Synthesis of symmetrical RC and RL lattice networks with maximum gain and minimum number of elements

New methods of synthesizing symmetrical lattice networks using resistors and capacitors, or resistors and inductors, are presented in the paper. The methods permit the synthesis of any transfer function that is a ratio of output voltage or current, to input voltage or current, as long as the transfer function satisfies the conditions of physical realizability of transfer functions with RC or RL networks. The load impedance can also be specified as long as it is realizable with an RC or RL network. A transfer function is synthesized by synthesizing an equivalent open-circuit voltage transfer function that is derived from the desired transfer function and load impedance. The resulting network is then modified, and the desired transfer function with the given load is obtained. Two root-loci plots are used in the synthesis procedures, as well as in a proof that any open-circuit voltage transfer function satisfying the conditions of physical realizability of RC transfer functions can be synthesized using the prescribed method. The network, resulting from the synthesis of an open-circuit voltage transfer function, has maximum gain and a minimum number of elements, if desired.