Maximally-Flat Time Delay Ladders

The driving-point impedance for a maximally-flat time delay response is derived. The impedance is synthesized as an infinite low-pass LC ladder that starts with an -farad shunt capacitor The ladder elements rapidly taper toward a capacitance of farads and an inductance of henries. The impulse and step responses of the impedance are derived as a series of Bessel functions. A three-terminal maximally-flat time delay transfer impedance is also considered. The conditions for a smoothly-tapering ladder structure are given. The transfer impedance is synthesized as an infinite low-pass LC ladder whose first two shunt capacitors are and farads, respectively. The impulse and step responses of the transfer impedance are also derived.