1/20

�The feedback – technique use to influence the behavior and

properties of a system by the output quantity of the system

� the effect produced by a certain cause influences the consequent

action of that cause

� fed back to the input a fraction of the output quantity

Feedback circuits

Two types of feedback:

• negative feedback (degenerative) NF. The signal fed back from

the output reduces the effect of the input signal; stabilizing effect

• positive feedback (regenerative) RP. The signal fed back from the

output intensifies the effect of the input signal; leads to instability

2/20

The general structure of the feedback circuit

xs – source signal, fed from an external signal source;

xo – output signal, fed to the load as well as to the feedback network;

xr – feedback signal, provided by the feedback network

xi – input signal to the basic amplifier, provided by the summing

element.

Signal flow

diagram

3/20

The general structure of the feedback circuit

• transmittance of the basic amplifier :

• transmittance of the feedback network:

• transmittance of the feedback circuit:

i

o

x

xa =

o

r

x

xr =

s

o

x

xA =

gain of the basic amplifier; open loop gain

gain of the feedback amplifier

feedback factor; transmittance of the reverse path

4/20

Equations of the ideal feedbackIdeal feedback:

• each block is unilateral (one way transmittance)

• the r circuit does not load the a circuit; that is, connecting the r

circuit does not change the value of a.

• assume that the source and the load resistance have been included

inside the a circuit

Negative

feedback

5/20

Negative feedback

rsivvv −=

6/20

Fundamental

equation of the NF

ar – loop gain

1+ar amount of feedback

ar > 0;

1+ar > 1

� If ar >> 1 (eg. for op amp )∞→a

The gain of the feedback amplifier is almost entirely determined

by the feedback network : accurate, predictable and stable gain.

Negative

feedback

7/20

Exemplification

a=1000, r=0.009

ar =?

1+ar =?

A=?

111,10,009

1

r

1A ≈==

Negative feedback: - reduces the gain

- improves some amplifier properties (stabilizes

the gain, reduce nonlinear distortion, improves the input and output

impedances, extend the bandwidth).

8/20

Positive feedback

rsixxx +=

ar

aA

−=

1

rsivvv +=

ar > 0; 0 < 1-ar < 1

Amplifier in the

linear domain

aA >

But the amplifier

performances get

worse

9/20

� Special case of PF:

∞→==− Aarar ;1;0)1(

soAxx = xo finite only if xs=0

It is used for sinusoidal oscillator with PF (signal generator)

� 0 >1-ar; ar>1

• still have RP, but the linear theory can not be used anymore for

circuit analysis;

• specific analyzing method will be used

• multivibrator circuits, bistable circuits

Positive feedback

10/20

The feedback topologies

• input and output signals: voltage and/or currents:

results four feedback topologies.

• the loop gain is dimensionless

11/20

PS

PS

Illustration

12/20

13/20

Analysis of the feedback amplifier

� Ideal feedback:

� there are no restrictions on the basic amplifier

� the other components of the circuit are made ideal

� the feedback network – a controlled source

� the signal source is assumed to be ideal (it is assumed that

the source resistance is included inside the basic amplifier)

� the load resistance does not load the output of the amplifier

(it is assumed that the load resistance is included inside the

basic amplifier)

� Real feedback:

� the feedback network loads the input and output of the basic

amplifier

� the circuit with real feedback ideal feedback

14/20

Ideal feedback, series-parallel topology

Structure of the

ideal feedback

amplifier

Equivalent circuit

of the amplifier

A=?

Rir=?

Ror=?

15/20

Rir

• increases the input resistance by a

factor equal to the amount of feedback.

• improves the input resistance

(amplifier with voltage as input)

Rir=?

16/20

Ror

• reduces the output resistance by a

factor equal to the amount of feedback.

• improves the output resistance

(amplifier with voltage as output)

Output in short-circuit , vo=0

iopeno,

sco,

openo,

or

avv

i

vR

=

=

ar1

avv s

openo,+

=

o

s

o

isco,

R

av

R

avi ==

17/20

Loads due to:

• feedback network

• source resistance

• load resistance

Real feedback, series-parallel topology

18/20

Approximation of the real feedback by the ideal feedback

series-parallel topology

orL

Lor

orRR

RRR

′−

′=

19/20

Illustration

20/20

a’=195487;

r=0,091