The Ideal Low-Pass Filter in the form of a Dispersionless Lag Line

Some theoretical and practical aspects of the design of the ideal low-pass filter in the form of a dispersionless lag line are considered. It is shown, in particular, that an artificial line made up of series inductances and shunt capacitances, with 18 per cent aiding mutual inductance between adjacent coils and 8 per cent shunt capacitance between alternate tie points, forms, for many purposes, a sufficiently good approximation of a dispersionless lag line. The mathematical study of the function f(n) = fo (1 -cos ϕ/ϕ
²
) cos nϕdϕ, which is of pertinent interest in lag-line theory, is given in an appendix.