NEC says,

according to NEC, and the like.

Readers should take this to mean that the author denies their contribution in making assumptions and building the model, and the influence on the stated results.

It is basically a disclaimer that disowns their work.

In a past life I wrote and maintained software tools used for design of buildings covering a wide range of disciplines (eg CAD, structure strength, power distribution, heating and cooling loads, passive solar design etc).

The people who used the tools were qualified engineers and architects who took total responsibility for their

design work, even when using tools created and tested by others. It was at all times the responsibility of the user their

to validate designs, they owned

the design and were held responsible and accountable.

When it was discovered that a certain series of Intel Pentium chips had a defect in floating point calculations, it sent us into a spin to find whether it impacted the accuracy of tools, particularly to compare test suite results with calculations on other unaffected processors… but it was made clear that at the end of the day, responsibility for a design lay entirely with the engineer or architect signing off on the work.

But in amateur radio forums, the accepted thing is to deny personal contribution to the building of NEC models, the oft unstated assumptions, blame it all on NEC. Certainly gives meaning to amateur.

]]>A first observation of listening to a SSB telephony signal is an excessive low frequency rumble from the speaker indicative of a baseband response to quite low frequencies, much lower than needed or desirable for SSB telephony.

The most common application of such a filter is reception of A1 Morse code.

Above is a screenshot of the filter settings.

Above is a plot of the response of the filter. It is hardly an idealised rectangular filter response. Though the response might be well suited to Morse code reception, it is an issue when measurements make assumptions about the ENB. The response is not well suited to narrowband data such as RTTY etc.

A summary of the filter response follows.

Locut 0Hz.

sox: bin_width_hz=10.000Hz

Filter -6dB response: 460-770Hz=310Hz.

ENB=224Hz with respect to gain at 610Hz (passband centre frequency).

ENB=222Hz with respect to gain at 590Hz (max gain frequency).

ENB=222Hz with respect to gain at 600Hz.

If we take the gain reference frequency to be 600Hz, there is 3.5dB less noise admitted by this filter than an idealised rectangular filter. Measurements such as the ARRL MDS that might assume 500Hz bandwidth will have 3.5dB error.

A 1000Hz filter might be well suited to narrow band data reception, many of the so-called ham digital modes.

Above is a screenshot of the filter settings.

Above is a plot of the response of the filter. It is fairly close to an idealised rectangular filter response.

There appears to be no means to offset the filter at baseband frequency.

A summary of the filter response follows.

Locut 0Hz.

sox: bin_width_hz=10.000Hz

Filter -6dB response: 110-950Hz=840Hz.

ENB=823Hz with respect to gain at 530Hz (passband centre frequency).

ENB=716Hz with respect to gain at 200Hz (max gain frequency).

ENB=800Hz with respect to gain at 500Hz.

If we take the gain reference frequency to be 500Hz, there is 0.97dB less noise admitted by this filter than an idealised rectangular filter.

Above is a screenshot of the filter settings.

Above is a plot of the response of the filter. It is fairly close to an idealised rectangular filter response.

There appears to be no means to offset the filter at baseband frequency.

A summary of the filter response follows.

Locut 0Hz.

sox: bin_width_hz=10.000Hz

Filter -6dB response: 110-2350Hz=2240Hz.

ENB=2353Hz with respect to gain at 1230Hz (passband centre frequency).

ENB=1829Hz with respect to gain at 210Hz (max gain frequency).

ENB=2255Hz with respect to gain at 1000Hz.

If we take the gain reference frequency to be 1000Hz, there is 0.27dB less noise admitted by this filter than an idealised rectangular filter.

SDR# does not appear to have a convenient facility to shift or offset the baseband response.

Above is the baseband response in 2400Hz USB mode as show in the SDR# window. Note that the response rolls off below 100Hz, whereas good conventional SSB Telephony receivers would have a 6dB response from say 250-2750Hz for a ENB of 2400Hz. The lower -6dB point for this response is 110Hz.

This leads to substantial low frequency component that is not a priority for SSB telephony, and in the case where the transmitter is band limited to 300-2700Hz, the filter admits unnecessary noise and the low end and cuts of a little of the high end. It is a hammy sammy approach where recognised speech characteristics, conventions and compatibility between transmitter and receiver are jettisoned.

The basic 1000Hz USB filter provides a response close to ideal, centred around 530Hz, and its ENB is 800Hz (-0.07dB on 1000Hz).

There appears no facility in SDR# to save a number of filter settings for later recall, so the process of configuring SDR# for measurement is a bit tedious.

My attention has been draw to the facility to drag the upper and lower limits of the IF passband, thanks Martin.

Above is an example where a 500Hz passband is centred on 1500Hz at baseband.

As soon as another mode is selected, the setting is lost and there appears no facility to save a set of settings for later recall. Note the inconsistency between the two displayed bandwidth figures.

Yes, it works but it is not convenient and not practical for save / recall of a standardised set of measurement or reception conditions.

]]>Having selected a candidate core, the main questions need to be answered:

- how many turns are sufficient for acceptable InsertionVSWR at low frequencies and core loss; and
- what value of shunt capacitance best compensates the effect of leakage inductance at high frequencies?

Lets look at a simplified equivalent circuit of such a transformer, and all components are referred to the 50Ω input side of the transformer.

Above is a simplified model that will illustrate the issues. For simplicity, the model is somewhat idealised in that the components are lossless.

- L1 represents the leakage inductance;
- L2 represents the magnetising inductance; and
- C1 is a compensation capacitor.

Since the magnetising inductance is assumed lossless, this article will not address design for core loss.

So, it is obvious that the InsertionVSWR curve is pretty poor at both high and low end.

Let’s look at a Smith chart presentation of the same information, it is so much more revealing.

Above is the Smith chart plot. Remember that the points go clockwise on the arc with increasing frequency, and that InsertionVSWR is a function of the distance from the centre to the point on the locus… we want to minimise that distance. Remember also that the circles that are tangential to the left had edge are conductance circles, they are the locus of constant G.

Now lets analyse the response.

Note that from 1 to 3MHz, the shape of the response tends to a circle tangential to the left hand edge, it a constant G circle. So, G is constant but susceptance B is frequency dependent and -ve. This the the response of a constant resistance R in parallel with a constant inductance (\(B=\frac {-1} {2 \pi f L}\), \(Y= G + jB = \frac 1 R – \frac {j} {2 \pi f L}\)). A part of that susceptance (shunt inductance) is due to the magnetising inductance L2 which contributes to the poor Insertion VSWR at low frequencies.

Note that from 12 to 15Hz, the shape of the response tends to a circle tangential to the left hand edge, it a constant G circle. So, G is constant but susceptance B is frequency dependent and +ve. This the the response of a constant resistance R in parallel with a constant capacitance (\(B=2 \pi f C\), \(Y= G + jB = \frac 1 R + j 2 \pi f C\)). A part of that susceptance (shunt capacitance) is due to the compensation capacitor C1 which contributes to the poor Insertion VSWR at high frequencies.

Lets adjust L2 and C1 for a better InsertionVSWR response.

Above is the response with L2=12µH and C1=80pF. Note that the distance to the centre is improved (and therefore InsertionVSWR is improved). The kink in the response is common, that is typically the mid region where InsertionVSWR is minimum.

It is still not a good response, the InsertionVSWR at the high end is too high, and compensation with C1 does not adequately address the leakage inductance. So, as a candidate design, this one has too much leakage inductance which might be addressed by improving winding geometry and increasing core permeability.

As mentioned, real tranformers using ferrite cores have permeability that is complex (ie includes loss) and dependent on frequency (ie inductance is constant).

Above, the magenta curve is measurement of a real transformer from 1-11MHz with nominal resistance load and three compensation options:

- cyan: 0pF, too little compensation;
- magenta: 80pF, optimal compensation; and
- blue: 250pF, to much compensation.

It should be no surprise that 80pF is close to optimal. Susceptance B at the cyan X is -0.00575S, and broadly, we want to cancel that with the compensation capacitor so we come so \(C=\frac{B}{2 \pi f}=\frac{0.00575}{2 \pi 11e6}=83pF\).

With optimal compensation (80pF in this case) The insertionVSWR at 3MHz is 1.8, probably acceptable for this type of transformer but it is still quite high (4.3) at 11MHz, which hints that leakage inductance needs to be addressed by improving winding geometry and possibly increasing permeability.

Keep in mind that measurements with a nominal resistive load are a guide, measurements with the real antenna wire are very important.

]]>A common piece of advice is to visualise the capture area

of the individual Yagi, and to stack them so that their capture areas just touch… with the intimation that if they overlap, then significant gain is lost.

Above is a diagram from F4AZF illustrating the concept. Similar diagrams exist on plenty of web sites, so it may not be original to F4AZF.

Now Capture Area or Effective Aperture Ae is a well known concept in industry and explained in most basic antenna text books. In concept, the amount of power available from a plane wave by an antenna is given \(P=S Ae\) where S is the power density of the wave (W/m^2) and Ae is the Effective Aperture. We can calculate \(Ae = G \frac{\pi {\lambda}^2}{4}\).

So, let’s consider a 17 element DL6WU for 144MHz, with a gain of 16.7dB (G=46.5) and optimal stacking distances of 4.133m and 4.332m (Estimating Beamwidth of DL6WU long boom Yagis for the purpose of calculating an optimum stacking distance).

We can calculate Ae to be \(Ae = G \frac{\pi {\lambda}^2}{4}=157.9m^2\).

Let’s calculate the area of a rectangular stacking box \(A_{sb}=4.133 \cdot 4.332 = 17.9m^2\).

So, how do you possibly contain the 157.9m^2 capture area within the 17.9m^2 stacking box, no matter what shape you make the capture area.

Clearly, the concept is flawed. It is another of those simplistic explanations that is appealing at first glance… but deeply flawed… specious!

Popularity does not determine fact… well in science anyway.

]]>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.

]]>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.

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.

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.

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

]]>From the basic definition \(\mu=B/H\) we can derive the relationship that the flux density in the core with current I flowing through N turns is given by \(B=\frac{\mu_0 \mu_r N I}{2 \pi r}\).

The incremental flux at any incremental radius is proportional to the flux path length \(2 \pi r\), so the total flux due to B(r) is \(\Phi_B=\int_{a}^{b}Bc \, dr=\frac{\mu_0 \mu_r N I}{2 \pi r}c \, dr=\frac{\mu_0 \mu_r N I}{2 \pi} c \, ln \frac b a\).

Note that the core geometry is captured in the term \( c \, ln \frac b a\).

From that we can calculate inductance \(L \equiv \frac{N \Phi_B}I=\frac{\mu_0 \mu_r N^2}{2 \pi} c \, ln \frac b a \) where \(\mu_0=4\pi 10^{-7}\), the permeability of a vacuum.

Ferrite datasheets commonly give \(\mu_r=\mu^{\prime}-j\mu^{\prime\prime}\), a complex value (note it is usually a frequency dependent parameter). The imaginary term represents the core loss.

We can calculate the impedance at frequency f by substituting the values.

\(Z=j 2 \pi f L=j 2 \pi f \frac{\mu_0 (\mu^{\prime}-j\mu^{\prime\prime}) N^2}{2 \pi}c \, ln \frac b a \\\)The model can be improved for frequencies approaching SRF by addition of a small equivalent shunt capacitance \(C_s\).

\(Z=\frac1{\frac1{j 2 \pi f \frac{\mu_0 (\mu^{\prime}-j\mu^{\prime\prime}) N^2}{2 \pi} c \,ln \frac b a}+ j 2 \pi f C_s}\)The calculator Calculate ferrite cored inductor – rectangular cross section does exactly this calculation. Note that a real FT240-43 has chamfered corners, so these calculations based on sharp corners will very slightly overestimate L, but the error is trivial in terms of the tolerance of µr.

µr comes from the datasheet, but you may find Ferrite permeability interpolations convenient.

The value Cs is best obtained by observation of SRF of a particular winding, it is sensitive to winding layout.

The calculated value \(\sum{\frac{A}{l}}=\frac{c \, ln \frac b a}{2 \pi}\) and captures the core geometry in a more general form. It or its inverse often appear in datasheets and can be used to calculate Z (Calculate ferrite cored inductor – ΣA/l or Σl/A).

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