fyse400 analog electronicsusers.jyu.fi/~loberg/fyse400slides/lecture12fyse400.pdf · calculate the...

FYSE400 ANALOG ELECTRONICS

LECTURE 12

Feedback Amplifiers

1

FEEDBACK AMPLIFIERS

Approximate analysis of a feedback amplifier Assumptions

1. The basic amplifier is unilateral.

2. The gain AOL of the basic amplifier is determined without feedback.

2

3. The calculated gain AOL is loaded gain : loading of the feedback network,

source and load resistanses are noticed.

4. The feedback network is unilateral.

©Loberg University of Jyväskylä

Outline of Analysis

1. Identify the topology → Xf is current or voltage.

2. Draw the basic amplifier circuit without feedback

Replace each active device by its proper model.

Identify Xf and Xo on the circuit obtained.

FEEDBACK AMPLIFIERS

Approximate analysis of a feedback amplifier

3

Identify Xf and Xo on the circuit obtained.

3. Evaluate : of XX====β

Evaluate AOL by applying KVL and KCL to the equivalent circuit obtained.

4. From AOL and β, find T and AF

5. From the equivalent circuit find RID and ROD. Apply the Backman's

impedance formula to obtain RIF and ROF.


Topology of a system

First step Identify input loop

It contains Vs , and (a) base-to-emitter region of the bipolar transistor.

(b) gate-to-source region of the first FET in the amplifier

(c) the section between the two inputs of a differential or

operational amplifier.

FEEDBACK AMPLIFIERS


Input

4

Topology of input loop Series topology

In the input circuit, there is a circuit component W in series

with Vs .

And W is connected to the output (portion of the system

containing the load).

Voltage across W is feedback signal ff VX ====⇒⇒⇒⇒

( Voltage source Vs )


Topology of input loop Shunt topology

Define input node

( Current source Is )


FEEDBACK AMPLIFIERS


First step Identify input loopInput

5

(a) The base of the first BJT

(b) The gate of the first FET

(c) The inverting terminal of a differential

or operational amplifier.

Shunt topology if there is a connection between the input

node and the output circuit.

The current in this connection is the feedback signalff IX ====


The voltage Vo (with respect to ground) at the output node appears

across the load resistor (RL) and output current Io is the current in RL.


Topology of output loop Shunt topology

FEEDBACK AMPLIFIERS


Second step Define Output NodeOutput

6

( Voltage sampling )

Set Vo = 0 (RL → 0) (short-circuiting the output)

0X f →→→→⇒⇒⇒⇒ ⇒⇒⇒⇒

( Current sampling )

Set Io = 0 (RL → ∞) (open-circuiting the output)

0X f →→→→⇒⇒⇒⇒

Topology of output loop Series topology

⇒⇒⇒⇒


Amplifier without feedback

AOL

Calculate the gain of the basic amplifier without feedback but taking the

loading of the β network into account.

Modify circuit first

Input circuit :

Output topology is shunt Output topology is series

βand

FEEDBACK AMPLIFIERS


Third step

7

0=oV

Output topology is shunt

Short-circuit output node →

Voltage sampling

Output topology is series

0=oIOpen-circuit the output loop →

Current sampling

Output circuit :

0Vi ====Short-circuit input node →

Input topology is shunt

Current comparison

(none of the feedback current

enters to the amplifier input)

0Ii ====Open-circuit the input loop →

Input topology is series

Voltage comparison

(none of the feedback voltage

reaches the amplifier input)


Topology of the Emitter follower

Example of analysis of emitter follower.

Input :

Input loop contains

RE , which is connec-

ted to the output.

Serial topology

Voltage comparison

One Stage

Vf

Vi

Input loop

FEEDBACK AMPLIFIERS


8

Output :

Shunt topology

Voltage sampling

By setting Vo = 0, the

feedback is eliminated

and Vf = 0. Thus the out-

put is shunt connected.

Series-Shunt topology



Modified input circuit

Output has shunt topology

Short-circuit the output node.

One Stage

FEEDBACK AMPLIFIERS



9

Modified output circuit

Open-circuit the input loop.

Input has series topology

Basic amplifier without feedback

Equivalent circuit of modified feedback amplifier


of VV −−−−====From picture (c) we get :

1VV of −−−−====≡≡≡≡β⇒⇒⇒⇒

βandAOL


One Stage

FEEDBACK AMPLIFIERS



10

Equivalent circuit of modified feedback amplifier

+

-

Vo

oE

'

E

'

Emo rRRwhereRVgV ======== π

π

ππ

rR

VrVand

s

s

++++====

⇒

π

π

rR

RrgA

s

'

EmOL ++++

====


FAandT

βOLAT −−−−====

1−−−−====β ⇒⇒⇒⇒ π

rR

RrgT Em

+=

'

whereoE

'

E rRR ====

One Stage

Amplifier with feedback

FEEDBACK AMPLIFIERS



11

πrRT

s +=

'

E0s

'

E0OLF

RrR

R

T1

AA

ββ

π ++++++++====

++++====

oEE rRR ====


E

'

E

E0s

E0F RRwhen

RrR

RA ≈≈≈≈

++++++++====

ββ

π

oE rR <<If we assumed that we can write :

Approximation

FA


One Stage

FEEDBACK AMPLIFIERS



12

E0s π

(((( ))))(((( )))) E

'

E

0Es

0EF RRwhen

1RrR

1RA ≈≈≈≈

++++++++++++++++====

ββ

π

(((( )))) 001 ββ →→→→++++

unilateral feedback networknonunilateral feedback network

See Millman,

Grabel table 10-3A

(assumption)


IFID RandR

Dead system impedance RID

πrRID ====


One Stage

FEEDBACK AMPLIFIERS



13©Loberg University of Jyväskylä


One Stage

IFID RandRInput has Series topology

TOC Open circuit the input : ∞∞∞∞→→→→→→→→ sRwhen0T

0TTsR

OC ======== ∞∞∞∞====

TSC 0RwhenRgT s

'

Em →→→→→→→→Short circuit the input :

FEEDBACK AMPLIFIERS



14

(((( )))) '

E0IF R1rR βπ ++++++++==== See Millman, Grabel table 10-3

(((( )))) 001 ββ →→→→++++unilateral feedback network

sEm

'

Em0RSC RgTTs

======== ====


(((( )))) '

E0

'

EmIF RrRg1rR βππ ++++====++++==== Approximation⇒⇒⇒⇒

Output has Shunt topology

oOD rR ====

Dead system impedance ROD


One Stage

OFOD RandR

FEEDBACK AMPLIFIERS



15©Loberg University of Jyväskylä

OFOD RandR


TSC Short circuit the output : 0Rwhen0T E →→→→→→→→

00

===ERSC TT

One Stage

Output has Shunt topology

FEEDBACK AMPLIFIERS



16

Open circuit the output : ∞∞∞∞→→→→++++

→→→→ E

s

o0 RwhenrR

rT

π

β

π

βrR

rTT

sROC

E +==

∞=00

( )[ ] 001 ββπ

π

rR

rRr

rR s

so

oOF

+≈

++=

(((( )))) 0so rRr βπ++++>>>>>>>>

when

⇒

TOC


Approximate analysis of a shunt-triple

In general, practical amplifiers have two or more stages. High closed-loop gain AF

High return ratio T

Local feedback

Global feedback

Three Common-emitter stages

sI sR

FR

LR

oV

+

R R

1Q 2Q3Q

iI

Feedback network

A bipolar shunt-triple feedback amplifier

Example of analysis of amplifier

having several stages

FEEDBACK AMPLIFIERS

17

The internal three-stage amplifier can be modeled as

a single equivalent amplifier.

sI sR oV

-1CR 2CR

3CR

IFZOFZ

Internal amplifier

Input:

Current comparison

SHUNT topology

Output:

Voltage sampling

SHUNT topology

SRsI oViV

imIZ

iror

FR

iI

LR

?Z

rrr

Rr

m

1b1i

3Co

====++++≈≈≈≈

≈≈≈≈

π


sI sR

FR

LR

oV

+

-1CR 2CR

3CR

1Q 2Q3Q

iI

Feedback network

A bipolar shunt-triple feedback amplifier

Voltage gain of the first (input) stage is :

1b1

1C01v

rr

RA

++++−−−−====

π

β


FEEDBACK AMPLIFIERS



SRsI oViV

imIZ

iror

FR

iI

LR

18

-

IFZOFZ

Internal amplifier

1b1i

iii

rrr

0rIV

++++========−−−−

π(((( ))))1b1ii rrIV ++++==== π⇒⇒⇒⇒

⇒⇒⇒⇒The unloaded voltage gain of the input stage (first stage).

(((( )))) 1C01i

1b1

1C011b1ivi1o RI

rr

RrrIAVV ββ

ππ −−−−====

++++++++−−−−========



SRsI oViV

imIZ

iror

FR

iI

LR

FEEDBACK AMPLIFIERS



19

Total gain (transimpedance)

of controlled source is:

3v2v1C01

i

om AAR

I

VZ β========

remember load effects



The approximate model of the basic amplifier (shunt-triple) without feedback

Feedback is removed, but not loading

effect of RF .

Modify Input side:

Output has shunt topology

Modify Output side:

Input has shunt topology

FEEDBACK AMPLIFIERS



20

SRsI oViV

imIZ

ir

or

FR

iI

LR

SRsI oViV

imIZ

ir

orFRiI

LR

Short circuit output Short circuit input

SRsI oViV

imIZ

ir

or

FR

iI

LR

SRsI oViV

imIZ

ir

or

FR

iI

LR

SRsI oViV

imIZ

ir

or

FR

iI

LR

SRsI oViV

imIZ

ir

or

FR

iI

LR



Vor

iI

Feedback is removed, but loading effect of RF on the input and output

circuits is included.

oriI'

sI

sI

I

OLAThe approximate model of the basic amplifier (shunt-triple) without feedback

FEEDBACK AMPLIFIERS



21

SRsI oViV

imIZir

or

FR

LRFR'

SRsI oViV

imIZir

or

'

LR

sI I

0IRV

0IZIrV

0RIV

0rIV

0III

'

Lo

imoo

'

s

'

si

iii

'

sis

====++++

====++++−−−−====−−−−

====−−−−====−−−−−−−−

⇒⇒⇒⇒'

Lo

'

L

'

si

'

sm

s

oOL

Rr

R

Rr

RZ

I

VA

++++++++−−−−========

FL

'

L

Fs

'

s

RRR

RRR

====

====where



K

o22s21i XtXtX ++++==== (Millman 12-23)

22

21

0Xs

o

t

t

X

XK

i

−−−−====−−−−========

See a General Analysis

of Feedback Amplifiers

FEEDBACK AMPLIFIERS



22

220Xs tXi ====

SR

sI oV0Vi ====imIZ

iror

FR

0I i ====

LR

IsI 0IRV

0II

Fo

s

====−−−−====++++

⇒⇒⇒⇒ F

s

o

0Xs

o RI

V

X

XK

i

−−−−========−−−−========



Treturn ratio

sF

F

i

'

s

s

o

'

L

L

FL

m

F

'

Lo

'

L

'

si

'

sm

OL

RR

R

rR

R

rR

R

RR

Z

R

1

Rr

R

Rr

RZ

K

AT

++++++++++++++++====

−−−−

++++++++−−−−======== See a General Analysis

of Feedback Amplifiers

FEEDBACK AMPLIFIERS



23

T1

KT

T1

KTA

T1

AA DOL

F ++++≈≈≈≈

++++++++====

++++==== when dead system gain AD

is very low

⇒⇒⇒⇒

sFisoLFL


The End of Part 12

FEEDBACK AMPLIFIERS

24

The End of Part 12


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