This article walks through a case study for a small single turn untuned loop with attached 50Ω balanced preamplifier and 50Ω coaxial output to a high grade communications receiver. The objective is to achieve system S/N ration not poorer than 1dB below the external S/N (ie ExternalS/ ExternalN).

Such an antenna has utility in that it can be rotated to null out a strong noise source from a direction other than the desired signal.

The analysis assumes linear components, that there is no significant intermodulation distortion in the preamplifier. That is a significant challenge on which success of the system depends.

This is a rework of an earlier article which presented a ‘back of the envelope' noise and gain analysis now presented as a more accurate model embodied in a spreadsheet to allow convenient exploration of variations to the scenario.

## External noise

From the above chart (ITU-R P.372-12 (7/2015)), we can take the external or ambient noise figure Fa to be about 45dB at 7MHz, Ta=290*10^(45/10)=9.17e6K.

## Combining noise sources

Given the requirement that the system S/N is not more than 1dB worse than external S/N, we can calculate the system noise that can be accommodated.

We can see from the chart above, that for the system internal noise to increase the total noise by less than 1dB, the system internal noise has to be about 6dB lower than the external noise, or conversely external noise at least 6dB higher than system internal noise.

## A trial loop

Lets run the calculations on a trial loop.

If we choose an untuned square loop of say 2m sides made from 1.5mm conductor loaded with a 50Ω preamplifier, we have a loop with antenna factor (AF) of 24.7dB/m, gain of -37.6dBi.

The spreadsheet above takes care of the tedium of the calculations.

The ambient noise Fa is taken from ITU P.372-12 as 45dB (but it varies with precinct type and frequency of course).

The loop antenna factor is calculated using Calculate small loop Antenna Factor. Antenna Factor is sensitive to the loop geometry, including wire diameter. Larger conductor diameter will reduce the loop inductance and decrease Antenna Factor, giving higher loop Gain.

The spreadsheet calculates the equivalent noise temperature of each element of the system, and their contribution to total noise temperature. (Keep in mind that noise power received is proportional to noise temperature.)

In this case, the receiver, loop amplifier and loop all contribute to the total noise temperature, such that the external noise is only 84% of the total noise and the S/N at the receiver output will be 0.7dB worse than the ratio of ExternalSignal to ExternalNoise.

To achieve better than 1dB degradation mentioned earlier, the internal noise needs to be less than a quarter of external noise, or less than a fifth of total noise.

Above is a recalculation with loop Antenna Factor 23dB which achieves a 0.5dB degradation in S/N. The improvement in Antenna Factor could be achieved by using a 6mm diameter conductor.

Of course amplifier parameters influence the outcome, but you might be quite surprised to find that throwing gain at the problem has diminishing returns. The spreadsheet is available for download, have a play with it (green cells are calculated, do not enter data in them).

Since the antenna and preamplifier are broadband, it is vital that the preamplifier can handle the total broadband signal without creating significant intermodulation products. That typically is achieved by designing a balanced antenna + amplifier with very good common mode rejection, and an amplifier with very high gain compression point.

## Published designs

### Clifton Laboratories

The Clifton Laboratories Z10040B amplifier (Smith 2010) was designed for this type of application and its specifications provide an example.

Above, an extract from the Z10040B manual.

### Lankford

(Lankford 2007) gives a number of graphs for variation in some key parameters with device current. From those, approximate specifications can be obtained:

- Gain 12dB
- IIP2 82dBm
- IIP3 37dBm

No noise figure is given, no P1db compression, a significant oversight.

Note that the Clifiton Laboratoies design is based on Lankford and does give a more complete set of measurements and specifications.

### Trask

(Trask 2010) published a two stage design using passive augmentation.

- Zin=2.25Ω
- NF 2.42dB
- Voltage gain 36dB
- OIP2 80dBm
- OIP3 40dBm

Note that Zin is very low and so AF of the loop is substantially higher (~25dB) with this load eroding most of the higher gain. He does not give a figure for P1db compression.

## Conclusions

- A small untuned loop has insufficient gain to be practical as a receive antenna at 7Mhz.
- A suitable loop preamplifier can make good the deficit.
- The requirements of the loop amplifier are demanding and specialised designs have evolved to satisfy the requirement.

## References / links

- ITU-R. Jul 2015. Recommendation ITU-R P.372-12 (7/2015) Radio noise.
- Lankford, D. May 2007. Common base transformer feedback Norton amplifiers rev 21 V0 7.
- Norton, D. Jun 1975. Transistor amplifier with impedance matching transformer – US Patent 3,891,934.
- Smith, J. Apr 2010. Z10040B broadband Norton amplifier.
- Trask, C. Aug 2010. Wideband loop antenna amplifier.
- owenduffy.net/files/NoiseAndReceivers.pdf
- Receiver sensitivity metric converter
- Calculate small loop Antenna Factor
- Convert Antenna Factor and Gain
- RxActiveNoiseXl.zip