My friend Carlos, VK1EA, made some measurements of an MFJ-1786 SUPER HI-Q 36″ (0.914m) DIA 10-30 MHz loop at 10.1MHz.

This article presents some modelling and analysis of the antenna principally to estimate its performance.

The loop was located at 2m above natural ground away from other conducting objects.

He tuned the loop for minimum VSWR at around 10.1MHz and took a sweep with a EU1KY antenna analyser looking through 0.5m of RG223 50Ω cable saving the results to a s1p file which was imported to Antscope.

## Measurement of the real antenna

Here is the impedance plot (excuse the |Z| plot as it is Rigexpert's concession to hams who do not understand impedance and I cannot disable it).

Above, the impedance plot. The cursor is at point of minimum VSWR, and the associated R and X values at the measurement point are not very useful.

Above, the Smith chart presentation is much more revealing.

### Expected behavior

Let's digress for a moment and consider the characteristics of a simple directly fed resonant loop with no coupling networks? Over a narrow frequency range about resonance, R will vary relatively slowly with frequency (in fact it will be approximately constant) and X will vary relatively quickly.

Above is an NEC4 model of such a loop, the impedance plot approximately coincides with the R'=1 circle about resonance.

### Actual

But the measured impedance looks quite different, lets look at it again.

It looks quite different to the expected behavior of the underlying loop, but it does contain an arc albeit rotated and offset (the latter a consequency of not being properly matched). In fact it can be transformed in two simple steps.

First step: the plotted locus is of the ‘C' shape that was expected, but it is rotated clockwise (ie towards the source) by some amount.

By eye, a line perpendicular to the locus at the point where it is closest to the Smith chart centre (min VSWR) through the centre is rotated clockwise by about 309° from the direction of the Gamma=1∠0° (or the X=0 axis).

That implies a transmission line like transformation of round trip delay 309°, or electrical length of 309/2=154.5°. Let us calculate the equivalent length of lossless line with VF=0.66, at 10.1MHz it is 8.4m.

Above is the plot with “cable subtracted” and in this case the length of cable subtracted was find tuned to 8.26m for best fit of the curve with a constant R circle, and in this case R=27.9Ω. The antenna is not unmatched, it is matched for a different impedance, and it is capable of analysis.

Step 2: the next step is to normalise the Smith chart to R=27.9Ω.

Above, the normalised plot now looks almost exactly as expected of the underlying loop, and here the cursor notes the lower 3dB bandwidth point (RL nominally 6.99dB). The upper point is 10.105MHz and without extrapolating, we can say the half power bandwidth is approximately 8kHz.

## NEC-4.2 model

So let's build and calibrate an NEC4 model for the same half power bandwidth as measured.

The model is based on measured dimensions and an assumption of “average” ground type (σ=0.005, ε_{r}=13) and loss of the tuning capacitor adjusted to calibrate the model to the same half power bandwidth as the measured antenna. The calculated efficiency, gain pattern etc should then be a good model of the real antenna.

Above is the calibrated model VSWR and |s11| response. The half power bandwidth of a matched antenna is the bandwidth between freqencies where |s11| is -6.99dB (or ReturnLoss is 6dB, or VSWR is 2.618), it is approximately 8kHz (to simulate the measured loop).

Above, the model summary gives us the radiation efficiency as 10.61% (-9.7dB).

Above is the gain pattern. Maximum gain is at the zenith, and whilst it is good at high elevations angles, it falls away quite quickly below 20° elevation. It is a good NVIS antenna at 10.1MHz, but there isn't often paths for NVIS at that frequency.