RLC Canonic Forms

Foster's reactance theorem synthesizes the class of lossless networks in a so‐called canonic form. This idea is here generalized in order to show that there is a distinct class of RLC networks possessing a canonic form. It will be shown that when an RLC driving‐point impedance or admittance possesses a canonic form, its poles and zeros must alternate on each and every ``separate part'' of an algebraic curve (c) of a special nature located in the left half of the frequency plane s=σ+jω, belonging to one of the following two families: a0+ ∑ 1nak(σ+αk)(σ+αk)2+ω2=0;  a0   ∑ 1nak(σ2+ω2+αkσ)(σ+αk)2+ω2=0. A corollary of this theorem, in the case (c) is a straight line or circle, symmetrically placed with respect to the real axis, unifies the three known cases of LC networks, RL‐RC networks, and networks with slight dissipation.Analysis and synthesis of RLC networks possessing a canonic form is introduced in the light of a more general approach to the problem based on the class consideration. The problem of the d...