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374 Other Direct Filter Design Methods
j-Transmitter~- - - - - - - ---'1
constant, I,
: 1 ~B,nd"" \;It"
I-?c!J!)$.
d B
i L, 0 f
I
L
I
..J
2 3
Transmission
fine lo. any
length
Zantenna
Figure 9.39.
5 22 SL
A transmitter connected to a narrow-band antenna.
60 dB below the fundamental power. Also, at the second-harmonic frequency,
SWR S" = 32 is measured with the power off, and the antenna SWR is
SL = 16. Assuming SL = I at the fundamental power, what is the possible range
of the second-harmonic, spurious output power? According to (9.80) and
(9.78), the second-harmonic power can increase by 8.8 dB and decrease by
11.8 dB, respectively. Therefore, the second-harmonic output power can range
between 51.8 and 71.8 dB below the fundamental power.
9.5.3. Bounds on input impedance and SWR. Maximum efficiency will be
the primary parameter for the analysis of bounds on input impedance and
SWR, and it is convenient to simplify its expression for passive reciprocal
networks. Maximum efficiency (7.64) was derived in terms of admittance
parameters in Section 7.3.3. Its definition was in terms of Rollett's stability
factor K in (7.57). A different constant is defined here:
2
Git = gllg" ~ g21 (9.81)
IY211
This constant is always positive because its numerator is the real-part requirement
for passive networks (according to Van Valkenburg, 1960, p. 312). It is
easily related to the stability factor:
K=2'it+1.
(9.82)
The maximum-efficiency expression in (7.64) may then be .formulated for the
passive reciprocal network:
(9.83)
This is a mono~onic function of 0t; therefore, many aspects of 'i1max may be
analyzed in terms of 'it instead. The corresponding choices of + / - signs will
be useful in Section 9.6.
It will now be shown thaC maximum efficiency is the single parameter that
controls the relative size of the input-plane image of the load plane. Consider
Figure 7.13 in Section 7.3.2. The ratio of image-circle diameter to the distance