Chapter 8 Feedback

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Chapter 8 Feedback
Introduction 8.1 The general feedback
structure 8.2 Some properties of negative
feedback 8.3 The four basic feedback
topologies 8.4 The series-shunt feedback
amplifier 8.5 The series-series feedback
amplifier 8.6 The shunt-shunt and shunt-series
feedback amplifier 8.10 Stability study using
bode plot 8.11 Frequency compensation
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Introduction

• Its impossible to think of electronic circuits
  without some forms of feedback.
• Negative feedback
• Desensitize the gain
• Reduce nonlinear distortion
• Reduce the effect of noise
• Control the input and output impedance
• Extend the bandwidth of the amplifier
• The basic idea of negative feedback is to trade
  off between gain and other desirable properties.
• Positive feedback will cause the amplifier
  oscillation.

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Three Parts

• PartI The basic concept and some Properties of
  negative feedback
• PartII The four basic feedback and analysis
• PartIII The loop gain, stability problem
• and frequency compensation

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PartI
The basic concept
Judgment and Properties of feedback
examples
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PartI The basic concept and some Properties of
negative feedback
8.1 The General Feedback Structure
This is a signal-flow diagram, and the quantities
x represent either voltage or current signals. In
electronic circuits, part of or all output signal
is fed back to input, and affects the input
signal value, which is called feedback.
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The feedback judgment for amplifier circuits
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Negative feedback and positive feedback According
to the effecting of feedback 1) positive
feedback increases the signal that appears
at the input of the basic amplifier 2) negative
feedback reduces the signal that appears at
the input of the basic amplifier

• DC feedback and AC feedback
• Feedback quantity only contains DC quantity,is
  called DC
• feedback
• 2) Feedback quantity only contains AC quantity,is
  called AC
• feedback
• Usually AC feedback and DC feedback are
  concomitant

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The feedback judgment

1. No feedback
2. Feedback exists
3. No feedback

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The judgment of feedback parity
Instantaneous polarity method
1) Regulate the polarity of input signal relative
to ground at sometime.
2) Decide all points parity step by step, at
last get the parity of output signal.
3) According to the parity of output signal
decides the parity of amount of feedback.
4) If amount of feedback increases the signal
that appears at the input of the basic
amplifier, the circuit inducts the positive
feedback. Otherwise, it inducts the
negative feedback.
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To integrated operational amplifiers,the input
quantity can be UD or iN(iP)
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To discrete components amplifiers,the input
quantity can be Ube or ib
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The judgment of DC feedback and AC feedback
DC feedback,no AC feedback
AC feedback,no DC feedback
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Example feedback?Positive or negative?DC or AC?
AC and DC negative feedback
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The General Feedback Equation

• Open loop gain A
• Feedback factor ß
• Loop gain Aß
• Closed loop gain Af
• Amount of feedback (1 Aß)

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The General Feedback Equation

• If Aß gtgt1, The gain of the feedback amplifier is
  almost entirely determined by the feedback
  network.
• If Aß gtgt1, which implies that the signal Xi at
  the input of the basic amplifier is reduced to
  almost zero.

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8.2 Some Properties of Negative Feedback

• Gain desensitivity

the percentage change in Af (due to variations in
some circuit parameter) is smaller than the
percentage change in A by the amount of feedback.
For this reason the amount of feedback, 1 Aß,
is also known as the desensitivity factor.
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Some Properties of Negative Feedback

• 2. Bandwidth extension

Note that the amplifier bandwidth is increased by
the same factor by which its midband gain is
decreased, maintaining the gain-bandwidth product
at a constant value.
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Some Properties of Negative Feedback

• 3. Noise reduction

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Some Properties of Negative Feedback

• 4. Reduction in nonlinear distortion

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Some Properties of Negative Feedback

• 4. Reduction in nonlinear distortion

21
Homework

• May 11th, 2008
• 8.1 8.7

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PartIIThe four basic feedback and analysis
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8.3 The Four Basic Feedback Topologies

• Voltage amplifier---series-shunt feedback
• voltage mixing and voltage sampling

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The Four Basic Feedback Topologies

• Current amplifier---shunt-series feedback
• Current mixing and current sampling

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Example
Figure 8.5 A transistor amplifier with
shuntseries feedback. (Biasing not shown.)
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The Four Basic Feedback Topologies

• Transconductance amplifier---series-series
  feedback
• Voltage mixing and current sampling

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Example
Figure 8.6 An example of the seriesseries
feedback topology. (Biasing not shown.)
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The Four Basic Feedback Topologies

• Transresistance amplifier---shunt-shunt feedback
• Current mixing and voltage sampling

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Example
Figure 8.7 (a) The inverting op-amp
configuration redrawn as (b) an example of
shuntshunt feedback.
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Homework

• May 11nd, 2008
• 8.14 8.15 8.17 8.19

31
8.4 The Series-Shunt Feedback Amplifier

• The ideal situation
• The practical situation
• Summary

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The Ideal Situation

• A unilateral open-loop amplifier (A circuit).
• An ideal voltage mixing voltage sampling feedback
  network (ß circuit).
• Assumption that the source and load resistance
  have been included inside the A circuit.

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The Ideal Situation
Equivalent circuit. Rif and Rof denote the input
and output resistance with feedback.
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Input and Output Resistance with Feedback

• Input resistance
• In this case, the negative feedback
  increases the input resistance by a factor equal
  to the amount of feedback.
• Output resistance
• In this case, the negative feedback reduces
  the output resistance by a factor equal to the
  amount of feedback.

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The Practical Situation

• Block diagram of a practical seriesshunt
  feedback amplifier.
• Feedback network is not ideal and load the basic
  amplifier thus affect the values of gain, input
  resistance and output resistance.

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The Practical Situation
The circuit in (a) with the feedback network
represented by its h parameters.
Omit the controlled source h21I1
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The Practical Situation
The circuit in (b) with h21 neglected.
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The Practical Situation

• The load effect of the feedback network on the
  basic amplifier is represented by the components
  h11 and h22.
• The loading effect is found by looking into the
  appropriate port of the feedback network while
  the port is open-circuit or short-circuit so as
  to destroy the feedback.
• If the connection is a shunt one, short-circuit
  the port.
• If the connection is a series one, open-circuit
  the port.
• Determine the ß.

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Summary

• Ri and Ro are the input and output resistances,
  respectively, of the A circuit.
• Rif and Rof are the input and output resistances,
  respectively, of the feedback amplifier,
  including Rs and RL.
• The actual input and output resistances exclude
  Rs and RL.

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Example of Series-Shunt Feedback Amplifier
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Example of Series-Shunt Feedback Amplifier

• Op amplifier connected in noninverting
  configuration with the open-loop gain µ, Rid and
  ro
• Find expression for A, ß, the closed-loop gain
  Vo/Vi , the input resistance Rin and the output
  resistance Rout
• Find numerical values

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Example of Series-Shunt Feedback Amplifier
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Example of Series-Shunt Feedback Amplifier
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8.5 The Series-Series Feedback Amplifier

• The ideal situation
• The practical situation
• Summary

46
The Ideal Situation
Transconductance gain
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The Ideal Situation
Tranresistance feedback factor
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Input and Output Resistance with Feedback

• Input resistance
• In this case, the negative feedback increases
  the input resistance by a factor equal to the
  amount of feedback.
• Output resistance
• In this case, the negative feedback
  increases the output resistance by a factor equal
  to the amount of feedback.

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The Practical Situation
Block diagram of a practical seriesseries
feedback amplifier. Feedback network is not
ideal and load the basic amplifier thus affect
the values of gain, input resistance and output
resistance.
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The Practical Situation
The circuit of (a) with the feedback network
represented by its z parameters.
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The Practical Situation
A redrawing of the circuit in (b) with z21
neglected.
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The Practical Situation

• The load effect of the feedback network on the
  basic amplifier is represented by the components
  Z11 and Z22.
• Z11 is the impedance looking into port 1 of the
  feedback network with port 2 open-circuited.
• Z22 is the impedance looking into port 2 of the
  feedback network with port 1 open-circuited.
• Determine the ß.

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Summary

• Ri and Ro are the input and output resistances,
  respectively, of the A circuit.
• Rif and Rof are the input and output resistances,
  respectively, of the feedback amplifier,
  including Rs and RL.
• The actual input and output resistances exclude
  Rs and RL.

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Example of Series-Series Feedback Amplifier
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Example of Series-Series Feedback Amplifier
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Example of Series-Series Feedback Amplifier
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Example of Series-Series Feedback Amplifier
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8.6 The Shunt-Shunt and Shunt-Series Feedback
Amplifiers
Fig8.19. Ideal structure for the shunt-shunt
feedback amplifier.
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The practical Shunt-Shunt feedback amplifier
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Example 8.3
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The shunt-series configuration
Fig 8.22 Ideal structure for the shuntseries
feedback amplifier.
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A practical shunt-series feedback amplifier
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Example 8.4
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summary
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The method of finding A circuit

• h,z,r,g parameter method for two-port feedback
  network.
• Equivalent circuit method
• Find the feedback network
• Find the feedback network equivalent load
  Resistance to amplifier input, for output voltage
  sampling feedback, output short-circuit (Vo0)
  for current sampling feedback, output Io
  open-circuit (Io0).
• Find the feedback network equivalent load
  Resistance to amplifier output, for input voltage
  mixing feedback, it should be disconnected from
  input to feedback network (Ii0) for input
  current mixing feedback, let input connect to
  ground to disconnect from input signal to
  feedback network.

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• ????????,????????
• ?????????,????????
• ??????????????????,????????
• ??????????????????,????????

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• ?????????????,????????
• ?????????????, ????????
• ?????????????,??????????(shunt-shunt)
• ?????????????, ??????????(series-series)?

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Example
1)???????????????????????? 2)????????????????????
???? 3)???????????????
???series-shunt (???????) 8?10,3?9,4?6
???shunt-series(???????)7?10,2?94?6
?shunt-shunt(???????)2?9,8?10,5?6
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Homework

• May 13th, 2008
• 8.20 8.25 8.30 D8.37

75
The Stability Problem
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The Stability Problem

• The condition for negative feedback to oscillate
• Any right-half-plane poles results in
  instability.
• Amplifier with a single-pole is unconditionally
  stable.
• Amplifier with two-pole is also unconditionally
  stable.
• Amplifier with more than two poles has the
  possibility to be unstable.
• Stability study using bode plot

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Balance condition Magnitude condition Phase
Condition
Start up oscillation condition
Judgment method of amplifier stability 1) If
?180 is not exist, then the Amplifier is
stable 2) If ?180 is exist and ?180lt ?1, then
the amplifier is not stable 3) If ?180 is exist
and ?180gt ?1, then the amplifier is stable
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The Definitions of the Gain and Phase margins

• Gain margin represents the amount by which the
  loop gain can be increased while stability is
  maintained.
• Unstable and oscillatory
• Stable and non-oscillatory
• Only when the phase margin exceed 45º or gain
  margin exceed 6dB, can the amplifier be stable.

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Example
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Effect of phase margin on closed-loop response

• To see the relationship between phase margin and
  Close-Loop gain, consider a feedback amplifier
  with a large low-frequency loop gain.

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Stability analysis using Bode plot of A.
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Stability Analysis Using Bode Plot of A

• Gain margin and phase margin
• The horizontal line of inverse of feedback factor
  in dB.
• A rule of thumb
• The closed-loop amplifier will be stable if the
  20log(1/ß) line intersects the 20logA curve at
  a point on the 20dB/decade segment.
• The general rule states
• At the intersection of 20log1/ ß (j?) and
  20log A(j?) the difference of slopes should
  not exceed 20dB/decade.

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Frequency Compensation

• The purpose is to modifying the open-loop
  transfer function of an amplifier having three or
  more poles so that the closed-loop amplifier is
  stable for any desired value of closed-loop gain.
• Theory of frequency compensation is the enlarge
  the 20dB/decade line.
• Implementation
• Capacitance Cc added
• Miller compensation and pole splitting

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Frequency Compensation
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Frequency Compensation-Miller compensation

• A gain stage in a multistage amplifier with a
  compensating capacitor connected in the feedback
  path
• An equivalent circuit.
• Miller compensation can reduce the value of C

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Homework

• May 20th, 2008
• 8.51 8.54 8.63 8.66