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264 Linear Amplifier Design Tools
It can be shown that this reduces to
'1 = !log" (7.109)
where!lo in (E.14) is the maximum 50-ohm transducer gain, and g, is defined
as:
I -lr,I'
g, = I I' I'
(1- S" )+Ir, O,-2Re(r,C,)
(7.110)
The maximum possible efficiency from (7.64) is similarly expressed in scattering
notation by (E. 11 ), because
I~:~I= I~:~ I·
(7.111)
The power available at output terminals 2-2' in Figure 7.17 relative to the
power available from the source is the available power gain:
where g, is defined as:
IS' I'
G = " =
A 1-\S2,I' &Jg, ,
1-lr,I'
g,
" .
(1-IS"j )+lr,1 O,-2Re(r,C,)
(7.112)
(7.113)
Conjugate-image matching occurs when the source and load reflection
coefficients are given by (E.12) and (E.13). These may be derived by solving
the pair of equations obtained by setting the magnitudes of (7.92) and (7.95)
to zero. Another approach is to convert the conjugate-image admittance
expressions in (7.78) and (7.79). Load reflection coefficient r ML
from (E.13)
results in maximum efficiency, (E. 11). Maximum gain is obtained when the
source reflection coefficient is r M
, from (E.12):
G m .x='1 m .x when r,=r M ,. (7.114)
It was remarked in Section 7.3.4 that generalized reflection coefficients
normalized to conjugate-image immittances map constant-efficiency loci onto
concentric circles on the generalized Smith charts. It can be shown that
equations (7.110) and (7.112) define the related eccentric family of constant g,
and g, circles on the r, and r, reflection planes, respectively. Bodway (1967)
gives the centers of such circles,
with radius
POj
!Oi-
-( I + g, Djg j
)c* j,
(1- 2KIS I ,S2Ilg, + IS 12 S"I'g,)1/'
1+0,&
(7.115)
(7.116)
for the r, planes, where i= 1,2. These are valid for K < I as well as for K> I.