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Network Objective Functions 155
Table 5.5.
Some Lowpass L-Section Results for ZL= 0.25 + jO
SWR at Radian Frequency
p L C 0.8 1.0 1.2
2 1 1 3.1733 4.2656 7.0016
1.6471 0.4117 1.8626 1.1545 1.5670
10 1.6710 0.4192 1.8122 1.1040 1.6686
30 1.6903 0.4226 1.7817 1.0739 1.7338
subroutine 2100, which ends at line 2190. Line 2170 corresponds to the ilh
term in (5.88), where the response R; is the standing-wave ratio (SW), weight
W; is fixed at unity, and goal G; is fixed at zero.
The standing-wave ratio SW is computed at each sample frequency by the
GOSUB3000 in line 2160. Subroutine 3000 calculates the input impedance of
the network in Figure 4.1gb according to the easily obtained expression
_ [Rc]+j[wL+Xc]
2\- [i-wC(wL+XdJ+j[wCRc]' (5.90)
The SWR calculation is that defined by (4.59) and (4.57) when R\ = I is
assumed. The four real and imaginary parts of (5.90) are assembled and
employed in lines 3010-3070. Note that this lowpass-network SWR function
assumes a unit source and is frequency normalized, so that units of henrys,
farads, and radians are appropriate. Also, note that network analysis Program
B4-1 could have been used for more general networks, especially since the
likely variables for optimization -appear in the X(·) array in both B4-1 and
B5-2.
Table 5.5 shows some results obtained by starting L-section optimizer B5-2
at L=C= 1 for P=2 and continuing, after sequential minimizations, with
P= 10 and P= 30. The load impedance was specified as 0.25 +jO ohms at each
of three sample frequencies, but arbitrary impedances at any number of
frequencies could have been employed. The SWR values shown were printed
by Program B5-2, line 2165, when the variables were unperturbed (flag
variable C=O set by line 1005). Note the tendency for equal SWR deviations
at the band edges for increasing values of P. According to (4.59), SWR can be
no less than unity, so that the squared error cannot be less than 3; it started at
77.29 and decreased to 7.26 in ITN = 7 iterations (linear searches) using
IFN = 26 function evaluations (not counting the additional 52 perturbed
evaluations). Also, each of the 78 error function evaluations required network
analyses at three frequencies. It is easy to see why more efficient network
response and sensitivity calculations are essential when optimizing more than
just a few variables.
5.5.5. Summary ofNetwork Objective Functions and Optimization. The concept
of the area between desired and approximating functions over a range