Synthesis of Unbalanced RLC Networks

摘要

A method is demonstrated for synthesizing an unbalanced RLC network with lossy coils, i.e., each inductance has an associated series resistance. The network realizes a minimum phase transfer function whose numerator and denominator are of degree not higher than the third and fourth, respectively, and whose poles and zeros may lie anywhere in the left half of the complex frequency plane. It is shown that in many cases higher degree functions may be realized as one network. For a transfer function of arbitrary degree, factoring into component transfer functions is carried out, each component having the above characteristics; the components are then realized separately and isolated from each other by vacuum tubes supplying gain. The method makes use of the following new features: 1. A breakdown of a Hurwitz polynomial into two Hurwitz polynomials so that a division by one of them yields a sum of unity plus a positive real RLC function, each of whose partial‐fraction terms (complex poles taken in pairs, or course) is positive real. 2. An application of a network theorem which divides the desired network into two networks, thus simplifying the synthesis problem. 3. A method of zero shifting to any point in the left half‐plane with at least one pair of complex poles. A further advantage of the procedure is that the network may be designed to possess input and output shunt capacitances so that tube capacitances may be automatically provided for.