Network Functions with a Constant Imaginary Part

The paper considers the problem, suggested by the circuitry of the so-called seven-league oscillator, of constructing a positive-real rational function whose imaginary part makes an equal-ripple approximation to a constant value over a wide band of frequencies. It gives an exact solution using elliptic functions and shows that the resulting function satisfies the conditions for realization with either an or an circuit. Performance curves and computing details are included.