# Electronic Circuits by xiaoyounan

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```									                           Feedback

2010 Electronic Circuits
Feedback
 For an amplifier:
A=f(gm,Qpoint,temperature etc.)
Using feedback we can obtain precise and reproductible A
 Feedback amplifier topology:

Xe

xe  xi  xr  xi  x0                             x0    A
 Ar     
xi 1  A
x0  Axe  A( xi  x0 )
Assuming Σ, A si β are ideal and uncorrelated

2010                                 Electronic Circuits Course                                Slide 2
Negative Feedback
   Loop phase shift must be - k π, (k – integer)

2010                              Electronic Circuits Course   Slide 3
Feedback
    For amplifiers with feedback we can assume that the
gain:                        ax
f ( x) 
1 b x

    Then for

A
Ex: if          10%
A
and F=100

          Ar
 0,1%
Ar

For A=1000

A 1000
 Ar                10
F   100
2010                             Electronic Circuits Course       Slide 4
Feedback effect over gain
   For amplifiers with feedback we can assume that the

If nonfeedback amplifier has :
A
A
A
Ar 
1   A
???
Ar              A
Ar              A
At small variations :

1  A  A              1                 A      1      A
Ar                A               A                     
(1  A) 2
(1  A) 2
1  A 1  A A
Ar A        1       A 1
                  
Ar     A 1  A       A F               F times improvement !!!
2010                                   Electronic Circuits Course                             Slide 5
Influence of the feedback on freq. response

If                             and                      a real number,

Then:

only the poles are shifted

2010                              Electronic Circuits Course                    Slide 6
Influence of the feedback on freq. response(@high freq.)

where                       &

Then:

Note: only if circuit still behave linear !!!
2010                                     Electronic Circuits Course   Slide 7
Influence of the feedback on freq. response(@low freq.)

where

Then:

Note: only if circuit still behave linear !!!
2010                                     Electronic Circuits Course   Slide 8
GBW=ct.

F= βA = loop gain
2010    Electronic Circuits Course                       Slide 9
2010   Electronic Circuits Course   Slide 10
Perturbation influence in Feedback Amps

Perturbations are reduced as
they are closer to output

2010                  Electronic Circuits Course                            Slide 11
Feedback
Two-Terminal Representation of a Single-Loop, Negative Feedback System

2010                                Electronic Circuits Course             Slide 12
Feedback topologies

2010        Electronic Circuits Course   Slide 13
Feedback Topology Identification Procedure
1.) Identify the feedback loop by tracing around the feedforward and feedback
path. Also check to see if the feedback is positive or negative.
2.) Identify whether or not the mixing network is series or shunt. If the signal
source has one terminal on ac ground then:
a.) If the input active device has one of its input terminals on ac ground, then the
mixing network must be shunt
b.) If the signal and feedback sources are applied to different input terminals of the
input active device, then the mixing network is series (this includes differential
amplifiers where two devices form the input active device).
c.) If the signal source does not have one of its input terminals on ac ground or to
check the above steps, try to assign the variables xi, xfb, and xe on the
schematic in such a manner as to implement the equation,
xe = xi ± xfb
If this equation can be written using voltages (currents) then the mixing
circuit is series (shunt).

2010                                     Electronic Circuits Course                     Slide 14
Feedback Topology Identification Procedure
3.) Next identify the sampling circuit as series or shunt. If the load is grounded
then,
a.) If the out active device has one of its two possible output terminals grounded,
then the feedback is shunt.
b.) If the output active device has neither of its output terminals on ground and if
the output signal is taken from one of its output terminals and the fed back
signal from the other output terminal, then the feedback is series.
c.) If the load is not grounded or to check the above test, identify the load resistor,
RL, and apply the following test:
i.) If xfb becomes zero when RL = 0, then the sampling network is shunt.
ii.) If xfb becomes zero when RL = ∞, then the sampling network is series.

2010                                      Electronic Circuits Course                     Slide 15
Feedback variables for all topologies

2010                 Electronic Circuits Course   Slide 16
Feedback
  A real case with A having an input resistance Ri and an output resistance
Ro, and the signal source is not ideal, and the feedback netw. has R.
- Can be equivalent with an ideal case in which the feedback network has Rif
and Rof the extreme values , and the signal source is ideal.
 We obtain a “loaded amplifier” without feedback and with pasive influences
of the signal, load and feedback netw. included.

2010                                 Electronic Circuits Course                 Slide 17

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