Electronics
Software to calculate resistance vs. frequency & temperature

# Wire Resistance vs. Frequency & Temperature

Author: R.J.Edwards G4FGQ © 9th November 2003

This program calculates frequency and temperure effects on conductor resistance.

Enter metric values in the program. Other measurement units will be displayed.

All conductors: round solid copper. Program frequency range: 50Hz - 1GHz.

Examples

1. Single straight wire of any length and diameter.
2. Open-wire line of any diameter, spacing and length.
3. 1/2-wave, centre-fed dipole radio antenna at any frequency >100 kHz.

At HF it will be noticed loop resistance and attenuation increase very fast as wire spacing becomes small. This is the "proximity effect" due to line current being concentrated on the close, facing wire surfaces.

A very long open-wire phone line is still usable at 30 dB or more. Check loss from 300 to 3000Hz. Note how loss changes between summer sunlight and winter night temperatures. A phone or telegraph line may have 1/6" dia. (4mm) wires spaced at 12" (300mm). Zo is then 600 ohms. Try distance 600 miles (1000km).

The program assumes open-wire line leakage resistance is 1 megohm per km.

Check the loss of 1" (25mm) dia. wires spaced 10 feet (3m) at power frequencies.

A 1/2-wave dipole of normal construction has high efficiency at all radio frequencies. Of interest is the variation in Q and bandwidth as the length/diameter ratio of the conductor changes. The "End effect", where the actual resonant length is shorter than 150/FMHz metres, is taken into account. Resonant length is that at which the feedpoint impedance is purely resistive.

Below a few hundred kHz computed dipole data is of academic interest only as it applies to an isolated dipole. In practice a dipole can be considered isolated when it is 1/2 or 3/4-wavelength or more above ground.

For round copper wire, electrical grade purity, at 20 degrees Celsius:

DC resistance = 0.022/Sqr(D) ohms per metre.
RF resistance = Sqrt(F)/12/D ohms per metre, provided SD < D/5
Skin depth, SD = 0.066/Sqrt(F) millimetres.
Resistance temperature coeff = +0.4 percent per degree C.

Where F is frequency in MHz and D is diameter in mm.