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Theory of Direct-Coupled-Cavity Filtersby: R. Levy
Microwave Theory and Techniques, IEEE Transactions on In Microwave Theory and Techniques, IEEE Transactions on, Vol. 15, No. 6. (1967), pp. 340-348.
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AbstractA new theory is presented for the design of direct-coupled-cavity filters in transmission line or waveguide. It is shown that for a specified range of parameters the insertion-loss characteristic of these filters in the case of Chebyshev equal-ripple characteristic is given very accurately by the formula P<sub>0</sub> / /P<sub>L</sub> = 1+h<sup>2</sup>T<sub>n</sub><sup>2</sup>[ω<sub>0</sub> / ω sin(π ω / ω<sub>0</sub>) / sinθ<sub>0</sub>'] where h defines the ripple level, T<sub>n</sub> is the first-kind Chebyshev polynomial of degree n, ω / ω<sub>0</sub> is normalized frequency, and θ<sub>0</sub>' is an angle proportional to the bandwidth of a distributed lowpass prototype filter. The element values of the direct-coupled filter are related directly to the step impedances of the prototype whose values have been tabulated. The theory gives close agreement with computed data over a range of parameters as specified by a very simple formula. The design technique is convenient for practical applications.
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