A Simplified Derivation of Causality From Passivity for the Impedance Representation of Transmitting Antennas

A relatively simple, straightforward, self-contained derivation, sufficiently general for most engineering purposes, is given to show that passivity implies causality for the input-impedance representation of linear, single-port, time-invariant transmitting antennas. The necessary and sufficient condition on the time-domain input impedance for the electrical stability of these antennas is also derived. It is shown that a series resistance-reactance representation of the input impedance of an antiresonant passive antenna has a noncausal and nonpassive time-domain resistance and reactance, even though the total time-domain input impedance satisfies the passivity, causality, and stability conditions.