**Authors:** Hans G. Schantz

**Source:** FERMAT, Volume 4, Article 2, Jul-Aug., 2014

**Abstract:** â€”Superposition demands that a linear combination
of solutions to an electromagnetic problem also be a solution.
This paper analyzes some very simple problems â€“ the
constructive and destructive interferences of short impulse
voltage and current waves along an ideal free-space
transmission line. When voltage waves constructively interfere,
the superposition has twice the electrical energy of the
individual waveforms because current goes to zero, converting
magnetic to electrical energy. When voltage waves destructively
interfere, the superposition has no electrical energy because it
transforms to magnetic energy. Although the impedance of the
individual waves is that of free space, a superposition of waves
may exhibit arbitrary impedance. Further, interferences of
identical waveforms allow no energy transfer between opposite
ends of a transmission line. The waves appear to recoil
elastically one from another. Although alternate interpretations
are possible, these appear less likely. Similar phenomenology
arises in waves of arbitrary shape and those propagating in free
space as well. We may also interpret this behavior as each wave
reflecting from the impedance variations the superposition
imparts on free space. This work has practical implications to
quantum mechanics, field diversity antenna systems, and nearfield electromagnetic ranging.

**Index Terms:** Superposition, electromagnetic energy,
quantum mechanics, near-field electromagnetic ranging,
diversity.

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