R2

Lecture 25, Slide 13
Prof. Liu, UC Berkeley
Modification of I/O Impedances (cont’d)
Open Loop
Rout  RD
EE105 Fall 2007
Closed Loop
Rout
Lecture 25, Slide 14
RD

R2
1
g m RD
R1  R2
Prof. Liu, UC Berkeley
Benefit #4: Linearity Improvement
w/o feedback
with feedback
EE105 Fall 2007
Lecture 25, Slide 15
Prof. Liu, UC Berkeley
Sensing a Voltage
• In order to sense a voltage across two terminals, a voltmeter
with ideally infinite impedance is used.
EE105 Fall 2007
Lecture 25, Slide 16
Prof. Liu, UC Berkeley
Sensing and Returning a Voltage
• Similarly, for a feedback network to correctly sense the output
voltage, its input impedance needs to be large.
• R1 and R2 also provide a means to return the voltage.
– To return a voltage, the output impedance of an ideal feedback
network should be small.
Feedback
Network
R1  R2  
EE105 Fall 2007
Lecture 25, Slide 17
Prof. Liu, UC Berkeley
Example: Sense and Return
• R1 and R2 sense and return the output voltage to the
feedforward network consisting of M1, M2, M3, and M4.
• M1 and M2 also act as a voltage comparator.
EE105 Fall 2007
Lecture 25, Slide 18
Prof. Liu, UC Berkeley
Example (cont’d)
Vout

Vin
EE105 Fall 2007
g mN ( rON || rOP )
R2
1
g mN ( rON || rOP )
R1  R2
Lecture 25, Slide 19
Prof. Liu, UC Berkeley
Input Impedance with Feedback
• Negative feedback raises the input impedance.
Vin
 Rin (1  A0 K )
I in
EE105 Fall 2007
Lecture 25, Slide 20
Prof. Liu, UC Berkeley
Output Impedance with Feedback
• Negative feedback lowers the output impedance.
Rout
VX

I X 1  KA0 
EE105 Fall 2007
Lecture 25, Slide 21
Prof. Liu, UC Berkeley
Example
Rout,closed 
EE105 Fall 2007
roN roP
R2
1
g mN roN
R1  R2

R1  1

 1 
R2  g mN
roP  
Lecture 25, Slide 22
Prof. Liu, UC Berkeley
Summary: Benefits of Negative Feedback
1) Gain desensitization
to variations in gm, RD, RL
2) Bandwidth enhancement
by the factor (1 + loop gain)
3) Modification of I/O impedances
– Rin is increased by the factor (1 + loop gain)
– Rout is decreased by the factor (1 + loop gain)
4) Linearity improvement
– Gain is more uniform for different signal levels.
EE105 Fall 2007
Lecture 25, Slide 23
Prof. Liu, UC Berkeley