Small untuned single turn square loop for field strength measurements

This article describes the design of a loop antenna for field strength measurement.

Design criteria:

The first choice is a single turn square loop. A square loop is:

Figure 1 shows the prototype small small untuned square loop. Note the lightweight timber frame, 1:1 voltage balun and RG58C/U feedline.

Fig 1: Prototype small untuned square loop


Analytic model

The analytic model assumes a small single turn square loop in free space with uniform current distribution, using a circular copper conductor. The assumptions, relevant physical constants and loop parameters are set out in Figure 2.

Note that many of the functions defined below are functions of frequency (f), and will use the frequency defined above for example values.

Fig 2: Constants

The next stage is to calculate the voltage induced in the loop by the changing magnetic flux due to the incident EM wave, see Fig 3..

Fig 3: Open circuit voltage

The equivalent source impedance of the antenna must be determined to later calculate the loading effect of the receiver. The equivalent impedance is an inductance in series with the radiation resistance and loss (or ohmic) resistance. At the upper end of the frequency range where the stated assumptions apply, the impedance is dominated by the inductance. Accuracy of the estimation of the resistances is not very important, but the inductance is very sensitive to the diameter of the wire. See Fig 4 for the calculations of antenna equivalent source impedance.

Fig 4: Equivalent source impedance

The load voltage can be calculated from the open circuit loop voltage by voltage divider action of the receiver input impedance and the antenna source impedance, see Fig 5.

Fig 5: Load voltage

The antenna factor is found by dividing the magnitude of the incident E field by the magnitude of the voltage at the receiver input terminal. Fig 6 shows the calculation of the Antenna Factor

Fig 6: Antenna Factor

Fig 7 shows a plot of Antenna Factor against frequency. At low frequencies, it decreases at about 20dB/decade, transitioning to 0dB/decade at the upper end of its useful range. The loop will often be used in this transition area, and piecewise estimation of AF is not sufficiently good, the exact value must be obtained from a chart or table for each frequency.

Fig 7: Antenna Factor vs Frequency

The Antenna Factor at 3.5MHz is 35.7dB/m, so it satisfies the design criteria. Note that further allowance must be made balun loss and transmission line loss, but there is sufficient margin to still comfortably be better than 40dB/m.

The analytic model is available for download in Mathcad format and in Excel format.

NEC2 model

An NEC2 model of the square loop with same dimensions as above, in free space, was constructed and excited by a 1V/m linearly polarised plane wave from the direction of the maximum response of the loop. One segment of the wire model was loaded with a 50Ω load to represent the receiver and the Antenna Factor calculated as AF=-20*log(I * 50). Table 8 shows the Antenna Factor for two different feed configurations.

Table 8: Summary of NEC2 models
Configuration Current in 50Ω load (A) Antenna Factor (dB/m)
Load in end segment of leg (simulates corner feed) 3.8892E-004 34.223
Load in centre segment of leg (simulates centre feed) 3.8836E-004 34.236

Model comparison

The two models indicated very similar Antenna Factor, in fact they were in agreement to precision better than the expected accuracy of any construction. Fig 9 compares the two model results. 

Fig 9: Model comparison
Model Antenna Factor (dB/m)
Analytic 34.220
NEC2 34.223


Small loops are directional, with directivity of 1.5 or 1.76dB. Antenna Factor in the models above has been calculated on the major lobe of the loop. Antenna Factor averaged over the entire sphere will be 1.76dB lower. The Average Antenna Factor is appropriate for measurement of signals that full surround the antenna, or approximate such.

Fig 10 shows the polar pattern normal to the plane of the loop. The null occurs when the loop faces the source.

Fig 10: 2D Polar pattern normal to plane of the loop.

Fig 11 shows a 3D polar plot of the loop, the loop is in the Y plane.

Fig 11: 3D polar plot of loop


Preliminary measurements against a dipole indicate that the Antenna Factor is broadly consistent with the calculated value. Detailed measurements are planned subject to availability of suitable test resources.

Links and resources


Thanks to Keith (VK1ZKM) and Alan (VK2TWB), and the the participants of rec.radio.amateur.antenna for their comment and suggestions, particularly Reg (G4FGQ) and Frank (VE6CB), and anyone else that I have bothered with these models in the past weeks.


Version Date Description
1.01 30/11/2006 Initial.


© Copyright: Owen Duffy 1995, 2021. All rights reserved. Disclaimer.