Calculation of equivalent self capacitance of Small Transmitting Loop – ARRL

In Calculation of equivalent self capacitance of Small Transmitting Loop I mentioned that (Straw 2007), The ARRL Antenna Book 21, gave an expression for equivalent self capacitance of a Small Transmitting Loop of one turn:

C=HD where C is in pF, D in cm, and H comes from a given table of length/diameter ratios from 0.1 to 1.0. ARRL cites (Medhurst 1947) for this expression. Medhurst’s work was for solenoids.

Values of the Constant H for Distributed Capacitance

Length to
Ratio       H
=====       =====
0.10        0.96
0.15        0.79
0.20        0.78
0.25        0.64
0.30        0.60
0.35        0.57
0.40        0.54
0.50        0.50
1.00        0.46

A 1m diameter loop of 10mm diameter conductor has l/d=0.01, so it is not covered by the table, and you might form the view from the table that H tends to 1.0 or thereabouts as l/d approaches 0, but that is an extrapolation and dangerous.

Medhurst says of a single turn coil example:

A one turn coil (of 14SWG, mean diameter 23.9cm, length/diameter 0.0084) departed even more from the trend of the curve in Fig 9, the H value being only 0.23.

Screenshot - 09_11_2015 , 17_18_25

He has not given values for H below l/d=0.1, and his example indicates that there is at least one turning point below l/d=0.1. For an l/d value in the range that might be expected of a STL, the H value was well away from the range of  his curve and extrapolation is quite exposed to error.

It seems to me that Medhurst knew that this formula and table based on Fig 9 was not applicable to single turn coils of very small l/d ratio, and therefore it is not useful for the purpose of estimating the equivalent self capacitance of a typical single turn STL.


  • Medhurst, R. Feb 1947. HF resistance and self capacitance of
    single layer solenoids InWireless Engineer, Feb 1947.
    pp 35-43, and Mar 1947, pp 80-92.
  • Straw, Dean ed. 2007. The ARRL Antenna Book. 21st ed. Newington: ARRL.  Ch5.