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The Complex Frequency Variable
A Consideration of Energy with Some Remarkable
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admittance angle approximation band arbitrary behavior branch cut Brune process calculation capacitor Chebyshev approximation coefficients complex complex potential conductor consider constant corresponding cosh curve determine discussion dissipation driving-point immittance functions driving-point impedance function dual element values equations example finite function Z(p given Hence Hurwitz polynomial Illustrate imaginary axis imaginary zeros imation inductors infinite integral L-C network left half plane loop currents magnitude mapping method minimum-reactance multiplier mutual inductance number of elements numerator and denominator obtain odd function one-terminal pair origin p-r function partial-fraction expansion plot pole at infinity polynomial positive reality positive-real possible potential Prob problem properties quantization rational function reactance function real and positive real frequencies reduced relations removed residues resistance function resistor right half plane right-half-plane zeros Show shown in Fig simple Sturm functions Sturm's theorem surplus factor susceptance symmetry synthesis Taylor series voltage zeros and poles zeros or poles