Analytical Solution of the Problem of Synthesis of Three-Link Stepped Chebyshev’s Microwave Filter

The problem of synthesis of the three-link stepped Chebyshev’s microwave filter is reduced to two independent fourth-degree equations, including a single link wave impedance as unknown. The solution of Descartes—Euler is applied to these equations. It is proved that, in case wave impedances of extreme links are equal, the problem of the filter synthesis has two solutions. Identical phase-frequency responses correspond to these solutions. It is proved that for each link a product of the wave impedances relating to these solutions is equal to a square of the wave impedance of the transmission line including the filter.