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FeedbackFeedback
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.
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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.