2006-04-25-Ling82a Feedback in Amplifiers I

7/29/2019 2006-04-25-Ling82a Feedback in Amplifiers I

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Feedback in Amplifiers

Four Amplifier Types

Part 1

CopyrightCopyright The McGrawThe McGraw--Hill Companies, Inc. Permission required for reproduction or disHill Companies, Inc. Permission required for reproduction or display.play.


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Amplifier Types


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Input and Output Impedance

Voltage Amplifier: Large Rin , Low Rout

Transimpedance Amplifier: Low Rin , LowRout

Transconductance Amplifier: Large Rin ,Large Rout

Current Amplifier: Low Rin , Large Rout


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Gain Units

Voltage Amplifier: [A]=V/V, []=V/V

Transimpedance Amplifier: [A]=V/A,[]=A/V

Transconductance Amplifier: [A]=A/V,[]=V/A

Current Amplifier: [A]=A/A, []=A/A Loop Gain A is always unit-less.


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Amplifier Types Illustrated

CS amplifier can be used to implement simple voltage

and transconductance amplifiers - (a) and (c). CG amplifier can be implemented simpletransimpedance and current amplifiers (b) and (d).


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Improvements to Previous

Examples of Amplifiers Types

AddSourceFollower

todecreaseoutputresistance.


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Improvements to Previous

Examples of Amplifiers Types

Add CS(possibly withdegeneration)

to increaseoutputresistance.


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Sense Mechanisms (at output)

To sense voltage connect in parallel (like usinga voltmeter) Shunt feedback

To sense current connect in series (like usingan ammeter) Series feedback

Practical ammeter: A small resistor RS we

read voltage drop across resistor.


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Feedback Summation Mechanisms (at

input)

Go back to Kirchhoffs basics:

Current Addition: Create a node where input andfeedback currents meet.

Voltage Addition: Create a loop along which

input and feedback voltages reside.


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Feedback Subtraction at input

Current Subtraction: Create a node where inputand feedback currents meet. Let feedback

current come at opposite polarity. Voltage Addition: Create a loop along whichinput and feedback voltages reside. Let

feedback voltage come at opposite polarity.


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Examples: Feedback sensing andsubtraction Mechanisms

(a): Voltage sensing: Use resistive or capacitivevoltage divider.


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(b) And (c): Current sensing: Place small resistor in

series with wire carrying the current of interest. Usevoltage across this resistor.


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(d) Voltage subtraction: Can use a differentialamplifier.


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(e) and (f) Voltage Subtraction: Single transistorimplementation. ID depends on VGS = Vin - VF


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Note: For voltage subtraction voltages need tobe at two distinct nodes.


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Current subtraction mechanisms:

For current subtraction both input and feedbacksignals must be brought to the same node.


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Voltage-Voltage Amplifier Topology

Series atinput

Shunt at

output

Ideally, feedback network does not load theforward amplifier.

Practically, we try that feedback networks inputand output impedances be as shown above.


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Ideal Voltage-Voltage Gain

Derivation

Shunt at

output

Series atinput

VF=Vout where is a fraction resulting fromvoltage division.

Ve=Vin-VF if subtraction is implemented correctly.That is, if VF comes at the correct polarity.


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Ideal Voltage-Voltage Gain Result

Series atinput

Shunt at

output

Vout=A0(Vin-Vout) neglecting loading effects.Result: Vout/Vin=A0/(1+A0)

In practical computations we include feedbackloading within A0.


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Series atinput

Shunt at

output

Implementation

of usingresistive voltagedivision.


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Series atinput

Shunt at

output

Implementation

of subtractionusing differentialamplifying

Id l l l O


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Ideal voltage-voltage Output

Impedance Modification - Goal

Ideally we want that Vout be independent of loadresistance R

L.

For that we want the closed-loop Rout to be assmall as possible.


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Ideal voltage-voltage Output

Impedance Modification Setup

Let Rout be the output resistance of the forwardamplifier.

Input command is set to zero when testing forthe output resistance.

Id l O t t I d


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Ideal Output Impedance

Modification Computation

IX =VX

VM

Rout

=

VX

(

A

0VX )

Rout

VX

IX

= Rout,CL =

Rout

1+A0

Assuming thatno current goesto feedback


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Example: Differential Amplifier with Current MirrorLoad and Capacitive Voltage Division Feedback

DC Bias of M2 is not shown. Calculate gain and output resistance at relatively

low frequencies.


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Forward Gain Computation

At low frequencies capacitors dont load theamplifier. Therefore A0=gm1(ro2||ro4)

Shown above: To see loading at output we kill

the feedbackby grounding the output node.


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Loop Gain Computation

VF= - Vt(C1/(C1+C2))gm1(ro2||ro4)

A0= (C1/(C1+C2))gm1(ro2||ro4)


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Closed-Loop Gain

Lets substitute A0 and A0 into the closed-loop

gain formula: Vout/Vin=A0/(1+A0)=

=gm1(r02||ro4)/ [1+(C1/(C1+C2))gm1(ro2||ro4)]

1+(C2/C1)


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Closed-Loop Output Resistance

Recall: Open-loop Rout= ro2||ro4

Closed-loop Rout= (ro2||ro4) /(1+A0)==(r02||ro4)/ [1+(C1/(C1+C2))gm1(ro2||ro4)]

[1+(C2/C1)](1/gm1) independent of ro2||ro4.

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2006-04-25-Ling82a Feedback in Amplifiers I