Small untuned loop for receiving – simple model with transformer

Above is the Airspy Youloup-2T. Try to put the two turns thing out of your mind, it is misleading, panders to some common misunderstanding, and so does not help understanding.

This is somewhat similar to the simple loop, but now the transformer primary is connected to the loop gap terminals by two parallel sections of 50Ω transmission line, the combination being effectively a 100Ω with similar parameters to the component coax sections. Because of the series connection at the transformer and parallel connection at the loop gap, there is a 1:4 impedance transformation additional to that of the coax sections themselves.

The operation of the 1:4 impedance transformer is laid out at A transmission line 1:4 impedance transformer.

The currents shown above are differential currents in the coax (ie wholly inside the coax), the current on the outside of the shield is not shown on the diagram. In this application, the current on the outside of the loop shield flows into the terminals at the left, ie 2I1 flows on the outside of the shield.

So, knowing the characteristics of the RG402 coax used, and assuming a 1:1 ideal transformer, we can estimate the load impedance seen at the gap by the loop.

It is a little different to the simple loop with 0.5:1 transformer because the coax sections perform a little impedance transformation additional to the 1:4 due to the connection arrangement… but only a little different.

So, lets continue with the analysis using the new load impedance seen by the loop. Again in the context of a linear receive system (ie no IMD) of known Noise Figure.

## Receiver

The receiver has an idealised input impedance of 50+j0Ω, and known internal noise implied by its Noise Figure (NF). For the purpose of this analysis we will assume the NF is 5dB and from that we can derive an equivalent noise temperature Tr of 627K.

## External noise

After mentioning receiver internal noise, lets consider external noise.

For the purpose of estimating external noise, we can look to ITU-R P.372-14 for guidance, it gives us a median ambient noise figure from which we can calculate an external equivalent noise temperature. We will use the Residential precinct figures from P.372.

## Signal / Noise degradation

We can define S/N degradation (SND) to mean the reduction in external S/N being \(\frac{ExternalSignal}{ExternalNoise}\) by the addition of internal noise

\(\frac{\frac{ExternalSignal}{ExternalNoise}}{\frac{ExternalSignal}{ExternalNoise+InternalNoise}}=\frac{ExternalNoise+InternalNoise}{ExternalNoise}\) which we can convert to dB

\(SND=10log \frac{ExternalNoise+InternalNoise}{ExternalNoise}\)## An example loop for discussion

Let's consider the single turn untuned loop with cross over connections and RG401 sections, and an ideal 1:1 broadband transformer. The loop is 2.1m perimeter and 4mm diameter conductor situated in free space. The loop has perimeter less than λ/10 up to 15MHz, so we can regard that loop current is uniform in magnitude and phase. This simplifies analysis greatly.

A simple analysis is to consider the loop to have some fixed inductance (2.2µH in this case) and in series some resistance (radiation resistance Rr, and loss resistance which we will ignore). For simplicity, we are using an ideal transformer of some known turns ratio and a receiver.

We can consider the loop to have a Thevenin equivalent circuit of a voltage source with series equivalent impedance being Rr+j2πfL.

For this scenario, the loop is loaded with some impedance being the receiver input impedance transformed by the ideal n:1 turns ratio transformer. There is a large impedance mismatch, and the antenna system gain in this scenario is entirely due to mismatch loss, Gain=-MismatchLoss.

## Performance objective

One metric that could be used to assess performance is to calculate the SND of a receive system in a given noise environment.

To calculate SND, we need to refer internal and external noise to the same place to perform the calculation. In this instance, we will refer them to the receiver input terminals. We already have Tr=627, and we can calculate Tamr=Tam/Gain.

Above is the calculated SND from 0.3 to 9MHz.

It is a small untuned / unmatched loop and the naked truth is that the SND is significant.

## Conclusions

The results apply to the scenario described. The results are sensitive to most parameters so they cannot be blindly applied to another scenario.

The “two turns” in the loop name is not related to a valid explanation of how it works.

A real antenna should perform similarly, note though that a real receiver will probably depart from ideal in impedance and NF, the model does not include transformer loss (perhaps some tenths of a dB), proximity of ground (ie ground gain) and the largest source of variance may be in the actual ambient noise figure.