Cascade Driving-Point-Impedance Synthesis by Removal of Sections Containing Arbitrary Constants

Through extensions of Richards' theorem it is shown that certain realizable network sections containing one or more arbitrary constants may always be removed from an RLC driving-point-impedance function leaving, as a termination, another RLC driving-point-impedance function which contains the same arbitrary constants. These constants are utilized to produce desired characteristics in either the removed network section or the terminating impedance. Some of the removed sections contain a gyrator which, it is shown, may always be eliminated through proper choice of some of the arbitrary constants to yield other purely reactive reciprocal sections which still contain at least one arbitrary constant. The constants may also be chosen to reduce the rank of the terminating impedance. The result is a perfectly general reciprocal cascade-synthesis procedure applicable to any prf driving-point impedance. Specific impedance operators (associated with the removed sections) and their synthesis by Darlington-type procedures are considered in detail.