This article explains a little of the detail behind the graph.

The graph is based on a series of NEC-4.2 models of the loop in ground antenna. Key model parameters are:

- 3m a side;
- ‘average’ soil (σ=0.005, εr=13);
- depth=0.02m; and
- frequency 0.5 to 10MHz in 0.1MHz increments.

The models were scripted by a PERL script, and the output parsed with a Python script to extract feed point Z, structure efficiency, and average power gain (corrected to 4πsr).

The summarised NEC data was imported into a spreadsheet and an approximate model of the system built, comprising:

- Receiver input impedance 50+j0Ω;
- a length of transmission line (10m of Belden 8215 RG6/U);
- an ideal transformer (4:1);
- source impedance derived from the NEC data.

Calculation includes:

- transmission line loss and impedance transformation;
- transformer assumed ideal plus an allowance for transformer loss (1dB);
- mismatch loss; and
- average antenna gain.

Above is an extract of the spreadsheet.

Mismatch loss is an important element of the system behavior. A convenient place at which to calculate mismatch loss is the feed point of the loop in ground.

Above is a plot of the loop feed point impedance, the source impedance in the receive scenario.

Above is a plot of the loop load impedance, the receiver impedance transformed by transmission line and transformer. The varying impedance is a result of using 75Ω line.

The combination of these allows us to calculate mismatch loss.

Above is a plot of the calculated mismatch loss which must be added in to the system gain model.

From the system model, and an estimate of ambient noise from ITU-R P.372-14, we can calculate SND.

Above is a plot of SND.

Note that P.372-14 is based on a survey with short vertical monopole antennas, so it is likely to overestimate noise received by a horizontally polarised antenna (and therefore the SND estimate will be low).

Antenna performance is sensitive to soil parameters, especially those close to the surface and subject to variation with recent rainfall etc.

This is after all a feasibility study, and within acceptable uncertainty, the antenna system would seem to be feasible for low HF and even 160m receive.

]]>Let’s take ambient noise as Rural precinct in ITU-P.372-14.

An NEC-4.2 model of the 3m a side LiG gives average gain -37.18dBi. An allowance of 2.7dB of feed loss covers actual feed line loss and mismatch loss.

Above, calculated SND is 0.9dB. For this scenario (ambient noise and antenna system), the receiver S/N is 0.6dB worse than the off-air or intrinsic S/N ration. For Residential precinct ambient noise, SND is less at 0.3dB.

The above graph shows the system behavior over 0.5-10MHz, it is a combination of the effects of noise distribution; antenna gain; mismatch; transformer and feedline losses; and receiver internal noise.

A key measure of the ability to decode a radio signal is its Signal to Noise ratio (S/N) at the demodulator (or referred to some common point).

We can speak of think of an external S/N figure as \(S/N_{ext}=10 log\frac{S_{ext}}{N_{ext}}\) in dB.

Receiver systems are not perfect, and one of the imperfections is that they contribute undesired noise.

So, the S/N becomes \(S/N=10 log\frac{S_{ext}}{N_{int}+N_{ext}}\).

A useful metric in system design is the extent to which the external S/N is degraded by the receiver system, I will call it Signal to Noise Degradation (SND).

\(SND=10 log\frac{\frac{S_{ext}}{N_{ext}}}{\frac{S_{ext}}{N_{int}+N_{ext}}}\)Simplifying this by dividing top and bottom by \(S_{ext}\) we get

\(SND=10 log\frac{N_{int}+N_{ext}}{N_{ext}}\).

So, SND gives us a metric that simply depends on the external noise and the receiver internal noise, a quantitative measure of the system in an application context.

You might think that receiver Noise Figure does just that, but it does not. Receiver Noise Figure assumes the external equivalent noise temperature is 290K, a laboratory metric.

The methods presented here apply to linear systems, they do not capture the effects of non-linear behavior such as IMD noise.

Though the calculation is not difficult, a convenient online calculator is at Signal to Noise ratio degradation by receiver internal noise.

ITU P.372 ambient noise might also be useful.

Let’s work an example using Simsmith to do some of the calculations.

Scenario:

- 20m ground mounted vertical base fed against a 2.4m driven earth electrode @ 0.5MHz;
- 10m RG58A/U coax; and
- Receiver with 500+j0Ω ohms input impedance and Noise Figure 20dB.

An NEC-4.2 model of the antenna gives a feed point impedance of 146-j4714Ω and radiation efficiency of 0.043%, so radiation resistance \(Rr=146 \cdot 0.00043=0.0063\).

Above, the NEC antenna model summary.

Above is a Simsmith model of the system scenario.

R1 and G model the antenna, G uses Rr for Zo, and R1 contains the balance of the feed point impedance.

With the useZo source type, the source would deliver 1W or 0dBW to a conjugate matched load.

The next important figure is the power into the 500Ω load L. it is -58.3dBW. Simsmith has calculated the solution to the antenna loss elements, mismatches and coax loss under standing waves. Effectively, the average gain of the antenna system (everything to the right of L) is -58.3dB. Such an antenna is likely to have a Directivity of around 4dB, in fact the NEC model calculates 4.8dB. So the maximum gain is -58+4.8=-53.2dB.

The burning question is whether it is sufficiently good to hear most signals. Well, a better question is how much does it degrade off-air signal to noise ratio (S/N). All receivers degrade S/N, but how much degradation occurs in this scenario.

We need to think about the ambient noise. Lets use ITU-R P.372 for guidance on the expected median noise in a rural precint.

Above, ambient noise figure @ 0.5MHz is 75.54dB.

Now lets calculate the Signal to Noise Degradation (SND).

At 4.58 dB it is not wonderful, the weakest signals (ie those with low S/N) we be degraded significantly, stronger signals (those with high S/N) will be degraded by the SAME amount, but for instance reducing S/N from 20 to 15dB is not so significant.

Applying this to your own scenario

The information fed into the calculations included:

- Rr;
- feed point impedance;
- transmission line details;
- Rx input impedance and NF; and
- Ambient noise expectation.

To calculate your own scenario, you need to find these quantities with some accuracy.

Tools:

]]>The datasheet contains some specifications that should allow calculation of S/N degradation (SND) in a given ambient noise context (such as ITU-R P.372). Of particular interest to me is the frequency range 2-30MHz, but mainly 2-15MHz.

The specifications would appear to be based on models of the active antenna in free space, or measurements of the device using a dummy antenna. So, the challenge is to derive some equivalent noise estimates that can be compared to P.372 ambient noise, and with adjustment for the likely effects of real ground.

Key specifications:

- plot of measured output noise of the amplifier, and receiver noise in 1kHz ENB;
- Antenna Factor (AF) from a simulation.

Above is the published noise measurements at the receiver input terminals. The graph was digitised and then a cubic spline interpolation used to populate a table.

Above is the assumed test configuration. We will assume that the receiver is accurately calibrated (both power and bandwidth), and that the noise power due to internal noise in the amplifier is the reported noise (the orange curve) less the receiver internal noise (the blue curve) measured with a 50Ω termination on the input. Of course these measurements need to be converted to power to perform the subtraction, and as part of the calculation, power in 1kHz will be transformed to power/Hz because Noise Power Density (NPD) is easier to work with.

From the NPD of the amplifier internal noise at the output terminals, we can calculate component equivalent Noise Figure (NF) and equivalent noise temperature which are both frequency dependent. The output terminals of the amplifier are the reference terminals at which we will compare external noise and total internal noise, both referred to that reference point.

We can then build a more complex model incorporating the feed line loss (10m of CAT6 FTP) and a receiver of given NF, find the ambient noise referred to the amplifier output terminals and solve for SND. We will assume that the loss in the balun unit is so small that relocating it to after the CAT6 feed line does not introduce significant error.

Recall that Gain and AF are related, every one dB increase in Gain corresponds to exactly one dB decrease in AF.

It is the Average AF that is used to calculated ambient noise capture (assuming it is from all directions). We can calculate frequency dependent Average Gain from Average AF, and use that to calculate how much of the P.372 ambient noise appears at the reference terminals.

We will assume that the specification AF is given at maximum response (the usual convention), and that the Directivity of a short dipole in free space is 1.76dB, so the Average AF would be 3.76dB/m.

So, we will calculate Tamb’ being Tamp/Gain, and T’int being the sum of internal noise contributions of the receiver, lossy feed line, and amplifier all of these referred to the reference terminals. SND is then simply \(SND=10 log \frac{T_{amb}’+T_{int}’}{T_{amb}’}\).

Above is the table of calculations.

Above is a graphic summary of the analysis, the key metric being SND. Now P.372 is based on a survey with short vertical monopoles, so it probably overestimates noise captured by the short horizontal dipole by some dB.

The assumed Directivity and radiation efficiency based on a model at 7MHz are go to perhaps 15MHz at which point the length of the dipole and its height become more significant in terms of electrical length, and the pattern changes.

Note that this analysis assumes a linear receive chain, it does not include the effects of IMD.

So, whilst active short dipole antennas are not very popular in the ham world, they are popular in commercial and military applications, and in this instance, the AAA-1C would appear to perform quite well. This is of course only a desk study, the final test is of the real antenna system… though that is a little way off as post from Bulgaria to Australia is currently suspended.

Discussion with Chavdev (LZ1AQ) suggests that the assumptions made in this article are reasonable.

]]>In that instance, the design approach was to find a loop geometry that when combined with a practical amplifier of given (frequency independent) NoiseFigure (NF), would achieve a given worst case S/N degradation (SND). Whilst several options for amplifier Rin were considered in the simple analytical model, the NEC mode of the antenna in presence of real ground steered the design to Rin=100Ω.

A question that commonly arises is that of Rin, there being two predominant schools of thought:

- Rin should be very low, of the order of 2Ω; and
- Rin should be the ‘standard’ 50Ω.

Each is limiting… often the case of simplistic Rules of Thumb (RoT).

Let’s plot loop gain and antenna factor for two scenarios, Rin=2Ω and Rin=100Ω (as used in the final design) from the simple model of the loop used at Small untuned loop for receiving – a design walk through #2.

Above, loop gain is dominated by the impedance mismatch between the source with Zs=Rr+Xl and the load being Rin. We can see that the case of Rin=100Ω achieves higher gain at the higher frequencies by way of less mismatch loss than the Rin=2Ω case.

Above is a plot of AF for the two cases. Recall that AF is the ratio of the electric field strength to the loaded loop terminal voltage. Note that the Rin=2Ω case has almost flat AF from 0.2MHz up, whereas the Rin=100Ω is only flattening towards 10MHz. A very flat AF response is a desirable feature of a field strength measuring instrument, but is has much less value for a conventional receiving system.

Looking back at the gain plot, it is evident that the flat AF response comes at the cost of considerably lower gain at the higher frequencies. The effect of that is that receiver internal noise becomes more limiting unless that gain shortfall can be made up with low loss amplification, and therein lies the challenge.

The approach discussed at Small untuned loop for receiving – a design walk through #1 was not a design for constant AF, the main design objective was SND in a given ambient noise context… and that objective is directly relevant to ordinary receivers.

]]>Let’s review of the concepts of noise figure, equivalent noise temperature and measurement.

Firstly let’s consider the nature of noise. The noise we are discussing is dominated by thermal noise, the noise due to random thermal agitation of charge carriers in conductors. Johnson noise (as it is known) has a uniform spectral power density, ie a uniform power/bandwidth. The maximum thermal noise power density available from a resistor at temperature T is given by \(NPD=k_B T\) where Boltzmann’s constant k_{B}=1.38064852e-23 (and of course the load must be matched to obtain that maximum noise power density). Temperature is absolute temperature, it is measured in Kelvins and 0°C≅273K.

Noise Figure NF by definition is the reduction in S/N ratio (in dB) across a system component. So, we can write \(NF=10 log \frac{S_{in}}{N_{in}}- 10 log \frac{S_{out}}{N_{out}}\).

One of the many methods of characterising the internal noise contribution of an amplifier is to treat it as noiseless and derive an equivalent temperature of a matched input resistor that delivers equivalent noise, this temperature is known as the equivalent noise temperature Te of the amplifier.

So for example, if we were to place a 50Ω resistor on the input of a nominally 50Ω input amplifier, and raised its temperature from 0K to the point T where the noise output power of the amplifier doubled, would could infer that the internal noise of the amplifier could be represented by an input resistor at temperature T. Fine in concept, but not very practical.

Applying a little maths, we do have a practical measurement method which is known as the Y factor method. It involves measuring the ratio of noise power output (Y) for two different source resistor temperatures, Tc and Th. We can say that \(NF=10 log \frac{(\frac{T_h}{290}-1)-Y(\frac{T_c}{290}-1)}{Y-1}\).

AN 57-1 contains a detailed mathematical explanation / proof of the Y factor method.

We can buy a noise source off the shelf, they come in a range of hot and cold temperatures. For example, one with specified Excess Noise Ratio (a common method of specifying them) has Th=9461K and Tc=290K. If we measured a DUT and observed that Y=3 (4.77dB) we could calculate that NF=12dB.

This method of noise figure measurement is practical and used widely. Note that the DUT always has its nominal terminations applied to the input and output, the system gain is maintained, just the input equivalent noise temperature is varied.

Some amplifiers are not intended to be impedance matched at the input (ie optimised for maximum gain), but are optimised for noise figure by controlling the source impedance seen at the active device. Notwithstanding that the input is not impedance matched, noise figure measurements are made in the same way as for a matched system as they figures are applicable to the application where for example the source might be a nominal 50Ω antenna system.

So, NF is characterised for an amplifier with its intended / nominal source and load impedances.

Nothing about the NF implies the equivalent internal noise with a short circuit SC or open circuit OC input. The behaviour of an amplifier under those conditions is internal implementation dependent (ie variable from one amplifier design to another) and since it is not related to the amplifier’s NF, it is quite wrong to make inferences based on noise measured with SC or OC input.

So this raises the question of NF measurements made with a 50Ω source on an amplifier normally used with a different source impedance, and possibly a frequency dependent source impedance. An example of this might be an active loop amplifier where the source impedance looks more like a simple inductor.

Well clearly the measurement based on a 50Ω source does not apply exactly as amplifier internal noise is often sensitive to the source impedance, but for smallish departures, the error might be smallish.

A better approach might be to measure the amplifier with its intended source impedance. In the case of the example active loop antenna, the amplifier could be connected to a dummy equivalent inductor, all housed in a shielded enclosure and the output noise power measured with a spectrum analyser to give an equivalent noise power density at the output terminals. Knowing the AntennaFactor of the combination, that output power density could be referred to the air interface. This is often done and the active antenna internal noise expressed as an equivalent field strength in 1Hz, eg 0.02µV/m in 1Hz. For example the AAA-1C loop and amplifier specifies Antenna Factor Ka 2 dB meters-1 @ 10 MHz

and MDS @ 10MHz 0.7 uV/m , Noise bandwidth =1KHz and

to mean equivalent internal noise 0.022µV/m in 1Hz @ 10MHz at the air interface. 0.022µV/m in 1Hz infers Te=6.655e6K and NF=43.608dB again, at the air interface. These figures can be used with the ambient noise figure to calculate the S/N degradation (SND).

A spectrum analyser or the like can be used to measure the total noise power density at the output of the loop amplifier with the input connected to a dummy antenna network (all of it shielded) and to calculate the equivalent noise temperature and noise figure at that point. For example, if we measured -116dBm in 1kHz bandwidth, Te=1.793e+5K and NF=27.9dB. Knowledge of the gain from air interface to that reference point is needed to compare ambient noise to the internal noise and to calculate SND, that knowledge might come from published specifications or a mix of measurements and modelling of the loaded antenna.

The mention of a spectrum analyser invites the question about the suitability of an SDR receiver. If the receiver is known to be calibrated, there is no non-linear process like noise cancellation active, and the ENB of the filter is known accurately, it may be a suitable instrument.

In both cases, the instruments are usually calculated for total input power, ie external signal and noise plus internal noise, so to find external noise (ie from the preamp) allowance must be made for the instrument NF (ie it needs to be known if the measured power is anywhere near the instrument noise floor).

Field strength / receive power converter may assist in some of the calculations.

The foregoing discussion assumes a linear receiver, and does not include the effects of intermodulation distortion IMD that can be hugely significant, especially in poor designs.

Part of the problem of IMD is that the effects depend on the individual deployment context, one user may have quite a different experience to another.

There are a huge number of published active loop antenna designs and variant, and a smaller number of commercial products. Most are without useful specifications which is understandable since most of the market are swayed more by anecdotal user experiences and theory based metrics and measurement.

- Hewlett Packard. Jul 1983. Fundamentals of RF and microwave noise figure measurement. AN 57-1

Small untuned loop for receiving – a design walk through #2 developed a simple spreadsheet model of the loop in free space loaded by the amplifier andperformed some basic SND calculations arriving at a good candidate to take to the next stage, NEC modelling.

The simple models previously used relied upon a simple formula for predicting radiation resistance Rr in free space, and did not capture the effects of proximity of real ground. The NEC model will not be subject to those limitations, and so the model can be run from 0.5-30MHz.

The chosen geometry was:

- loop perimeter: 3.3m;
- conductor diameter: 20mm;
- transformer ratio to 50Ω amplifier: 0.7; and
- height of the loop centre: 2m;
- ground: average (σ=0.005 εr=13).

The effect of interaction with nearby real ground is to modify the free space radiation pattern. The pattern at low frequencies has maximum gain at the zenith, and above about 15MHz the pattern spreads and maximum gain is at progressively lower elevation. For the purposes of a simple comparison, the AntennaFactor was calculated for external plan wave excitation at 45° elevation in the plane of the loop.

Above is a plot of loop Gain and AntennaFactor at 45° elevation along the loop axis. The frequency range is 0.5-30MHz as the NEC model is not limited by the simple Rr formula. Additionally there is some ‘ground gain’ of around 5dB due to lossy reflection of waves from the ground interface.

The SND statistic was the target of optimisation, so let’s look at that. For simplicity, let’s assume that Directivity is 6dB, and calculate average Gain from the gain reported above using Directity.

Though the initial design criteria was that SND<3dB to 9MHz, the NEC model just misses that (3.15dB), but it is close.

The plot shows the wider perspective that although the optimisation pretty much contained SND up to 9MHz, it continues to grow above that reaching 11dB at 30MHz. If that parameter was important above 9MHz, iterative tweaking and running of the NEC models may provide an optimisation.

Above is the result of a NEC model run with a 1.4:1 transformer at the feed point, effectively loading the loop with 100Ω.

Small untuned loop for receiving – a design walk through #4

ITU-R. Aug 2019. Recommendation ITU-R P.372-14 (8/2019) Radio noise.

]]>There have been many credible designs of loop amplifiers of gain in the region of 25+dB and NoiseFigure NF around 2dB. So lets work with that as a practical type of amplifier, though we will not commit to input Z just yet.

I might note that a certain active loop manufacturer claims NF in the small tenths of a dB, but it appears they needed to invent their own method of measurement… when questions the credibility of their claims.

Let’s calculate the NF of a cascade of the NF=8dB receiver, coax with loss of 2dB and a loop amplifier with NF=2dB and Gain=25dB.

The NF looking into the loop amplifier is 2.08dB.

Let’s try for something relatively compact, say around 3m perimeter, and a medium diameter conductor to reduce inductance a little and rigid enough to be self supporting. Let’s assume that the loop is in free space and that the perimeter is less than λ/10 so that a simple prediction of radiation resistance Rr can be made. The behaviour near real ground is a little different, tending to better gain. The behaviour a little above λ/10 also tends to be a little better than predicted.

None of the modelling is applicable to a small loop on the kitchen table coupled to the house wiring, other metallic services and structure.

So the loop source impedance and Rr are used to predict the mismatch loss to the amplifier input to calculate active antenna average Gain or average AntennaFactor, and signal to noise degradation SND calculated for the given external noise context, P.372 Rural.

Key parameters were adjusted to arrive at a compact configuration that met the SND<3dB design criteria. The chosen geometry was:

- loop perimeter: 3.3m;
- conductor diameter: 20mm;
- transformer ratio to 50Ω amplifier: 0.7; and
- perimeter=λ/10 frequency: 9.1MHz.

Above is a plot of the source impedance of the lossless loop. The loop is treated as lossless for simplicity as the mismatch loss to the amplifier is not very sensitive to the very small equivalent conductor loss resistance.

Above is a plot of the loaded loop Gain (average gain is 1.76dB lower, average AntennaFactor is 1.76dB higher). The low gain is due to the mismatch when loaded with the amplifier Zin=25+j0Ω (50Ω amplifier with 0.7:1 transformer input). AntennaFactor is calculated from gain, and it can be seen that from about 4MHz it is almost flat, and Gain∝-log(f).

The important metric is SND, the SND objective was the target of tweaking of the geometry.

Above is the calculated SND, it meets the objective SND<3dB over the range 0.3-9+MHz.

Above is the same plot with the loop terminated in 50Ω. SND below 1MHz is degraded and a small improvement in SND near 10MHz. Some users might judge that the design criteria is not too precious and simplification to use a 50Ω amplifier is a worthwhile benefit.

Note that the results apply to the scenario discussed, and are not necessarily extensible to other scenarios such as a lower ambient noise context.

So, with a little simple spreadsheet work, we have a candidate to take to the next stage, NEC modelling.

Small untuned loop for receiving – a design walk through #3

ITU-R. Aug 2019. Recommendation ITU-R P.372-14 (8/2019) Radio noise.

]]>Fairly good practical sensitivity

is to mean that the recovered S/N ratio is not much worse than the off-air S/N ratio. Let’s quantify not much worse

as the Signal to Noise Degradation (SND) statistic calculated as \(SND=10 log\frac{N_{int}+N_{ext}}{N_{ext}}\), and lets set a limit that \(SND<3 dB\).

Since Next is part of the criteria, let’s explore it.

ITU-R P.372 gives us guidance on the expected median noise levels in a range of precincts. Since most hams operate in residential areas, you might at first think the Residential precint is the most appropriate, but ambient noise more like the Rural precinct is commonly observed in residential areas, so let’s choose Rural as a slightly ambitious target.

Above is Fig 39 from ITU-R P.372-14 showing the ambient noise figure for the range of precincts. Readers will not that that are all lines sloping downwards with increasing frequency, so the external noise floor is greater at lower frequencies in this range.

In terms of achieving our 3dB SND target, we need the receive system NoiseFigure to be no higher than Fam.

Broadband amplifiers will tend to have gain and noise fairly independent of frequency, so an amplifier with low enough noise for the higher frequencies is better than needed at the lower frequencies.

Let’s look at the element that sits between the external noise environment and the amplifier input, the antenna.

Simple broadband antennas tend to fall into two categories:

- the short electric dipole; and
- the small magnetic dipole (loop).

A short electric dipole has a Thevenin equivalent source impedance of a small resistance in series with a very small capacitance. To capture much power from a short electric dipole, the amplifier must have a very high impedance.

A small loop has a Thevenin equivalent source impedance of a small resistance in series with a moderate inductance. To capture much power from the untuned loop, the amplifier must have a moderate impedance.

For this article we will concentrate on the loop option.

The article Small untuned loop for receiving – it’s not rocket science gave a simple equivalent circuit for a small untuned loop loaded by a moderate resistive load (the loop amplifier). The effect of the loop inductance in series with the total circuit resistance (mainly the amplifier input R) is an LR low pass filter (LPF), with gain falling with frequency above the break frequency.

The combination of the loaded loop as a LPF, and amplifier with constant gain and NoiseFigure is a block with gain and noise figure roughly proportional to inverse of frequency.

The graph above shows P.372 ambient noise (Rural), and an idealised LPF + amplifier with NF∝-log(f). Also plotted is the calculated SND for this scenario.

So this analysis suggests that it may be possible to make an antenna system with an untuned small loop and amplifier, having SND<3dB over the range 0.5-10MHz.

The next article will explore a practical loop geometry and amplifier characteristics to achieve the objective.

Small untuned loop for receiving – a design walk through #2

ITU-R. Aug 2019. Recommendation ITU-R P.372-14 (8/2019) Radio noise.

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