Broadband matching of an RLC load by optimal Chebyshev gain functions

By using the polynomial formalism, the gain-bandwidth restrictions are determined in the case of the single broadband matching of an RLC load when the Chebyshev gain function is used. The roots of polynomial h associated to a global 2-port Q are assumed to be located in the closed right half-plane. A theorem is stated which allows one to determine under which condition an RLC load can be matched by using a Chebyshev gain function. A method is proposed to find automatically the Chebyshev gain function which maximizes the minimum passband gain F_m. For a fixed value of R_L C_L ω_c, the curve of the optimal value of F_m, as a function of L´´ ω_c/R_L, is shown. Finally, the elements of the equalizer are calculated by using the explicit Weinberg relations