ABSTRACT
The properties satisfied by a rational one-port immittance to be LPR were given in the Foster Theorem. A function with these characteristics is often termed a Foster function. The crucial conditions are that all poles of the function be simple, all occur in conjugate pairs except at zero or infinity and be confined to jω, and all have positive real residues. Although lossless one-ports can be considered within the purview of resistively terminated lossless two-ports by including zero or infinite resistors as loads, practically a lossless one-port is synthesized in Foster or Cauer canonic forms, or possibly by more complicated purely lossless structures. It is a straightforward matter to count the number of circuit elements required for the Foster synthesis by inspection of the partial fraction expansion. The result for either the impedance or admittance representation is the same and is given as twice the number of internal poles plus the number of external poles.
