# Review of Austin et al paper “Loss mechanisms in the electrically small loop antenna”

(Austin et al 2014) made measurements of feed point impedance of a small transmitting loop using a calibrated transformer, and discussed the loss mechanisms. They also extrapolated their measured data to a larger conductor.

Let me focus on their measurements, the loop was:

• a 1m diameter circular loop of 6.3mm copper;
• tuned with a low loss tuning capacitor (ATC chip capacitor);
• at heights of 3m and 6m above ground;
• from 3.3 – 12.8MHz.

They did not report the capacitor loss, but gave some likely range from manufacturer’s data.

They used ground parameters G-0.007, εr=17 at 7MHz for their NEC models..

Above is a reconstruction of the measured data from their Fig 3. They measured Rin to their matching transformer and used calculated inductance (relying on the calibrated matching transformer) to calculate Q at each measurement frequency.

Some back of the envelope calculations of the loop basics at 7.2MHz in free space are:

• inductance=3.23µH;
• Xl=146Ω
• Loop conductor resistance (Rloop)=0.111Ω;
• Radiation resistance (Rr) in free space 0.00638Ω.
• Rcap in the range 2-20mΩ, if Q was 10,000 then Rcap=14.6mΩ;
• Q in that case would be 146/(0.111+0.00638+0.0146)=1106.

The measured Q at 3m and 6m above ground at 7MHz were 913 and 955 respectively, a little lower than the calculated free space figures which is expected as Rr will be a little different and equivalent ground loss resistance will increase Rtotal by something of the order of Rr. These correspond to half power bandwidths of 7.9 and 7.5kHz respectively, and on the surface of it, suggest that loop efficiency is better than many loops described with larger loop conductor.

## NEC model

A NEC-4 model was constructed to compare the measurement results and a model estimate.

Rr is taken to be the resistance that for a given feed point current would account the total power in the radiation far field.

The NEC-4.2 model was of:

• an octagonal loop of 6.35mm copper of the same enclosed area as a 1m circular loop at 7.2MHz;
• tuned with a capacitor with Q=10,000;
• at a range of heights to 10m above ‘average ground’.

The loop has a very slightly larger perimeter (2.6%) than the circular loop so one expects a slight difference in calculated loop resistance.

Above, the results of the NEC model used to disaggregate loop feed point R into its components.

Calculated R is a little higher than Austin et al, understandable as we do not know the actual ground parameters at the measurement site..

Rr differs to Austin el al which treats Rr as a constant value. The value derived from the model varies with height above ground.

Ground loss resistance Rg also varies with height above ground.

(The first pass of this article was based on models using NEC-4.1, but anomalies were detected for some ground scenarios and referred NEC’s author J Burke who provided an update to NEC-4.2 and its GN 3 ground worked better for the most part.)

Above is the Q calculated from the model. It can be seen that model Q is quite sensitive to height around 3m and a little higher than Austin et al’s measurements (1039 vs 913). At 6m height, the model Q of 1055 is a little higher than the measured 955.

If we take Rr at 3m to be 6.4mΩ, and their reported Q of 913 indicates Rtotal=160mΩ and radiation efficiency=4%.

The main purpose of Austin et al was to:

• show that a coupling transformer could be used to make measurements of the loop’s total resistance;
• to account for ground loss using published curves; and
• show using extremely low loss capacitors that losses implicated in some types of capacitors are a major cause of loss in STL.

Above is the breakup of feed point R for the NEC model at 3m at 7.2MHz. Radiation efficiency is 4.6% or -13.4dB.