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A Complete Design Example 327
using a high-impedance vector voltmeter:
l. Adjacent node voltages should differ in phase by ± 90 degrees.
2. Node voltage magnitudes are easily related to the node's parallel
resistance, based on power.
3. The L-section end-coupling phase should agree with (6.7) or (6.8), as
appropriate.
The swept-frequency display of input node voltage V, during the node-tuning
sequence should appear as in Figure 8.29. Waveguide and other distributed
filters are tuned according to the same principles, namely ideal resonator and
inverter behavior. However, slotted lines and lightly coupled probes are often
required. This is discussed by Matthaei et al. (1964, p. 668).
Dishal (1951) gives relationships that enable the calculation of coupling
coefficients as in (8.26), based on the frequencies of the response peaks in
Figure 8.29. These are often useful for evaluating aperture and other inaccessible
coupling implementations.
8.5.6. Summary ofComments on a Design Procedure. A step-by-step design
procedure for narrow-band, direct-coupled filters has been discussed in terms
of the flowchart in Figure 8.28. The next section will proceed through almost
all of these steps to illustrate the procedure in terms of the tabulated equations
in Appendix G.
Design step 13 is the observation of filter behavior in the laboratory. The
intent of the design procedure is to produce a first-time design success. The
physical properties of many sophisticated filters, especially microwave filters,
make final tweaking in the laboratory very difficult and expensive. Besides the
analysis to determine proper coupling coefficients just suggested, an optimizer
used in conjunction with a network analysis program often can confirm the
presence and values of parasitic elements not previously considered. Such
optimization can then be used to predict new filter component values that
may offset the undesirable effects of the unexpected parasitic elements.
Finally, the great virtue of the loaded-Q filter design method should now be
apparent: it is a flexible procedure that accommodates component limitations
in nearly every stage of the design.
8.6. A Complete Design Example
The design steps in Figure 8.28 will be calculated for the network in Figure 8.2
using an undercoupled response shape with selectivity, as in Figure 8.3. The
step numbers appear after the last decimal in the following paragraph numbers.
The equation numbers correspond to those in Appendix G.