Resonance Characteristics by Conformal Mapping

The analytical expression f(¿) = a¿+ b + c/¿, where ¿ = ¿+j¿ may be called the "resonance function." It represents, for example, the impedance of the series-connected LRS circuit and the admittance of the parallel-connected CGT circuit. The conformal mapping of the ¿-plane onto the f(¿)-plane yields a figure of considerable usefulness in clarifying the meaning of the resonance function for complex frequencies. Typical examples illustrate the application of the figure to the parallel circuit and one of its intrinsic generalizations. A brief discussion of the mapping of the reciprocal of the resonance function is included for completeness.