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Feedback (2) Section

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Topics Feedback topologies Loading Effects Effect of Feedback on Noise

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**Feedback Topologies Types Parameters Voltage-voltage Voltage-Current**

Current-Voltage Current-Current Parameters Closed Loop Gain Input Impedance Output Impedance

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Summary

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**General Comment Parallel Connection: Impedance fall by 1+loop gain.**

Series Connection: Impedance Rises by 1+loop gain

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**Voltage-Voltage Feedback**

Sense Vout in parallel Return Vin in series Alternative name: Return-Sense=Series-Shunt feedback

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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.

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Example (R1+R2=large so as not to disturb Vout)

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Input Resistance Without feedback: With feedback: (non-ideal) (ideal)

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Example

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Output Resistance (ideal)

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Example

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**Voltage-Voltage Feedback**

Sense Vout in parallel Return Vin in series

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**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

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**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

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**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.

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**Calculation of Input Impedance**

(small resistance)

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**Example (Open loop input-impedance) R0=RD1(-gm2RD2) IRF=Vout/RF**

K=-1/RF

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**Calculation of Output Impedance**

VA=(-IF)RoRout (small resistance) (Current drawn by the feedback network is neglected)

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Example Rout=RD2 R0=RD1(-gm2RD2) IRF=Vout/RF K=-1/RF

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**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)

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**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.

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**Example (polarity check) (Calculate the open loop gain) (For sensing**

current) (polarity check) (Calculate the open loop gain)

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**Calculation of Input Impedance**

(Vin-VF)/Rin=Iin VF=KIinRinGm

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Example Open Loop Input impedance: 1/gm

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**Calculation of Output Impedance**

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Example Open Loop Input impedance: 1/gm2

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**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

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**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

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**Ideal Forward Current Amplifier**

Zero input impedance in order to maximize current transfer. Infinite output impedance in order to behave as a current source.

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Polarity of Feedback

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**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.

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**Calculation of Input Impedance**

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Example

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**Calculation of Output Impedance**

AI

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Example

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In Summary

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**Inclusion of I/O Effects**

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**Rules for Breaking the Feedback Network (1)**

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**Rules for Breaking the Feedback Network (2)**

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**Voltage-Voltage Feedback**

K is driven by a zero source impedance. K sees the infinite input impedance of the forward amplifier.

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**Voltage-Current Feedback**

K is driven by a zero source impedance. K sees a zero input impedance of the forward amplifier.

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**Current-Voltage Feedback**

K is driven by an infinite source impedance. K sees the infinite input impedance of the forward amplifier.

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**Current-Current Feedback**

K is driven by an infinite source impedance. K sees the zero input impedance of the forward amplifier.

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**Rules for Breaking the Feedback Network**

Applicable for both sense and return duplicate. Open for series connection Shorted for parallel connection

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**Calculate the Feedback Factor**

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**Voltage-Voltage Feedback**

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**Voltage-Current Feedback**

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**Current-Voltage Feedback**

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**Current-Current Feedback**

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**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.

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**Voltage-Voltage Example (1)**

(R1+R2 is not much larger than RD)

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**Voltage-Voltage Example(1)**

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**Voltage-Voltage Example (2)**

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**Voltage-Voltage Example (2)**

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**Voltage-Current Example (1)**

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**Voltage-Current Example (1)**

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**Current-Voltage Example (1)**

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**Current-Voltage Example (1)**

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**Current-Current Example (1)**

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**Current-Current Example (1)**

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