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# Open Circuit Voltage Coupled into a Semi-Infinite Transmission Line by an Exponential, Plane Waveform

This Demonstration calculates the open circuit voltage coupled into a semi-infinite transmission line above a conductive ground by a plane incident electric field with an exponentially decaying magnitude. The graph shows the variation of the voltage as a function of time for three transmission line heights: 5 meters (green), 10 meters (red), and 15 meters (blue). The peak magnitude of the incident electric field is 1 volt/meter. The calculated voltage waveform has been normalized by a directivity function that depends on the elevation and azimuthal angles of the incident field and the attenuation and propagation constants of the transmission line.

### DETAILS

You can vary the time constant of the exponential decay, the elevation angle of the incident field's arrival, the conductivity of the ground, and the polarization of the incident electric field. The first snapshot is an example where the time constant and the incident angle are taken to opposite extremes. All three voltage waveforms are present but overlapping. The second snapshot changes the ground beneath the transmission line to a perfect conductor, creating the sharp transition point when the ground bounce arrives. The third snapshot changes the polarization of the electric field. In each case, all variables other than those specified as being changed are the same as in the original plot.
Based on Equation 3.30, page 54, in the textbook, Edward F. Vance, Coupling to Shielded Cables, New York: Wiley, 1978.
Approved for Unclassified-Unlimited release as SAND2009-0187P.

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