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A correspondent wrote suggesting that he had seen online NEC patterns showing a 30″ square small untuned loop to have a gain of around 10dBi, more than 30dB better than given by Calculate small loop Antenna Factor.

Firstly, lets describe a loop for study, a square diamond with sides of 760mm (30″) of 2mm diameter copper fed in one corner at 7.1MHz.

Calculate small loop Antenna Factor

Calculate small loop Antenna Factor models a small loop in free space (therefore does not include ground losses).

Above is the calculator result, the key figures are Antenna Factor 31.75dB and Gain -44.5dBi.

NEC-4.2 model

An NEC-4.2 model was constructed with external excitation (1V/m) incident on the loop which has a 50+j0Ω load inserted at the feed point to represent the receiver load.

Here is the model source.

CM Small square untuned loop
CM NEC-4.2
CM 
CM 1. Plane wave excitation
CM 
CM Owen Duffy
CM Note: rotations might not work properly in various NEC-2 versions, beware of segment size issues in NEC-2.
CE
GW    1    5    -0.38    0    -0.38    0.38    0    -0.38    0.001
GM    1    3    0    90    0    0    0    0    1
GM    0    0    0    90    0    0    0    2    1
GE    0
LD    5    0    0    0    58000000
LD    4    1    1    1    50    0
GN    -1
EK
EX    1    1    1    0    45    0    0    0    0    0
FR    0    0    0    0    7.1    0
EN

The key result to be extracted from the model run is the current in the 50Ω resistor in segment 1 of wire 1. The magnitude of the current is 5.1204E-04, so the voltage developed in the resistor V=5.1074-04*50=0.02554V. Antenna Factor is the ratio of the E field excitation to the terminal voltage of the receiver, so in dB it is 20*log(1/0.02554) =31.83 dB/m.

The NEC model’s 31.83 dB/m is close to the calculator prediction of 31.75dB/m, but includes the benefit of the lossy ground reflection . Continue reading Small untuned loop for receiving – NEC model

Frank, W3LPL conducted two interesting experiments with WSPRlites on 20m from the US to Europe essentially. This article discusses the first test.

The first experiment was a calibration run if you like to explore the nature of simultaneous WSRP SNR reports for two transmitters using different call signs on slightly different frequencies (19Hz in this case) feeding approximately the same power to the same antenna.

The first test uses two WSPRlites feeding the same antenna through a magic-T combiner producing a data set consisting of 900 pairs of SNR reports from Europe with only about 70 milliwatts from each WSPRlite at the antenna feed.

The data for the test interval was extracted from DXplorer, and the statistic of main interest is the paired SNR differences, these are the differences in a report from the same station of the two signals in the same measurement WSPR interval.

There is an immediate temptation of compare the average difference, it is simple and quick. But, it is my experience that WSPR SNR data are not normally distributed and applying parametric statistics (ie statistical methods that depend on knowledge of the underlying distribution) is seriously flawed.

We might expect that whilst the observed SNR varies up and down with fading etc, that the SNR measured due to one transmitter is approximately equal to that of the other, ie that the simultaneous difference observations should be close to zero in this scenario.

What of the distribution of the difference data?

Above is a frequency histogram of the distribution about the mean (0). Interpretation is frustrated by the discrete nature of the SNR statistic (1dB steps), it is asymmetric and a Shapiro-Wik test for normality gives a probability that it is normal p=1.4e-43.

So lets forget about parametric statistics based on normal distribution, means, standard deviation, Student’s t-test etc are unsound for making inferences because they depend on normality.

Nevertheless, we might expect that there is a relationship between the SNR reports for both transmitters, We might expect that SNR_W3GRF=SNR_W3LPL.

So, lets look at the data in a way that might expose such a relationship.

Above is a 3D plot of the observations which shows the count of spots for each combination of SNR due to the two transmitters. The chart shows us that whilst there were more spots at low SNR, the SNRs from both are almost always almost the same.

A small departure can be seen where a little ridge exists in front of the main data.

Lets look at in 2D. Continue reading W3LPL’s paired WSPRlite test – test 1

A correspondent reading recent articles on active loops for receiving asks:

I have a 30″ square loop of #12 wire that I use for receiving, and when I attach it to the receiver on 40m, the audio output voltage goes up three times or more. Do I need an amplifiers, or will it worsen things?

It is possible to determine the ambient noise temperature from the true noise power change over that of a matched termination.

The equivalent noise temperature of the receiver is implied by its Noise Figure when it is terminated with a matched termination. Noise due to an open circuit or short circuit input is not defined.

The correspondent re-measured with a termination, and as it turned out, the results were much the same, so lets work the case of voltage increasing by a factor of three.

Without going any further, we can calculate the degradation in External S/N by the receiver, total noise power is proportional to (3^2) times internal noise, so S/N degradation is 10*log(9/(9-1))=0.51dB… very little.

It is true that an amplifier is unlikely to improve things and will be likely to degrade things because of intermodulation distortion that is inherent in them, more so if it overloads on broadband signal input.

But let’s go on to estimate the ambient noise figure Fa.

It is really important for this process that the AGC does not change the receiver gain, and there is no overload or clipping. The latter means DO NOT SWITCH THE AGC OFF, the S meter deflects, you need extra input attenuation to keep things linear.

Now lets assume the receiver has a Noise Figure of 6dB (most modern HF transceivers are in that ball park).

We need to estimate the gain of the antenna, we will use Calculate small loop Antenna Factor.

Ok, terminated in 50Ω, the untuned small loop has a gain of -43.4dBi. So, it captures only a very small portion of the external noise, but even so it delivers sufficient to the receiver to increase the output voltage by a factor of 3. Continue reading Small untuned loop for receiving – is an amplifier necessary?

Small untuned loop for receiving set out a model for calculating the S/N degradation of an active untuned small loop antenna system.

The calculations in Small untuned loop for receiving – Trask noise and gain analysis might prompt the question of what is the optimal resistive load for an untuned small loop.

This article explores the topic for a simple model where the equivalent noise temperature of the amplifier is independent of source impedance.

A simple model for a small loop

We can construct a simple model where the loop behaves as a fixed  pure inductance, and its load is a fixed pure resistance.

This is a reasonably good model for a small loop, perimeter < wl/10, not too bad for perimeter up to wl/3.

The source impedance becomes the loop’s inductive reactance Xl which is proportional to frequency, and the load is Rl.

Above is a plot of the relative power developed in the load vs the ratio of Rl/Xl.

There is a maximum where Rl=Xl, and the power captured falls away either side. Continue reading Small untuned loop for receiving – optimal loop load resistance

The article Small untuned loop for receiving mentioned Trask’s active loop amplifier.

(Trask 2010) published a two stage design using passive augmentation, arguing certain benefits of the approach.

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

This article presents a noise gain analysis for the 8m perimeter loop used in the article Small untuned loop for receiving to achieve a S/N degradation of no worse than 1dB at 7MHz.

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.

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. Continue reading Small untuned loop for receiving – Trask noise and gain analysis

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. Continue reading Small untuned loop for receiving