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A pair of filter design examples may help to demonstrate the effectiveness of the current, non-iterative design method. An evanescent mode filter can be designed using closed-form Eqs. 11 and 15. To check the results of the current design approach, they are compared in Table 1 with the example presented in ref. 3, which employed a lengthier iterative design approach. Given that the center frequency, fc, is 6.5571 GHz, and the cutoff frequency, f0, is 3 GHz, the ripple for this example lowpass filter is 0.01 dB and the minimum stopband attenuation is 50 dB at 328 GHz. The design employs WR-90 ridged waveguide, with a length, L, of 0.9 in. (2.29 cm) and width, W, of 0.4 in. (1.02 cm), which leads to:

The prototype parameters for this first example lowpass filter include g0 = 1; g1 = 0.7969; g2 = 1.3924; g3 = 1.7481; g4 = 1.6331; g5 = 1.7481; g6 = 1.3924; g7 = 0.7969; and g8 = 1, with differential, Γ, given by Eq. 17:

Solving for the inner resonators yields Eq. 18:

and results in the following values for the inner resonators:

l1 = l6 = 2.1026 cm; l2 = l5 = 2.4060 cm; and l3 = l4 = 2.4682 cm.

To solve for outer resonators, the largest g values are used. Since the outer resonator lengths are arbitrary, the largest g values are chosen to minimize the reflection from the end walls of the filter:

resulting in the following values: l0 = l7 = 2.7242 cm.

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