Above is the prototype transformer wound with 14t of 0.71mm ECW tapped at 2t. The mm rule gives some scale. The turns are close wound, touching on the inner diameter of the core.

Leakage inductance is the enemy of broadband performance, so it is important to minimise it.

Leakage inductance is affected by winding geometry. It is important to avoid opportunity for flux inside and around conductors that does not also ‘flow’ in the core, such flux does not ‘cut’ the other turns and is flux leakage. The winding should hug the core, so winding with wires with thick insulation, thick inflexible wires, and topologies like the Riesert cross over may compromise leakage inductance. High core permeability and high ΣA/l help to minimise wire length which helps in minimising flux leakage.

The transformer is configured as an autotransformer rather than separate primary and secondary windings to again minimise leakage inductance.

Above is a chart derived from s11 looking into the transformer primary with the 14t secondary short circuit showing the equivalent series inductance. The value will be taken as a total value of 236nH, or 118nH a side in the split model.

Note that the inductance at low frequencies is almost independent of frequency even though core permeability changes at these frequencies (see the #43 material data sheet), showing that, for the most part, leakage flux exists elsewhere than the core itself.

A simple model works quite well for predicting nominal load performance on low ratio transformers but less well for high ratio transformers, so best to proceed to measurement of the prototype with nominal load. A load was made from two small resistors in parallel having a combined DC resistance of 2480Ω, quite close to the nominal 2450Ω.

Measurement of the uncompensated transformer hinted that some 50-100pF was the likely optimum compensation capacitance. The transformer was measured with 47pF and it was under compensated, 100pF was perhaps more than needed but InsertionVSWR at the mid to high frequencies was not compromised so since there was a 100pF silver mica capacitor on hand, it was committed to the prototype.

Above is a plot of InsertionVSWR with 100pF silver mica compensation. InsertionVSWR is less than 2 from 1-30MHz. As this type of transformer goes, this is a very good result.

Note there is some contribution of the connecting wires to this response, it is just not possible to use zero length wires to connect the secondary load circuit… but then that applies to its application circuit as well.

Loss modelling ignores conductor loss. Even though the conductors are relatively small, the effective RF resistance referred to the primary side is very low and insignificant compared to core loss. Compensation capacitor loss is modelled, Q=1000 assumed for the silver mica capacitor, but his can be quite a deal lower and very significant for ceramic capacitors.

Above is a plot of the expected loss in dB, magenta on the left scale, and watts @ 50W continuous, red on the right scale. Maximum dissipation is less than 5W which should be accommodated within safe temperature rise for an unenclosed transformer.

Next step is to measure the transformer performance under power, capturing thermographs to confirm the predicted dissipation and power rating.

]]>I have also had lengthy discussions with Faraaz, VK4JJ, who is experimenting with a similar transformer.

This article describes my own design workup and measurements using a Fair-rite suppression core, 2643251002. The cores are not readily available locally, so I bought a bunch from Digi-key.

I really resist the tendency in ham radio to design around unobtainium, it is often quite misguided and always inconvenient. In this case, the motivation for these cores that use quite ordinary #43 material is the geometry of the core, they have ΣA/l=0.002995, a quite high and rivalling the better of binocular cores. High ΣA/l helps to minimise the number of turns which assists broadband performance. See Choosing a toroidal magnetic core – ID and OD for more discussion.

- EFHW;
- InsertionVSWR<2 3-22+MHz;
- nominal 49:1 transformation;
- compensated;
- autotransformer; and
- 50W average power handing.

Some key points often overlooked in published designs of EFHW transformers:

- Insufficient turns drives high core loss; and
- leakage inductance is the enemy of broadband performance, so the design tries to minimise leakage inductance.

Note that high number of turns drives high leakage inductance, so the design is to a large extent, a compromise between acceptable core loss and bandwidth.

From models, I expect that a turns ratio of 2:14 (ie 14t tapped at 2t) is likely to deliver the design criteria (with suitable compensation capacitor).

Above is a perhaps ambitious initial objective using a simple model of the transformer, dotted line is Loss and solid line is InsertionVSWR.

The first step is to measure a 2t winding alone on the core.

Above, the 2t winding measurement fixture. The wire is solid 0.5mm wire stripped from CAT5 LAN cable, the one end zip tied to the external threads of the SMA connector and the other end bent and inserted into the female part without damaging the connector.

Above, a plot or impedance. Note the resonance, the self resonant frequency (SRF) is 16MHz.

Above is a screenshot of a Simsmith model that will be used to develop the design.

It is initially configured to simply expose the impedance of the 2t winding using a simple model of the system as a resonator. The model estimates magnetising impedance from manufacturer’s complex permeability data and adds equivalent shunt capacitance cse as a first approximation of its first resonance. The model is calibrated by adjusting cse so that the model SRF coincides with the measurement.

In this case there is very good reconciliation between prediction and measurement, especially given the wide tolerance of ‘suppression’ ferrite components (see

Using complex permeability to design with Fair-rite suppression products).

The next step is to wind the 2:14 autotransformer winding and to make measurements of its SRF and leakage inductance to calibrate a predictive model.

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

The graph is based on a series of NEC-5.0 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-5.0 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.

Above is the transformer with 100pF compensation capacitor across the input, and two resistors to make up a 3300Ω load in combination with the VNA port.

The transformer is an autotransformer of 16t tapped at 2t, so the nominal turns ratio is 1:8, or impedance 1:64.

Looking into the 2t tap with the transformer loaded with 3250+50=3300Ω, Luis measured s11, s21 parameters from 1-45MHz with a nanoVNA. (Nominally this should be a 3200Ω load, but the error is very small, VSWR equivalent of 1.03.)

Above is my analysis of this data for InsertionVSWR and ReturnLoss. It gets a bit shabby above 15MHz.

Above is a plot of InsertionLoss and Loss (or TransmissionLoss). See On Insertion Loss for explanation of the terms.

Compensation of the transformer with 100pF in shunt with the input improves the broadband response.

Above is InsertionVSWR and ReturnLoss. It is not too bad over all of HF (3-30MHz).

Above is a plot of InsertionLoss and Loss (or TransmissionLoss). See On Insertion Loss for explanation of the terms.

Almost all of the Loss is in core loss, and it gives us a good indicator of core heating. The worst case is at 30MHz where the Loss is 0.7dB, so about 15% of input power is converted to heat.

The tests here were using a dummy load on the transformer, and that did allow confirmation of the design.

Real end fed antennas operated harmonically do not present a constant impedance, not even in harmonically related bands. Note that the resonances do not necessarily line up harmonically, there is commonly some enharmonic effect.

Being a more efficient design that some, it might result is a wider VSWR excursion that those others as transformer loss can serve to mask the variations in the radiator itself.

Hats off to Luis, CT2FZI for his work in building and measuring the transformer, and to have the flexibility to consider more than FTxxx-43 cores.

]]>Above is the model topology. D1 is a daemon block which essentially, calculates key values for the other blocks based on exposed parameters and the named ferrite material complex permeability data file. The prototype used a Fair-rite 2643625002 (#43) core.

D1 code:

//Misc //Updates Tfmr, CoreLoss, and Cse. $data=file[]; // core mu aol; np; ratio; cse; cores; k; $u1=$data.R; $u2=$data.X; //u1=$u1; //u2=$u2; $ns=np*ratio; Ym=(2*Pi*G.MHz*1e6*(4*Pi*1e-7*$u1*aol*cores*1e9)*np^2*1e-9*(1j+$u2/$u1))^-1; Cse.F=cse; CoreLoss.ohms=1/Ym.R; $l1=1/(2*Pi*G.MHz*1e6*-Ym.I); $l2=$l1*(($ns-np)/np)^2; $lm=k*($l1*$l2)^0.5; Tfmr.L1_=$l1+$lm; Tfmr.L2_=$l2+$lm; Tfmr.L3_=-$lm;

L is the load block.

Cse models the self resonance of the transformer at lowish frequencies, Cse is an equivalent shunt capacitance.

Tfmr is a coupled coils model (above) of a (nearly) lossless autotransformer (core loss will come later). Wire loss is usually insignificant in these type of transformers and is ignored. (It seems that Simsmith will not simulate a pure inductance, in this cases the loss of the ‘lossless transformer is of the order of 5e-6dB, so satisfactory.) It is possible to simplify declaration of this component by using Simsmith’s coupled coils in a RUSE block, I have chosen to take full control and solve the mutual inductance effects explicitly.

(The model assumes that k is independent of frequency which is not strictly correct, but for medium to high µ cores, measurement suggests it is a fairly good assumption.)

Coreloss brings the ferrite core loss to book.

Ccomp models a compensation capacitor used to improve broadband InsertionVSWR.

The G block provides the source and plot definitions.

Plots code:

//Plots //check lossless Tfmr behavior //tfmrloss_dB=10*Log10(Tfmr.P/(Tfmr.P-Tfmr.p)); //Plot("TfmrLoss",tfmrloss_dB,"LossdB",y1); coreloss_dB=10*Log10(CoreLoss.P/(CoreLoss.P-CoreLoss.p)); loss_dB=10*Log10(G.P/L.P); mismatchloss_dB=10*Log10(1/G.P); Plot("CoreLoss",coreloss_dB,"LossdB",y1); Plot("Loss",loss_dB,"LossdB",y1);;

The model was calibrated to measurement of the prototype, and the fit is quite good given tolerances on components.

The model allows convenient interactive sensitivity analysis where parameters can be dialed up and down with the mouse wheel and the response changes observed.

- FT82-43 matching transformer for an EFHW
- Find |Z|,R,|X| from VSWR,|Z|,R,Ro
- A new impedance calculator for RF inductors on ferrite cores
- Calculate ferrite cored inductor (from Al)
- Calculate VSWR and Return Loss from Zload (or Yload) and Zo
- Duffy, O. 2015. A method for estimating the impedance of a ferrite cored toroidal inductor at RF. https://owenduffy.net/files/EstimateZFerriteToroidInductor.pdf.
- ———. 2006. A method for estimating the impedance of a ferrite cored toroidal inductor at RF. VK1OD.net (offline).

At Ultrafire XML-T6 LED torch – a fix for the dysfunctional mode memory ‘feature’ I gave a fix for that revision of the electronics, and updated it with description of a later fixed production model.

Years later, I bought two more of these due to switch failures on the originals… and guess what, the flash on power on returns.

Let’s pull them apart.

They have a new revision / version of the LED driver PCB, and it has provision for a resistor in parallel with the capacitor, but the resistor pads are not populated.

Above, the LED driver board with a 100k resistor added, it is the far component. This was an 0805 part that was on hand, but ideally should be a 0603.

Above, the second torch could not be saved, the driver PCB was cracked, a result of heavy handed forcing the PCB into its recess when not properly aligned.

This model is a little different construction to the first ones I wrote about. To dismantle it:

- remove the cap and battery;
- prise the plastic lens retaining ring out without damaging anything (especially the lens);
- drop the lens out;
- using a pin spanner, rotate the LED housing against the main barrel and unscrew it;
- push the LED housing out the front of the torch; and
- carefully, prise the driver PCB out of its recess.

To finish, add the resistor, clean everything, wipe a little silicon grease inside the front barrel, slide the LED housing into it and screw the main barrel onto it. Tighten the LED housing, install the battery, lubricate the rear thread and o-ring with silicon grease, and test it all works. Then clean the LED, reflector and lens and reinstall the lens and retaining ring. All done.

]]>I bought this after seeing several recommendations on a nanoVNA forum.

Above is the factory pic of the SMA-8.

The one I purchased cost about $40 including post from an eBay store.

In the event, the thing arrived after nearly three weeks… so that was quick.

When the mechanism was operated by hand, it was obviously asymmetric.

But it came with a test certificate!

So I will measure it.

Above, force from the left peaks at 6.0N, @ 0.16m radius: 0.96Nm torque.

Above, force from the right peaks at 9.4N, @ 0.16m radius: 1.5Nm torque.

The thing is unusable and unrepairable.

I trust my measurements before the obviously phony Chinese test certificate.

This was purchased on eBay with the hope that it would be better quality than the last, and if it wasn’t there was better prospect of a refund. A full refund was obtained after making a compelling case.

I am not saying all MXITA product is low quality, but this item was such poor quality as to be consigned to the bin and if you trust MXITA as I did, you might do the same.

]]>Let’s demonstrate the measurement of Rin of an o/c resonant section around the 160m band, which we will then use to calculate MLL.

Above, the AA-600 connected to the cable using a F(F)-N(M) adapter, the cable is 305m in length and the far end is open circuit.

So lets scan around 1800kHz looking for a convenient resonance.

Ok, there is a resonance just a bit above 1800kHz. Let’s move the cursor using the freq+ arrow key, press the range- key a few times to narrow the scan and press to rescan.

Ok, closer now, but overshot a bit. Let’s move the cursor again and switch to All mode.

Above is All mode, X is just greater than zero, so we will shift freq down using the freq- arrow key watching X for the zero crossing.

Above, this is close enough. We can read Rin as 19.0Ω.

Above, calculating MLL from the input data we have 0.0074dB/m or 0.74dB/100m.

This whole procedure takes less than a minute using the stand alone instrument… in part due to the very effective human interface on the AA-600, you might think the designer knew how the instruments would get used, something you cannot say for a lot of analysers and VNAs (which are now the fashion).

The technique is particularly useful if the far end of the cable is not accessible, eg it is sometimes hidden in the interior of the drum.

(Ikin 2016) proposes a different method of measuring noise figure NF.

Therefore, the LNA noise figure can be derived by measuring the noise with the LNA input terminated with a resistor equal to its input impedance. Then with the measurement repeated with the resistor removed, so that the LNA input is terminated by its own Dynamic Impedance. The difference in the noise ref. the above measurements will give a figure in dB which is equal to the noise reduction of the LNA verses thermal noise at 290K. Converting the dB difference into an attenuation power ratio then multiplying this by 290K gives the LNA Noise Temperature. Then using the Noise Temperature to dB conversion table yields the LNA Noise Figure. See Table 1.

The explanation is not very clear to me, and there is no mathematical proof of the technique offered… so a bit unsatisfying… but it is oft cited in ham online discussions.

I have taken the liberty to extend Ikin’s Table 1 to include some more values of column 1 for comparison with a more conventional Y factor test of a receiver’s noise figure.

Above is the extended table. The formulas in all cells of a column are the same, the highlighted row is for later reference.

A test setup was arranged to measure the noise output power of an IC-7300 receiver which has a sensitivity specification that hints should have a NF≅5.4dB. The relative noise output power for four conditions was recorded in the table below.

Ikin’s method calls for calculating the third minus second rows, -0.17dB, and looking it up in his table. In my extended table LnaNoiseDifference=-0.17dB corresponds to NF=3.10dB.

We can find the NF using the conventional Y factor method from the values in the third and fourth rows.

The result is NF=5.14dB (quite close to the expected value based on sensistivity specification).

Ikin’s so called dynamic impedance method gave quite a different result in this case, 3.10 vs 5.14dB, quite a large discrepancy.

The chart above shows the relative level of the four measurements. The value of the last two is that they can be used to determine the NF using the well established theory explained at AN 57-1.

The values in the first columns are dependent on the internal implementation of the amplifier, and cannot reliable infer NF.

- Hewlett Packard. Jul 1983. Fundamentals of RF and microwave noise figure measurement. AN 57-1
- Ikin, A. 2016. Measuring noise figure using the dynamic impedance method.