# Feedback (2) Section 8.2-8.4.

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Feedback (2) Section

Feedback Topologies Types Parameters 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 (RF is large in order to return a current)
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 (polarity check) (Calculate the open loop gain) (For sensing
current) (polarity check) (Calculate the open loop gain)

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)