# Small untuned loop for receiving – it’s not rocket science

I have written several articles on untuned loops for receiving, as have others. A diversity of opinions abounds over several aspects, but opinions don’t often translate to sound theory.

This article analyses a simple untuned / unmatched loop in the context of a linear receive system.

## An example simple loop for discussion

Let’s consider a simple single turn untuned loop with an ideal broadband transformer. The example loop is 3.14m perimeter and 10mm diameter conductor situated in free space. The loop has perimeter 0.0744λ at 7.1MHz, less than λ/10 up to 9MHz, so we can regard that loop current is uniform in magnitude and phase. This simplifies analysis greatly. Above is a schematic diagram of the example loop. The transformer initially is a 1:1 ideal transformer, it serves to isolate the loop from a coaxial feedline, allowing fairly good loop symmetry and reduction of common mode feed line current contribution to pickup. This works, and subject to symmetry and a good transformer design, it will work well over the stated frequency range, though its gain at some frequencies might not be sufficient to overcome receiver internal noise.

The loop itself is a resonator, it has a resonance near where the length around the loop from one terminal to the other is a half wavelength… much like a half wave dipole formed into a nearly closed circular arc. At low frequencies it behaves much like a simple inductor, but departs from that as its self resonant frequency (SRF) is approached. This behaviour can be approximated as an inductor with a small equivalent shunt capacitance that modifies the behaviour as the SRF is approached.

The low frequency self inductance can be measured easily, and can also be calculated with reasonably good accuracy for practical conductors. External EM waves will induce a voltage in the loop inductance, and there is an equivalent series resistance to that voltage source, it is known as radiation resistance and is fairly easy to calculate for a loop with perimeter less than λ/10 in free space.  The loop conductor also has loss resistance. The effective RF loss resistance is easily calculated for a metal tube of sufficient wall thickness, but conductors like coax braid are higher and more challenging.

So the equivalent circuit becomes an inductor with series loss resistance and radiation resistance and voltage source, all of which us shunted by a small equivalent capacitance to model the effects of self resonance to some extent.

So, lets explore an example. The example loop uses a loop conductor of 10mm diameter and perimeter of 3.14m (it is a 1m diameter loop). We can reasonably calculate:

• loop self inductance is 2.94µH;
• equivalent shunt capacitance is 4.66pF (which we will assume lossless);
• radiation resistance @ 7.1MHz is 6.033mΩ.

We will capture loop conductor loss by estimating that it has a Q of 100 @ 10MHz. The results turn out to not be very sensitive to this value, so don’t agonise over it. Above is a Simsmith model of the example loop loaded with a 50Ω receiver connected directly to its terminals.

Because of significant mismatch, not much of the power available from the source (1W or 0dBW in this model by virtue of Simsmith’s UseZo option) reaches the receiver, in fact the system has a loss of 42.1dB, so the average gain is -42.1dB. The directivity of such a loop in free space is 1.5 or 1.76dB, so the antenna system (maximum) gain in this scenario is -40.34dB.

Is such a loop usable at 7.1MHz? Assuming a linear receive system (ie no IMD) with Noise Figure 5dB and using ITU-R P.372 prediction of median external noise in a Residential precint, the S/N degradation by receiver noise is 1.58dB. IOW, S/N is within a couple of dB of what would be observed with a much better antenna.

The same would not be true of a quieter place… For almost the same scenario but Quiet Rural external noise, S/N degradation is pretty poor at 16.2dB.

Note that receiver noise figure may vary with source impedance, it is assumed here that for the range of source impedances considered that the variation is insignificant.

## Shielded loops

Lets look at some shielded loops, there are very many configurations and most of them are not worth discussing because they fail the most important requirement of being electrically symmetric.

Let’s look at three to expose a method of analysis.

### N6RK shielded loop The diagram above from (Karlquist 2009) shows a simple shielded loop that is symmetric provided the feed network is a balanced feed and is approximately symmetric to the loop itself. Karlquist gives the above equivalent circuit, but it is naive and incomplete. The “1/4 coax capacitance” element is a crude approximation of the effect of the coax sections in each limb of the loop, it pretends that transmission line is adequately represented by some equivalent capacitance, and that is not very accurate in this scenario. It also lacks the source voltage and equivalent source resistance (radiation resistance). The above equivalent circuit models the coax as transmission line. The model assumes lossless 2×50Ω lines for each section forming the 100Ω line T1. Average gain is -43.2dB, a little worse than the simple loop.

A popular ham belief is that increasing Zo of the coax used for each limb of the loop improves gain, and there are articles on the net where people have tried to fabricate such loops but I have not seen convincing measurements. They are perhaps misinformed by the naive capacitance model and think that higher Zo reduces the equivalent C in isolation. Above is the same model with just the line Zo changed to 2×75Ω, and gain has not improved, it has decreased by 0.9dB in this scenario.

Karlquist’s complete antenna system includes a matching unit, the analysis here is of the shielded loop loaded by a 50Ω receiver and does not imply the performance of Karlquist’s complete antenna system.

## Moebius shielded loop The Moebius shield loop configuration is as shown above for Airspy’s YouLoop-2T, but this analysis is for a loop with perimeter 3.14m (as the others in this series). The above equivalent circuit models the coax as transmission line. The model assumes lossless 2×50Ω lines for  the section T1, F1 models the impedance transformation caused by the crossover connection at the gap. Average gain is -47.6dB, more than 5dB worse than the simple loop.

### Simple Shielded loop with integral balun Above is the detail of a simple shielded loop using 50Ω coaxial cable to a 50Ω receiver at the loop terminals. Note that the coax structure creates an integral balun. With 50Ω coax and 50Ω receiver, there are no significant standing waves on the feed line or coaxial loop section so the impedance presented at the loop gap is a broadband 50+j0Ω (approximately). The above equivalent circuit models the coax as transmission line. The model assumes lossless 50Ω line for  the section T1. Average gain is -42.1dB, similar to the simple loop.

## References

• Karlquist, R. Sep 2009. An improved feed network for loop type receiving antennas In NCJ Sep 2009.

## Conclusions

The results apply to the scenarios described at the test freqeuncy of 7.1MHz. Behaviour will be different under other conditions.

As usually the case, a few numbers are more revealing than a lot of hand waving.

Complicated structures don’t necessarily bring better results.