CIT 852 – Electronic Signals and Systems Chapter 4: Analogue Amplifiers 4.1 Characteristics of Analogue Amplifiers 4.2 Feedback: Gain Control and Frequency

CIT 852 – Electronic Signals and Systems

Chapter 4: Analogue Amplifiers4.1 Characteristics of Analogue Amplifiers

4.2 Feedback: Gain Control and Frequency Response

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2

Lecture 8 Power Amplifier (Class A)

• Induction of Power Amplifier• Power and Efficiency• Amplifier Classification• Basic Class A Amplifier• Transformer Coupled Class A Amplifier

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3

Introduction• Power amplifiers are used to deliver a relatively high amount of

power, usually to a low resistance load. • Typical load values range from 300W (for transmission

antennas) to 8W (for audio speaker). • Although these load values do not cover every possibility, they

do illustrate the fact that power amplifiers usually drive low-resistance loads.

• Typical output power rating of a power amplifier will be 1W or higher.

• Ideal power amplifier will deliver 100% of the power it draws from the supply to load. In practice, this can never occur.

• The reason for this is the fact that the components in the amplifier will all dissipate some of the power that is being drawn form the supply.


4

Amplifier Power Dissipation

P1 = I12R1

P2 = I22R2

ICQRC

RE

R1

R2

VCC

I1

I2

ICC

PC = ICQ2 RC

PT = ITQ2 RT

PE = IEQ2 RE

IEQ

The total amount of power being dissipated by the amplifier, Ptot , is

Ptot = P1 + P2 + PC + PT + PE

The difference between this total value and the total power being drawn from the supply is the power that actually goes to the load – i.e. output power.

Amplifier Efficiency Powered by DeSiaMore

5

Amplifier Efficiency • A figure of merit for the power amplifier is its efficiency, . • Efficiency ( of an amplifier is defined as the ratio of ac

output power (power delivered to load) to dc input power . • By formula :

• As we will see, certain amplifier configurations have much higher efficiency ratings than others.

• This is primary consideration when deciding which type of power amplifier to use for a specific application.

• Amplifier Classifications

%100)(

)(%100

dcP

acP

powerinputdc

poweroutputac

i

o


6

Amplifier Classifications • Power amplifiers are classified according to the percent of

time that collector current is nonzero. • The amount the output signal varies over one cycle of

operation for a full cycle of input signal.

vin voutAv Class-A

vin voutAv Class-B

vin voutAv Class-C


7

Efficiency Ratings • The maximum theoretical efficiency

ratings of class-A, B, and C amplifiers are:

Amplifier Maximum Theoretical Efficiency, max

Class A 25%

Class B 78.5%

Class C 99%


8

Class A Amplifier

• output waveform same shape input waveform + phase shift.

• The collector current is nonzero 100% of the time. inefficient, since even with zero input signal, ICQ is nonzero(i.e. transistor dissipates power in the rest, or quiescent, condition)

vin voutAv


9

Basic OperationCommon-emitter (voltage-divider) configuration (RC-coupled amplifier)

RC

+VCC

RE

R1

R2

RL

v in

ICQI1

ICC


10

Typical Characteristic Curves for Class-A Operation


11

Typical Characteristic

• Previous figure shows an example of a sinusoidal input and the resulting collector current at the output.

• The current, ICQ , is usually set to be in the center of the ac load line. Why?(DC and AC analyses discussed in previous sessions)


12

DC Input Power

RC

+VCC

RE

R1

R2

RL

v in

ICQI1

ICCThe total dc power, Pi(dc) , that an amplifier draws from the power supply :

CCCCiIVdcP )(

1III

CQCC

CQCCII )(

1II

CQ

CQCCiIVdcP )(

Note that this equation is valid for most amplifier power analyses. We can rewrite for the above equation for the ideal amplifier as

CQCEQiIVdcP 2)(


13

AC Output Power

R1//R2

vcevin

vo

ic

RC//RLrC

AC output (or load) power, Po(ac)

Above equations can be used to calculate the maximum possible value of ac load power. HOW??

L

rmso

rmsormsco R

vviacP

2

)(

)()()(

Disadvantage of using class-A amplifiers is the fact that their efficiency ratings are so low, max 25% .

Why?? A majority of the power that is drawn from the supply by a class-A amplifier is used up by the amplifier itself.

Class-B Amplifier Powered by DeSiaMore

14

IC(mA)

VCE

VCE(off) = VCC

IC(sat) = VCC/(RC+RE)

DC Load LineIC

VCE

IC(sat) = ICQ + (VCEQ/rC)

VCE(off) = VCEQ + ICQrC

ac load line

IC

VCE

Q - point

ac load line

dc load line

L

PP

CQCEQ

CQCEQ

o R

VIV

IVacP

82

1

22)(

2

%25%10022

1

%100)(

)( CQCEQ

CQCEQ

dci

aco

IV

IV

P

P


15

Limitation


16

ExampleCalculate the input power [Pi(dc)], output power [Po(ac)], and efficiency [] of the amplifier circuit for an input voltage that results in a base current of 10mA peak.

RCRB

+VCC = 20V

IC

Vi

25

20k1

Vo

%5.6%100

6.9)48.0)(20(

625.0)20(2

10250

2

250)10(25

20

1100020

20

4.10)20)(48.0(20

48.05.482)3.19(25

3.191

7.020

)(

)(

)(

232)(

)(

)(

)()(

)(

dci

aco

CQCCdci

CpeakC

aco

C

CCsatc

B

P

P

WAVIVP

WA

RI

P

peakmApeakmAII

VVV

AmAV

R

VI

VAVRIVV

AmAmAII

mAk

VV

R

VVI

peakbpeakC

CCcutoffCE

CCCCCEQ

CQ

B

BECC

BQ


Part 1


18

Power Amplifier

• Small-signal approximation and models either are not applicable or must be used with care.

• Deliver the power to the load in efficient manner.

• Power dissipation is as low as possible.


19

Classification of Power Amplifier

• Power amplifiers are classified according to the collector current waveform that results when an input signal is applied.

• Conducting angle.


20


Collector current waveforms for transistors operating in (a) class A, (b) class B


21


class AB class C


22

Class B Output Stage

A class B output stage.

Complementary circuits.

Push-pull operation

Maximum power-conversion efficiency is 78.5%


23

Transfer Characteristic


24

Crossover Distortion


25

Power Dissipation

• The load power

• Maximum load power

L

oL R

VP

2ˆ

2

1

L

CC

VVL

oL R

V

R

VP

CCo

2

ˆ

2

1 2

ˆ

2

max


26

Power Dissipation

• Total supply power

• Maximum total supply power

CCL

os V

R

VP

ˆ2

L

CC

VV

CCL

os R

VV

R

VP

CCo

2

ˆ

max

2ˆ2


27

Power Dissipation

• Power-conversion efficiency

• Maximum power-conversion efficiency

CC

o

V

V̂

4

%5.78ˆ

4 ˆ

max CCo VVCC

o

V

V


28

Power Dissipation

• Power dissipation

• Maximum Power dissipation

L

oCC

L

oD R

VV

R

VP

2ˆ

2

1ˆ2

max2

2

2ˆ

2

maxmax

2.02

ˆ

2

1ˆ2

LL

CC

VVL

oCC

L

oDPDN

PR

V

R

VV

R

VPP

CCo


29

Class AB Output Stage

A bias voltage VBB is applied between the bases of QN and QP, giving rise to a bias current IQ . Thus, for small vI, both transistors conduct and crossover distortion is almost completely eliminated.


30

A Class AB Output Stage Utilizing Diodes for Biasing


31

A Class AB Output Stage Utilizing A VBE Multiplier for Biasing


Part 2


Control and Feedback• Introduction• Open-loop and Closed-loop Systems• Automatic Control Systems• Feedback Systems• Negative Feedback• The Effects of Negative Feedback• Negative Feedback – A Summary

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What is a Control System?

• System- a combination of components that act together and perform a certain objective.

• Control System- a system in which the objective is to control a process or a device or environment.

• Process- a progressively continuing operations/development marked by a series of gradual changes that succeed one another in a relatively fixed way and lead towards a particular result or end.


Control Theory

• Branch of systems theory (study of interactions and behavior of a complex assemblage)

Control SystemManipulated Variable(s)

Control Variable(s)

Open Loop Control System

Control System

Manipulated Variable(s)

Control Variable(s)

Closed Loop Control System

Feedback function35Powered by DeSiaMore

Introduction

• Earlier we identified control as one of the basic functions performed by many systems– often involves regulation or command

• Invariably, the goal is to determine the value or state of some physical quantity– and often to maintain it at that value, despite

variations in the system or the environment


Open-loop and Closed-loop Systems

• Simple control is often open-loop– user has a goal and selects an input to a system to

try to achieve this


• More sophisticated arrangements are closed-loop– user inputs the goal to the system


Automatic Control Systems

• Examples of automatic control systems:– temperature control using a room heater


• Examples of automatic control systems:– Cruise control in a car


• Examples of automatic control systems:– Position control in a human limb


• Examples of automatic control systems:– Level control in a dam


Feedback Systems

• A generalised feedback system


• By inspection of diagram we can add values

or rearrangingoi

o BXXAX

ABA

XX

i

o

1


• Thus

• This the transfer function of the arrangement• Terminology:

• A is also known as the open-loop gain• G is the overall or closed-loop gain

ABA

XX

i

o

1G gain Overall


• Effects of the product AB– If AB is negative

• If AB is negative and less than 1, (1 + AB) < 1• In this situation G > A and we have positive feedback

– If AB is positive• If AB is positive then (1 + AB) > 1• In this situation G < A and we have negative feedback• If AB is positive and AB >>1

- gain is independent of the gain of the forward path A

BABA

ABA

G1

1


Negative Feedback

• Negative feedback can be applied in many ways– Xi and Xo could be temperatures, pressures, etc.– here we are mainly interested in voltages and currents

• Particularly important in overcoming variability– all active devices suffer from variability

• their gain and other characteristics vary with temperature and between devices

– we noted above that using negative feedback we can produce an arrangement where the gain is independent of the gain of the forward path

• this gives us a way of overcoming problems of variability


• Consider the following example below:

• We will base our design on our standard feedback arrangement

Example: Design an arrangement with a stable voltage gain of 100 using a high-gain active amplifier. Determine the effect on the overall gain of the circuit if the voltage gain of the active amplifier varies from 100,000 to 200,000.


• We will use our active amplifier for A and a stable feedback arrangement for B

Since we require an overall gain of 100

so we will use B = 1/100 or 0.01

BG

1


• Now consider the gain of the circuit when the gain of the active amplifier A is 100,000

B

ABA

G

1

90.99000 11000 100

)01.0000 100(1000 100

1


• Now consider the gain of the circuit when the gain of the active amplifier A is 200,000

B

ABA

G

1

95.99000 21000 200

)01.0000 200(1000 200

1


• Note that a change in the gainof the active amplifier of 100%causes a change in the overallgain of just 0.05 %

• Thus the use of negative feedback makes the gain largely independent of the gain of the active amplifier

• However, it does require that B is stable– fortunately, B can be based on stable passive

components


• Implementing the passive feedback path– to get an overall gain of

greater than 1 requires a feedback gain B of less than 1

– in the previous example the value of B is 0.01

– this can be achieved using a simple potential divider


• Thus we can implement our feedback arrangement using an active amplifier and a passive feedback network to produce a stable amplifier

• The arrangement onthe right has a gain of 100 …

… but how do weimplement thesubtractor?


• A differential amplifier is effectively an active amplifier combined with a subtractor. A common form is the operational amplifier or op-amp

• The arrangement onthe right has a gain of 100.


• In this circuit the gain is determinedby the passive components and wedo not need to know the gain of theop-amp– however, earlier we assumed

that AB >> 1– that is, that A >> 1/B– that is, open-loop gain >> closed-loop gain– therefore, the gain of the circuit must be much less

than the gain of the op-amp– see Example 7.2 in the course text


The Effects of Negative Feedback

• Effects on Gain– negative feedback produces a gain given by

– there, feedback reduces the gain by a factor of 1 + AB

– this is the price we pay for the beneficial effects of negative feedback

7.6

ABA

1G


• Effects on frequency response– from earlier lectures we know that all amplifiers have

a limited frequency response and bandwidth– with feedback we make the overall gain largely

independent of the gain of the active amplifier– this has the effect of increasing the bandwidth, since

the gain of the feedback amplifier remains constant as the gain of the active amplifier falls

– however, when the open-loop gain is no longer much greater than the closed-loop gain the overall gain falls


– therefore the bandwidth increases as the gain is reduced with feedback

– in some cases the gain x bandwidth = constant


• Effects on input and output resistance– negative feedback can either increase or decrease the

input or output resistance depending on how it is used.• if the output voltage is fed back this tends to make the output

voltage more stable by decreasing the output resistance• if the output current is fed back this tends to make the output

current more stable by increasing the output resistance• if a voltage related to the output is subtracted from the input

voltage this increases the input resistance• if a current related to the output is subtracted from the input

current this decreases the input resistance• the factor by which the resistance changes is (1 + AB)• we will apply this to op-amps in a later lecture


• Effects on distortion and noise– many forms of distortion are caused by a non-linear

amplitude response• that is, the gain varies with the amplitude of the signal

– since feedback tends to stabilise the gain it also tends to reduce distortion - often by a factor of (1 + AB)

– noise produced within an amplifier is also reduced by negative feedback – again by a factor of (1 + AB)

• note that noise already corrupting the input signal is not reduced in this way – this is amplified along with the signal


Negative Feedback – A Summary

• All negative feedback systems share some properties

1. They tend to maintain their output independent of variations in the forward path or in the environment

2. They require a forward path gain that is greater than that which would be necessary to achieve the required output in the absence of feedback

3. The overall behavior of the system is determined by the nature of the feedback path

Unfortunately, negative feedback does have implications for the stability of circuits – this is discussed in later lectures


Key Points

• Feedback is used in almost all automatic control systems• Feedback can be either negative or positive• If the gain of the forward path is A, the gain of the feedback

path is B and the feedback is subtracted from the input then

• If AB is positive and much greater than 1, then G 1/B• Negative feedback can be used to overcome problems of

variability within active amplifiers• Negative feedback can be used to increase bandwidth, and to

improve other circuit characteristics.

ABA

1G


Classification of Systems

Classes of Systems

Lumped ParameterDistributed Parameter (Partial Differential Equations, Transmission line example) Deterministic

Discrete TimeContinuous Time

NonlinearLinear

Time Varying

Stochastic

Constant Coefficient

Non-homogeneous Homogeneous (No External Input; system behavior depends on initial conditions)


Example Control Systems• Mechanical and Electo-mechanical (e.g. Turntable) Control Systems• Thermal (e.g. Temperature) Control System• Pneumatic Control System• Fluid (Hydraulic) Control Systems• Complex Control Systems • Industrial Controllers

– On-off Controllers– Proportional Controllers– Integral Controllers– Proportional-plus-Integral Controllers– Proportional-plus-Derivative Controllers– Proportional-plus-Integral-plus-Derivative Controllers


Mathematical Background

• Why needed? (A system with differentials, integrals etc.)• Complex variables (Cauchy-Reimann Conditions, Euler

Theorem)• Laplace Transformation

– Definition– Standard Transforms – Inverse Laplace Transforms

• Z-Transforms• Matrix algebra


Laplace Transform

• Definition• Condition for Existence• Laplace Transforms of exponential, step, ramp,

sinusoidal, pulse, and impulse functions• Translation of and multiplication by• Effect of Change of time scale• Real and complex differentiations, initial and final

value theorems, real integration, product theorem• Inverse Laplace Transform

dtetfsFtf st

0)()()]([L

0|)(|0

tfe t

t

suchthat Limit

te)(tf


Inverse Laplace Transform

• Definition• Formula is seldom or never used; instead,

Heaviside partial fraction expansion is used.• Illustration with a problem: Initial conditions: y(0) = 1, y’(0) = 0, and r(t) = 1, t >= 0. Find the steady state response• Multiple pole case with • Use the ideas to find and

dsesFj

tfsFjc

ic

st

)(2

1)()]([1

L

)(2342

2

trydt

dy

dt

yd

22

1

)( as

L

22

1

)( as

asL

3

2

)1(

32)(

s

sssF


Applications

• Spring-mass-damper- Coulomb and viscous damper cases

• RLC circuit, and concept of analogous variables• Solution of spring-mass-damper (viscous case)• DC motor- Field current and armature current

controlled cases• Block diagrams of the above DC-motor problems• Feedback System Transfer functions and Signal flow graphs


Block Diagram Reduction

• Combining blocks in a cascade• Moving a summing point ahead of a block• Moving summing point behind a block• Moving splitting point ahead of a block• Moving splitting point behind a block• Elimination of a feedback loop

G1 G2 G3 G4

H2

H1

H3

R(s)Y(s)

+ +

+ -

-+


Signal Flow Graphs

• Mason’s Gain Formula

Solve these two equations and generalize toget Mason’s Gain Formula

r1

r2

x1

x2

a21 a12

a22

a1111212111 xrxaxa

22222121 xrxaxa

k

ijkijk

ij

FG

G1 G2 G3 G4

G5G6 G7 G8

H2 H3

H7H8

R(s) Y(s)

Find Y(s)/R(s) using the formula 71Powered by DeSiaMore

Another Signal Flow Graph Problem

R(s) C(s)

1 G1 G2 G3 G4 G5 G6

G8G7

-H4-H1

-H2

-H3


Documents

CIT 852 – Electronic Signals and Systems Chapter 4: Analogue Amplifiers 4.1 Characteristics of Analogue Amplifiers 4.2 Feedback: Gain Control and Frequency