Theory of Direct-Coupled-Cavity Filters

A 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 P₀ / /P_L = 1+h²T_n²[ω₀ / ω sin(π ω / ω₀) / sinθ₀´] where h defines the ripple level, T_n is the first-kind Chebyshev polynomial of degree n, ω / ω₀ is normalized frequency, and θ₀´ 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.