# Small square un-tuned loop for field strength measurement - NEC models

This article documents a theoretical model of the Antenna Factor of a small square loop in free space, connected by a balun and specified length of coaxial transmission line to a 50Ω receiver.

Antenna Factor is the ratio of electric Field Strength to voltage on the receiver input terminals.

# Model

The models are created over a range of frequencies using:

• NEC-2 for calculation of the current that flows in a 50Ω load inserted in a corner of the loop as a result of incident radiation from the direction of greatest loop directivity; and
• a detailed RLGC loss model of the transmission line connecting the loop to the receiver.

The number of model segments in each side of the loop varies with frequency, the number of segments is the greater of 5 and int(<side>/(299.792458/<freq>/20)*2)+1.

 CM Small square untuned loop CM Extended thin wire kernel used CM 1. Free Space CM 2. Plane wave excitation CM CM Parms 12.109 1 5 CM CM Owen Duffy (VK1OD) CE GW 1 5 -0.500 0 1.000 -0.500 0 2.000 0.000800 GW 2 5 -0.500 0 2.000 0.500 0 2.000 0.000800 GW 3 5 0.500 0 2.000 0.500 0 1.000 0.000800 GW 4 5 0.500 0 1.000 -0.500 0 1.000 0.000800 GE EK FR 0,1,0,0,12.109 EX 1 1 1 0 90 0 0 0 0 0 LD 5 0 0 0 1.35E6 LD 4 1 1 1 25 0 0 LD 4 4 5 5 25 0 0 GN -1 XQ EN

The Antenna Factor is calculated as AF=-20*log(I*R).

The loop described in this article has 1m sides and consists of 1.6mm diameter bare 316 stainless steel conductor.

The analysis assumes / includes:

• 10m of RG58C/U matched line loss (frequency dependent) included;
• ideal balun (losses included in previous item);
• feedline is adequately decoupled and does not contribute to received signal.

Loop load impedance may be stabilised by a minimum level of Z-matched attenuation ahead of the receiver.

This loop will be self resonant at about 75MHz. Use near resonance is to be avoided because of the steeper slope of the AF curve and the resultant increased sensitivity to small physical implementation details.

The self inductance of the loop tends to compensate the loop to within +/- 1dB over about a decade from 3 to 30MHz, or within +/- 0.5dB over the range from 4 to 20MHz.

For more exact measurement results, the AF can be looked up and entered into the measurement system automatically, or the loop calibration curve loaded for automated correction. FSM has been enhanced in V1.0.12 to read an antenna calibration table and automatically perform a cubic spline interpolation at the frequency of measurement.