# The Behaviour of a Single-Layer Solenoid Coil as a Transmission Line

Author: R.J.Edwards G4FGQ © 2nd April 2006All conductors possess inductance and have capacitance to their environment. Series L and shunt C are distributed along their length. The inductance due to a coil winding is added to the inductance of a solid cylinder of the same diameter and length of the coil. The distributed capacitance of the coil is the same as that of the solid cylinder provided the turns are not spaced too wide apart. L and C can be estimated mathematically from coil dimensions.

So the coil behaves as a transmission line with the inductance being greatly increased due to its diameter and number of turns. Velocity is much reduced. For given length, diameter and number of turns, this program calculates:

- Overall primary constants of inductance, capacitance, and loss resistance.
- Secondary constants of impedance Zo, phase delay, velocity factor and attenuation. Also calculated are the 1/4-wave resonant frequency when the coil is mounted vertically above a ground plane, and the input or feed-point impedance when the coil is used as an antenna.

For a sacrifice in radiating efficiency the coil can be far shorter than a full size 1/4-wave vertical antenna. The coil is often top-capacitance loaded with a short whip, rod or capacity-hat which much reduces the resonant frequency. Further calculations are needed.

Program Notes

- Input impedance measurements are made with the coil open circuit at the top.
- Phase shift, in degrees, along the coil is proportional to test frequency.
- As the test frequency is varied through 1/4-wave resonance, note that the phase shift goes through 90 degrees. Also note that the input impedance falls to a low value and input reactance passes through zero with a change in sign.
- Examine input impedance when phase shift is 180 degrees corresponding to a line resonant length of 1/2-wavelength. Do likewise at 270 and 360 degrees.
- When phase shift is 45, 135, 225 degrees etc., input reactance equals Zo.
- When the number of turns on the coil and the coil diameter are small then coil inductance is very small and the velocity factor approaches or equals 1.0.
- Put coil length to 1000mm, diameter to 1mm, pitch to 1000mm, and coil inductance falls to zero. Computed inductance and capacitance are then that of a 1-metre length of wire with a resonant frequency of 75 MHz and a velocity factor = 1.00.
- Radiating efficiency is approximate. Additional loss will also occur in an impedance matching network to a transmitter.

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