download searchable PDF of Circuit Design book - IEEE Global ...

Comments on a Design Procedure 325
with respect to the synchronous capacitance of the Kth node:
S~'; = ±jQLK ' (8.117)
where the + sign is for even values of N. The ± signs come from the identity
(8.118)
which must be considered by comparing (8.113) and (8.114). It should now be
clear why minimum-loss filters also have minimum sensitivity.
Similar consideration of (8.113) with respect to any ZOij yields the surprising
result
Also, a detuning analysis of simple LC resonance shows that
(8.119)
8L/L+8C/C
2
(8.120)
for the small perturbation factor 8.
The effect of small changes in the load reflection coefficient r L on transfer
function S" is often of interest, especially the effect of changes in the transfer
angle 0". It can be shown that
ti1S 21 1= ±2010g lO (I+IS"IIfLi) dB,
M 21 = ± 57.3I S,,11fLI degrees,
where S22 is the output scattering coefficient.
and
(8.121)
(8.122)
8.5.5. Tuning. Refer to Figure 8.1 and recall that an inverter changes a
short circuit to an open circuit, and vice versa, according to (8.7). A synchronous
filter-tuning procedure was described by Dishal (1951). Suppose that
there are no end couplings. The following procedure is then used:
1. Set trap frequencies with a grid-dip meter and verify all inverter
reactances on an impedance bridge.
2. Short-circuit to ground (or severely detune) the second node, lightly
couple excitation to the first resonator with a small loop or small
capacitive coupling, and then tune the first resonator for maximum
voltage across it. Measure voltage VI with a very high-impedance
voltmeter.
3. Remove the short circuit from node 2 and place it across node 3. Then
tune resonator 2 for minimum VI (yes, VI!)'
4. Continue moving the short circuit to nodes nearer the load, consecutively
tuning the newly unshorted odd (even) resonators for maximum
(minimum) voltage V, across the input node.