Feedback

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Feedback
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• What is feedback? Taking a portion of the signal
  arriving at the load and feeding it back to
  the input.
• What is negative feedback? Adding the feedback
  signal to the input so as to partially cancel
  the input signal to the amplifier.
• Doesnt this reduce the gain? Yes, this is the
  price we pay for using feedback.
• Why use feedback? Provides a series of benefits,
  such as improved bandwidth, that outweigh the
  costs in lost gain and increased complexity
  in amplifier design.

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Feedback Amplifier Analysis
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Advantages of Negative Feedback

• Gain desensitivity - less variation in amplifier
  gain with changes in ? (current
  gain) of transistors due to dc bias,
  temperature, fabrication process variations,
  etc.
• Bandwidth extension - extends dominant high and
  low frequency poles to higher and lower
  frequencies, respectively.
• Noise reduction - improves signal-to-noise ratio
• Improves amplifier linearity - reduces
  distortion in signal due to gain variations
  due to transistors
• Cost of these advantages
• Loss of gain, may require an added gain stage to
  compensate.
• Added complexity in design

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Basic Types of Feedback Amplifiers

• There are four types of feedback
  amplifiers. Why?
• Output sampled can be a current or a
  voltage
• Quantity fed back to input can be a
  current or a voltage
• Four possible combinations of the type of
  output sampling and input feedback
• One particular type of amplifier, e.g.
  voltage amplifier, current amplifier, etc. is
  used for each one of the four types of
  feedback amplifiers.
• Feedback factor ?f is a different type of
  quantity, e.g. voltage ratio, resistance, current
  ratio or conductance, for each feedback
  configuration.
• Before analyzing the feedback amplifiers
  performance, need to start by recognizing
  the type or configuration.
• Terminology used to name types of feedback
  amplifier, e.g. Series-shunt
• First term refers to nature of feedback
  connection at the input.
• Second term refers to nature of sampling
  connection at the output.

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Basic Types of Feedback Amplifiers
Series - Shunt
Shunt - Series
Series - Series
Shunt - Shunt
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Method of Feedback Amplifier Analysis

• Recognize the feedback amplifiers
  configuration, e.g. Series-shunt
• Calculate the appropriate gain A for the
  amplifier, e.g. voltage gain.
• This includes the loading effects of the
  feedback circuit (some combination of
  resistors) on the amplifier input and
  output.
• Calculate the feedback factor ?f
• Calculate the factor ?f A and make sure
  that it is 1) positive and 2)
  dimensionless
• Calculate the feedback amplifiers gain with
  feedback Af using
• Calculate the final gain of interest if
  different from the gain calculated, e.g.
  Current gain if voltage gain originally
  determined.
• Determine the dominant low and high
  frequency poles for the original amplifier,
  but taking into account the loading effects
  of the feedback network.
• Determine the final dominant low and high
  frequency poles of the amplifier with
  feedback using

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Series-Shunt Feedback Amplifier - Ideal Case

• Assumes feedback circuit does not load down the
  basic amplifier A, i.e. doesnt change its
  characteristics
• Doesnt change gain A
• Doesnt change pole frequencies of basic
  amplifier A
• Doesnt change Ri and Ro
• For the feedback amplifier as a whole, feedback
  does change the midband voltage gain from A to Af
• Does change input resistance from Ri to Rif
• Does change output resistance from Ro to Rof
• Does change low and high frequency 3dB frequencies

Basic Amplifier
Feedback Circuit
Equivalent Circuit for Feedback Amplifier
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Series-Shunt Feedback Amplifier - Ideal Case
Midband Gain
Input Resistance
Output Resistance
It
Vt
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Series-Shunt Feedback Amplifier - Ideal Case
Low Frequency Pole
Low 3dB frequency lowered by feedback.
High Frequency Pole
Upper 3dB frequency raised by feedback.
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Practical Feedback Networks

• Feedback networks consist of a set of resistors
• Simplest case (only case considered here)
• In general, can include Cs and Ls (not
  considered here)
• Transistors sometimes used (gives variable amount
  of feedback) (not considered here)
• Feedback network needed to create Vf feedback
  signal at input (desirable)
• Feedback network has parasitic (loading) effects
  including
• Feedback network loads down amplifier input
• Adds a finite series resistance
• Part of input signal Vs lost across this series
  resistance (undesirable), so Vi reduced
• Feedback network loads down amplifier output
• Adds a finite shunt resistance
• Part of output current lost through this shunt
  resistance so not all output current delivered to
  load RL (undesirable)

Vi
Vo
Vf

• How do we take these
• loading effects into account?

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Equivalent Network for Feedback Network

• Need to find an equivalent network for the
  feedback network including feedback effect and
  loading effects.
• Feedback network is a two port network (input and
  output ports)
• Can represent with h-parameter network (This is
  the best for this particular feedback amplifier
  configuration)
• h-parameter equivalent network has FOUR
  parameters
• h-parameters relate input and output currents and
  voltages
• Two parameters chosen as independent variables.
  For h-parameter network, these are input current
  I1 and output voltage V2
• Two equations relate other two quantities (output
  current I2 and input voltage V1) to these
  independent variables
• Knowing I1 and V2, can calculate I2 and V1 if you
  know the h-parameter values
• h-parameters can have units of ohms, 1/ohms or no
  units (depends on which parameter)

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Series-Shunt Feedback Amplifier - Practical
Case

• Feedback network consists of a set of resistors
• These resistors have loading effects on the basic
  amplifier, i.e they change its characteristics,
  such as the gain
• Can use h-parameter equivalent circuit for
  feedback network
• Feedback factor ?f given by h12 since
• Feedforward factor given by h21 (neglected)
• h22 gives feedback network loading on output
• h11 gives feedback network loading on input
• Can incorporate loading effects in a modified
  basic amplifier. Basic gain of amplifier AV
  becomes a new, modified gain AV (incorporates
  loading effects).
• Can then use feedback analysis from the ideal
  case.

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Series-Shunt Feedback Amplifier - Practical
Case
Summary of Feedback Network Analysis

• How do we determine the h-parameters for the
  feedback network?
• For the input loading term h11
• Turn off the feedback signal by setting Vo 0.
• Then evaluate the resistance seen looking into
  port 1 of the feedback network (also called R11
  here).
• For the output loading term h22
• Open circuit the connection to the input so I1
  0.
• Find the resistance seen looking into port 2 of
  the feedback network (also called R22 here).
• To obtain the feedback factor ?f (also called h12
  )
• Apply a test signal Vo to port 2 of the feedback
  network and evaluate the feedback voltage Vf
  (also called V1 here) for I1 0.
• Find ?f from ?f Vf/Vo

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Series-Shunt Feedback Amplifier - Practical
CaseSummary of Approach to Analysis

• Evaluate modified basic amplifier
  (including loading effects of feedback network)
• Including h11 at input
• Including h22 at output
• Including loading effects of source resistance
• Including load effects of load resistance
• Analyze effects of idealized feedback network
  using feedback amplifier equations derived
• Note
• Av is the modified voltage gain including the
  effects of h11 , h22 , RS and RL.
• Ri, Ro are the modified input and output
  resistances including the effects of h11 , h22 ,
  RS and RL.

Basic Amplifier
Practical Feedback Network
Modified Basic Amplifier
Idealized Feedback Network
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Example - Series-Shunt Feedback Amplifier

• Two stage amplifier
• Each stage a CE amplifier
• Transistor parameters Given ?1 ?2 50,
  rx1rx20
• Coupled by capacitors, dc biased separately
• DC analysis

DC analysis for each stage can be done separately
since stages are isolated (dc wise) by coupling
capacitors.
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Example - Series-Shunt Feedback Amplifier

• Redraw circuit to show
• Feedback circuit
• Type of output sampling
• (voltage in this case Vo)
• Type of feedback signal to input (voltage in this
  case Vf)

_
Vi


Vo
Vf
_
_
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Example - Series-Shunt Feedback Amplifier
Input Loading Effects
Vo0
Output Loading Effects
I10
Amplifier with Loading Effects
R2
R1
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Example - Series-Shunt Feedback Amplifier

• Construct ac equivalent circuit at midband
  frequencies including loading effects of
  feedback network.
• Analyze circuit to find midband gain
• (voltage gain for this series-shunt
  configuration)

R1
R2
R2
R1
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Example - Series-Shunt Feedback Amplifier
Midband Gain Analysis
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Midband Gain with Feedback

• Determine the feedback factor ?f
• Calculate gain with feedback Avf
• Note
• ?f Avo gt 0 as necessary for negative feedback
• ?f Avo is large so there is significant feedback.
  For ?f Avo ? 0, there is almost no feedback.
• Can change ?f and the amount of feedback by
  changing Rf1 and/or Rf2.
• NOTE Since ?f Avo gtgt 0

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Input and Output Resistances with Feedback

• Determine input Ri and output Ro resistances with
  loading effects of feedback network.
• Calculate input Rif and output Rof resistances
  for the complete feedback amplifier.

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Equivalent Circuit for Series-Shunt Feedback
Amplifier

• Voltage gain amplifier
• Modified voltage gain, input and output
  resistances
• Included loading effects of feedback network
• Included feedback effects of feedback network
• Include source resistance effects
• Significant feedback, i.e. ?f Avo is
  large and positive

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Low Frequency Poles and Zeros for
Series-Shunt Feedback Amplifier

• Six capacitors
• Input and output coupling capacitors C1 and C5
• Emitter bypass capacitors C3 and C4
• Interstage coupling capacitors C2
• Feedback coupling capacitor C6
• Analyze using Gray-Searle (Short Circuit)
  Technique one capacitor at a time
• Find dominant low frequency pole (highest
  frequency one)

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Example - Input Coupling Capacitors Pole
Frequency
Equivalent circuit for C1
Note that there are some loading effects of the
feedback network on this pole frequency. In Ri1
the feedback resistors determine R1
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Example - Interstage Coupling Capacitors Pole
Frequency
Equivalent circuit for C2
Note No RE2 since C4 shorts it out.
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Example - Feedback Coupling Capacitors Pole
Frequency
Equivalent circuit for C6
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Example - Emitter Bypass Capacitors Pole
Frequency
Equivalent circuit for C3
IE1
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Example - Emitter Bypass Capacitors Pole
Frequency
Equivalent circuit for C4
IE2
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Example - Output Coupling Capacitors Pole
Frequency
Equivalent circuit for C5
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Zeros for Series-Shunt Feedback Amplifier
Example

• Coupling capacitors C1, C2 and C5 give zeros at ?
  0 since ZC 1/sC and they are in the signal
  line.
• Emitter bypass capacitors C3 and C4 give a zero
  when the impedance ZCE RE??.
• Feedback capacitor C6 gives a zero when ZC6 R2
  RC2?? when

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Series-Shunt Example - Low Frequency

• Midband Gain Low Frequency Poles
  Low Frequency Zeros

Low 3dB Frequency
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Series-Shunt Example - High Frequency

• Substitute hybrid-pi model for transistor with C?
  and C?
• Short all coupling capacitors and emitter bypass
  capacitors
• Include loading effects of feedback network R1
  and R2
• Find high frequency poles and zeros using
  Gray-Searle (Open Circuit) Method

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Series-Shunt Example - High Frequency Pole - C?1
Given C?1 15 pF
IS
I1
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Series-Shunt Example - High Frequency Pole - C?1
Given C?1 1.2 pF
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Series-Shunt Example - High Frequency Pole - C?2
Given C?2 12 pF
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Series-Shunt Example - High Frequency Pole - C?2
Given C?2 1.4 pF
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Series-Shunt Example - High Frequency Zeros -
C?1 C?2
I?2
For CE amplifier, a high frequency zero occurs
when ?ZH gm/C?
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Series-Shunt Example - High Frequency

• Midband Gain High Frequency Poles
  High Frequency Zeros

High 3dB Frequency