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3. This block diagram shows the evanescent-waveguide equivalent circuit.

Figure 3 shows the schematic of an evanescent-mode waveguide length as a Π network. The relationships in Eq. 5 are valid for any of the internal resonators:

where:

X0 = the reactive impedance of the evanescent waveguide filter;

γ = the complex propagation constant in the evanescent waveguide; and

L = the length of the evanescent waveguide resonator. 

For the end resonators, the relationships in Eq. 6(a)-6(c) can be used:

Similarly, for the output resonator, Eqs. 6(d-f) can be used:

From Seymour Cohn’s classic work on filters:5

where:

w = 2πf = 1 = the cutoff frequency of the lowpass prototype;

g = the normalized elements of the lowpass prototype; and

ki, i + 1 = the coupling coefficient between sections i and i + 1.

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