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 parallelReturn 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

(non-ideal)

(ideal)

Without feedback:

With feedback:

Example

Output Resistance

(ideal)

Example

Voltage-Voltage Feedback

Sense Vout in parallel

Return Vin in series

Voltage-Current Feedback

Sense Vout in parallelReturn current in parallel

Alternative name:Return-Sense=Shunt-Shunt feedback

K has a dimension of conductance:K=IF/Vout

Example

(RF is largein order to returna current)

(Open-loop gain)Assumption:RF is large!Or RF>>RD2

IRF=Vout/RF

K=-1/RF (- comes from the The direction of IF)

Ideal R0

Zero input impedance so that it can Measure currents as an ideal current meter.

Zero output resistance so as to behaveas 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

(small resistance)

VA=(-IF)RoRout

(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 seriesReturn 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 behaveas an ideal current source.

Example

(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 parallelReturn 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 seriesReturn current in parallel

Alternative name:Return-Sense=Shunt-series feedback

K has a dimension of conductance:K=IF/Iout

(current gain)

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 FeedbackRM 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)