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# Behaviour of a Solenoid Coil as a Transmission Line

Author: R.J.Edwards G4FGQ © 16th March 2006

There is a short vertical antenna less than 1/4-wavelength in height. It is loaded at the bottom end with a single-layer solenoid-wound coil. The top section is a vertical rod or wire. Both the coil and rod are considered to be transmission lines.

The input impedance of the rod terminates the coil and is calculated. The input impedance of the coil, the antenna feed-point, is also calculated.

The distributed capacitance of the coil is that of a cylinder in space with the same length and diameter as the coil.

The distributed inductance of the coil is that of a cylinder plus the inductance due to the turns on the coil itself.

The loss resistance of both sections of the antenna includes conductor resistance and radiation resistance.

Program Operating Notes
The antenna is usually used in its resonant condition. The program analyses behaviour at any test frequency.

When there is no rod the antenna is just a close-wound helix with an electrical length of 1/4-wavelength. (Set rod length and diameter to zero).

To resonate the helix, vary test frequency until its electrical length is 90 degrees, or until the coil's input impedance is purely resistive, jXin = 0.

The antenna can be resonated to a particular frequency by varying the number of coil turns. But remember that the number of coil turns also affects things such as wire diameter, wire length and electrical parameters as well as resonant F.

In practice, to resonate to a particular frequency, it is usual to prune the length of the rod or antenna wire. The program can simulate this.

The velocity of light is 300 metres per microsecond.

The resonant condition is when the feed-point reactance, jXin, is at or very near to zero ohms.

You can check accuracy of calculations by setting F = 30 MHz and entering rod length to 2500 mm which is 1/4-wavelength at that frequency. The input resistance is the resultant of radiation resistance plus wire loss resistance. Similar calculations are made to determine the feed-point input resistance.

In general, calculating accuracy is good enough for the purpose intended.

The coil's free-space resonant frequency is not the same as it is when mounted vertically above a ground plane and when connected to the rod.

When the antenna is in a quarter-wave resonant condition, note that the sum of the rod and coil phase-shift angles differs considerably from 90 degrees.

Operation of the program at frequencies greater than 1/4-wave resonance has not been checked and is unreliable.

Winding pitch is coil length divided by the number of turns. Check that calculated wire diameter does not exceed winding pitch or is not too small. If too small increase diameter/pitch ratio.

To simplify calculations the program neglects "end effect" which results in the resonant length of transmission lines and antenna wires being somewhat shorter than their actual length in wavelengths. In the present context the effect is important only when conductor diameter approaches or exceeds its length. A conductor behaves as if its length is greater than its actual length.