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IntroductionFeedback loop gain, stability

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Introduction

• Physical systems incorporate some form of feedback

• Theory of negative feedback developed by Electrical Engineers.

• Feedback theory used in modeling of systems.

• Negative or Positive Feedback

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Today

• Stability• Loop Eqn

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Sampling & MixingHere, we look at feedback ckts

voltage-sampling series-mixing (series-shunt) topology

β

β

AA

xxA

xxAxx

sf

f

i

+==

==

10

0

0

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current-sampling shunt-mixing (shunt-series) topology

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current-sampling series-mixing (series-series) topology

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voltage-sampling shunt-mixing (shunt-shunt) topology.

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Series-shunt feedback amplifier:

• Ideal ckt

• Equivalent ckt.

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Measuring the output resistance of the voltage-sampling

series-mixing (series-shunt) topology

feedback amplifier of Rof ≡ Vt/I.

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Derivation of the A circuit and β circuit for the series-shunt feedback amplifier.

(a) Block diagram of a practical series-shunt feedback amplifier.

(b) The circuit in (a) with the feedback network represented by its hparameters.

(c) The circuit in (b) after neglecting h21.

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Summary of the rules for finding the Acircuit and β for the voltage-sampling

series-mixing

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Example 8.1

• Amplifier shown, find simplified feedback models

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(a) ideal structure;

(b) equivalent circuit.

Series-series feedback amplifier

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Ideal structure for the shunt-shunt feedback amplifier.

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Shunt-shunt feedback amplifier.

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Finding the Acircuit and β for the voltage-sampling shunt-mixing (shunt-shunt) case.

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Ideal structure

Shunt-series feedback amplifier.

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Block diagram

Shunt-series feedback

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Finding the A circuit and β for the current-sampling shunt-mixing (shunt-series) case.

Amplifier instability

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)()(1)()(

180180

180180 ωβω

ωωjjA

jAjAf +=

999.0)()( 180180 −=ωβω jjA

A(jώ180) =999β(jώ180) = -0.001

)sin(1.0)( 180ttxi ω= )sin(100)( 180ttxo ω=

)sin(1.0)( 180ttx f ω−=

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Bode plot for the loop gain Aβ illustrating the definitions of the gain and phase margins.

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Stability analysis using Bode plot of |A|.

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Frequency compensation for β = 10-2.

• The response labeled A’ is obtained by introducing an additional pole at fD.

•The A” response is obtained by moving the original low-frequency pole to f’D.