Feedback (2)
Section 8.2-8.4
Topics
• Feedback topologies
• Loading Effects
• Effect of Feedback on Noise
Feedback Topologies
• Types
– Voltage-voltage
– Voltage-Current
– Current-Voltage
– Current-Current
• Parameters
– Closed Loop Gain
– Input Impedance
– Output Impedance
Summary
General Comment
• Parallel Connection: Impedance fall
by 1+loop gain.
• Series Connection: Impedance Rises
by 1+loop gain
Voltage-Voltage Feedback
Sense Vout in parallel
Return Vin in series
Alternative name:
Return-Sense=Series-Shunt feedback
Ideal A0
Infinite input resistance so it can sense voltage as an ideal voltmeter.
Zero output resistance so as to serve as an ideal voltage source.
Example
(R1+R2=large so as
not to disturb Vout)
Input Resistance
Without feedback:
With feedback:
(non-ideal)
(ideal)
Example
Output Resistance
(ideal)
Example
Voltage-Voltage Feedback
Sense Vout in parallel
Return Vin in series
Voltage-Current Feedback
Sense Vout in parallel
Return current in parallel
Alternative name:
Return-Sense=Shunt-Shunt feedback
K has a dimension of conductance:
K=IF/Vout
Example
IRF=Vout/RF
K=-1/RF (- comes from the
The direction of IF)
(RF is large
in order to return
a current)
(Open-loop gain)
Assumption:
RF is large!
Or RF>>RD2
Ideal R0
Zero input impedance so that it can
Measure currents as an ideal current meter.
Zero output resistance so as to behave
as an ideal voltage source.
Calculation of Input Impedance
(small resistance)
Example
(Open loop input-impedance)
R0=RD1(-gm2RD2)
IRF=Vout/RF
K=-1/RF
Calculation of Output
Impedance
VA=(-IF)RoRout
(small resistance)
(Current drawn by
the feedback
network is
neglected)
Example
Rout=RD2
R0=RD1(-gm2RD2)
IRF=Vout/RF
K=-1/RF
Current-Voltage Feedback
Sense Iout in series
Return Vin in series
Alternative name:
Return-Sense=series-series feedback
(K=VF/Iout, hence a
dimension of resistance)
Gm
Infinite input resistance so it can sense
voltage as an ideal voltmeter.
Infinite output resistance in order to behave
as an ideal current source.
Example
(For sensing
current)
(Calculate the open loop gain)
(polarity check)
Calculation of Input Impedance
(Vin-VF)/Rin=Iin
VF=KIinRinGm
Example
Open Loop Input impedance: 1/gm
Calculation of Output
Impedance
Example
Open Loop Input impedance: 1/gm2
Current-Current Feedback
Sense Vout in parallel
Return current in parallel
Alternative name:
Return-Sense=Shunt-Shunt feedback
K has a dimension of conductance:
K=IF/Vout
Current-Current Feedback
Sense Iout in series
Return current in parallel
Alternative name:
Return-Sense=Shunt-series feedback
(current gain)
K has a dimension of conductance:
K=IF/Iout
Ideal Forward Current Amplifier
Zero input impedance in order to maximize current transfer.
Infinite output impedance in order to behave as a current source.
Polarity of Feedback
Current and Current Feedback
RM is small, therefore VP is small.
Vp is IoutRM
(RF>>1/gm1)
RF is large in order for K to behave
as a current source.
Calculation of Input Impedance
Example
Calculation of Output
Impedance
AI
Example
In Summary
Inclusion of I/O Effects
Rules for Breaking the Feedback
Network (1)
Rules for Breaking the Feedback
Network (2)
Voltage-Voltage Feedback
K is driven by a zero source impedance.
K sees the infinite input impedance of the forward amplifier.
Voltage-Current Feedback
K is driven by a zero source impedance.
K sees a zero input impedance of the forward amplifier.
Current-Voltage Feedback
K is driven by an infinite source impedance.
K sees the infinite input impedance of the forward amplifier.
Current-Current Feedback
K is driven by an infinite source impedance.
K sees the zero input impedance of the forward amplifier.
Rules for Breaking the Feedback
Network
• Applicable for both sense and return
duplicate.
– Open for series connection
– Shorted for parallel connection
Calculate the Feedback Factor
Voltage-Voltage Feedback
Voltage-Current Feedback
Current-Voltage Feedback
Current-Current Feedback
Rules for Determining the
Feedback
• If the output of the feedback depends
on voltage, open it.
• If the output of the feedback depends
on current, short it.
Voltage-Voltage Example (1)
(R1+R2 is not much larger than RD)
Voltage-Voltage Example(1)
Voltage-Voltage Example (2)
Voltage-Voltage Example (2)
Voltage-Current Example (1)
Voltage-Current Example (1)
Current-Voltage Example (1)
Current-Voltage Example (1)
Current-Current Example (1)
Current-Current Example (1)