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BaruJpass Network TransJof1lUltions 211
to L, = 0 and L,= 0, respectively. Thus n must be chosen in the closed range
(
L )-1
1+ L; "n" 1. (6.93)
Note that when L,=O (n= I), the Tsection degenerates into the L section. All
possible results for transformations of this type appear in Table 6.4.
Program A6-4 in Appendix A performs all of the preceding calculations for
all possible cases in only 80 steps. Compare the operations in Table 6.4 with
the L-section matching operations in Figure 6.2. The former are frequency
independent and involve only one type of reactance (L or C) at a time,
whereas the latter are mixed Land C cases valid only at a single frequency.
Example 6.17. Complete the broadband-matching problem posed in Example
6.15 by replacing the capacitive type-B L section in Figure 6.32 by a pi of
capacitors. Use Program A6-4 by entering 1/3.6534 and 1/2.6548 into the
HP-67/97 stack and pressing key A. Then select the type-B-to-pi case by
pressing key B. The result is the allowable extreme value of n' farthest from
unity, in this case 0.1771. It is determined from Figures 6.29 and 6.32 that
n 2 =20/51.722=0.3867 is required, and it is within the allowable range.
Entering 0.3867 and pressing the R/S "continue" key produces the first value
of reciprocal C in the X register, namely 1/C, = 0.4905, or C, = 2.0389. The Y
register contains 1/C b =0.2342, or C b = 4.2693. Similarly, the Z register in the
stack contains 1/C,=0.3852, or C,=2.5963. The network to the right of the
capacitive type-B L section in Figure 6.32 must be an impedance scaled down
by the factor 0.3867, as previously mentioned. Doing this completes the final
design shown in Figure 6.34. Observe that the total requirements stated in
Example 6.15 and shown in Figure 6.29 have been fulfilled.
50 n
4.2692
1IVV 1 J
1 1
1 I
: : L 2.59~ l- I
2.039 I
1 I
I
I
Figure 6.34.
"
64166
12.658 4.0045 :r: 20 n.
I
IpFandnH
Final broadband design for Example 6.15 following the Norton transformation.
I
11
6.5.4. Summary of BaruJpass Network Transformations. The standard geometric
frequency mapping from lowpass to bandpass response was stated, and
the easily remembered design rules for network element conversions were
stated. The main parameter is the fractional bandwidth w. The resulting
bandpass networks were created by converting all lowpass shunt C's into