Numerical synthesis of RLC one-port networks

An iterative numerical technique is used to synthesize a given minimal RLC network with a prescribed admittance function. A minimal network is one containing the minimum number of capacitors and inductors and as many elements as there are independent coefficients in the admittance function. Reducing the given network through certain reduction techniques to one that can be synthesized by routine methods produces the initial element values. Coefficient matching of admittance functions is used to establish evaluating equations for element parameters. The concept of sensitivities of the evaluating equations with respect to element parameters is used to achieve fast convergence. The element values can be determined to any degree of accuracy desired. Special attention is paid to biquadratic functions realized by networks containing one inductor, one capacitor, and three resistors. It is noted that there may or may not be a solution