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288 Direct~CoupleJ Fi/ters
MHz, it is found that these reactances must be in the range 6.2832-94.2478
ohms. The synchronous resonator reactances are calculated next using (8.3).
Thus X,=9.2141 and X",= 18.4283 ohms. The value of R" shown in Figure
8.12a does not effect selectivity; trying R" = 75 ohms yields XII = 6.9106
ohms, which is within limits. However, it is still necessary to be sure that the
inverter reactances are within limits. Using (8.9), Xl." = J50· 75 = 61.2372 and
X U3 = J75· 100 = 86.6025 ohms, which are within limits. A new trial value of
R 22 would be necessary if any of these three inductive reactances were out of
the allowable range. The circuit reactances are shown in Figure 8.12b.
It is now necessary to absorb the negative reactances. This is conveniently
accomplished by Program A6-1, using key C. The final reactance values are
indicated in Figure 8.12b. There is a very convenient rule illustrated in Figure
8.12b: all the L's touching a node must resonate all the C's touching that
node. This is easily seen, because the two inverter branches touching a node
cancel when in parallel, i.e., when adjacent nodes are grounded. The final
element notation is shown in Figure 8.12e. The rule says that L, and L t2 in
parallel will resonale Ct. Similarly, L", L" and L 23 in parallel will resonate
C,. Designs should always be checked to ensure that this rule is satisfied.
Table 8.1.
Element Values and Data for the Design Example in
Figure 8.12 and for Analysis Program B4~1
Units: Frequency Induclance Capacitance
IE6 IE-9 IE-12
Load (ohms): Resistance Reactance
100 0
Power in load= 1/4R 5
=0.005 watts
Topology: Type Value Q Remarks
3 17273 0 C3 PF
-2 74.52 0 L, nH
2 275.66 0 L'3
3 460.6\ 0 C,
-2 27.25 0 L,
2 194.92 0 L"
2 34.52 0 L,
-3 345.46 0 C,
I 50.00 0 R,
Note: Q=O implies an infinite Q value.
At 50 MHz, Zi"~49.9994+jO.0752 ohms.
At 90 MHz, 15,,/=60.11 dB.
There is a loss of 3 dB at 45.0 and 54.3 MHz (18.81% handwidth).
The ideal, maximally flat case has 3 dB at 45.6 and 54.82 MHz
(18.43%).