0195136047.pdf

5.1 THE AMPLIFIER BLOCK 227

Time average of[v(t)v(t)]=

1

2

Re

[

V ̄V ̄∗

]

=

∣

∣V ̄

∣

∣^2

2

The maximum power is derived from a Thévenin source when it is loaded by a resistance

equal toRTh. The maximum power thus obtainable, known asavailable power PAV L, is given by

PAV L=

∣

∣V ̄Th

∣

∣^2

8 RTh

In this circuit,

∣

∣V ̄in

∣

∣^2 = R

2

i

(Ri+RTh)^2

∣

∣V ̄Th

∣

∣^2

Note that the peak value of the sinusoid is used here for the magnitude of the phasor in these

expressions. Thus,

GP=

PL

PAV L

=

4 A^2 RLRi^2 RTh

(Ro+RL)^2 (Ri+RTh)^2

Substituting the values given, one gets

GP=

4 ( 1 )^2 ( 100 ) 108 (20,000)

( 100 + 100 )^2 (10,000+20,000)^2

=

200

9

= 22. 22

Note that although the amplifier’s open-circuit voltage amplificationAis only unity, substantial

power gain is obtained in this case since the current gain is greater than unity andGP=GVGI.

In applications of microwave technology, the function of the amplifier is to magnify very small

power to a measurable level with as little random noise as possible. The source signal may be

from a radio telescope, and the available power may be determined by the power captured by the

antenna dish.

EXAMPLE 5.1.3

Quite often an amplifier is used as a component of an amplifier circuit. Consider the amplifier
circuit shown in Figure E5.1.3, which contains an amplifier block as an internal component. Find
the input resistanceRi′, the output resistanceR′o, and the open-circuit voltage amplificationA′of
the larger circuit.

RS A

B

vout R 2

Amplifier

block

with constants

Ri, Ro, A

vS RL

+

−

R 1

+

−

C

D

vin

+

−

Figure E5.1.3

Solution

The input resistance looking into terminalsAandBis