Synthesis of symmetrical dual mode in‐line prototype networks

An analytic synthesis technique is developed for symmetrical dual mode in‐line prototype networks up to and including degree 12 networks. Due to the symmetrical realization, the even mode coupling matrix completely defines the network and one particular form representing the double cross‐coupled array, may be obtained directly from the transfer function. Commencing with this matrix, rotational transformation are used to transform the even mode matrix into the form required for a dual mode in line structure. Analytical solutions are obtained for degrees up to and including 12 and the necessary realizability conditions are determined for each case. Explicit formulas for the angles of rotation are given and for degrees up to and including 10, a complete set of explicit formulas are provided for the final coupling matrix. To assist in the design of the in‐line structure, tables of element values for filters having 20 dB and 26 dB return loss and possessing the minimum number of transmission zeros at infinity are tabulated.