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Maximally-Flat Time Delay Ladders

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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 anepsilon G/omega_0-farad shunt capacitor The ladder elements rapidly taper toward a capacitance of2G/omega_0farads and an inductance of2R/omega_0henries. 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 are32G/(9omega_0)andepsilon^{3}G/(9omega_0)farads, respectively. The impulse and step responses of the transfer impedance are also derived.

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Circuit Theory, IRE Transactions on  (Volume:6 ,  Issue: 2 )