Jaycar’s LO1238 ferrite toroid is readily available in Australia at low cost and quite suits some HF RF projects.

The published data is near to useless, so a long time ago I measured some samples and created a table of complex permeability of the L15 material which I have used in many models over that time. It did concern me that measured µi was about 25% higher than spec, which is the limit of stated tolerance. Keep in mind that this is Chinese product with scant data published.

I have measured some samples purchased recently, and µi is closer to the specified 1000, so I intend using this new data in future projects.

Above is complex permeability calculated from s11 measurement of a single turn on the LO1238.

Downloads

L15.7z

Derivation of the expression for the unknown impedance in an s21 series through measurement arrives at the following expression:

\(Zu=(Zs+Zl)(\frac{1}{s_{21}}-1)\).

The diagram above is from (Agilent 2009) and illustrates the configuration of a series-through impedance measurement.

It is commonly assumed that Zs+Zl=100Ω, as is done in (Agilent 2001). That might be a reasonable assumption if the VNA correction scheme corrects source and load mismatch, but let’s consider the NanoVNA-H running NanoVNA-D v1.2.29 (Apr 2024) firmware (the current release).

It is good practice to validate a measurement system by measuring a known component. Let’s measure a 200Ω 1% resistor that measures 200.23Ω at DC (it is actually 2 x 0806 100Ω 1% resistors in series.

Above is the test setup, the SDR-kits test board fixture was SOLIT calibrated 1-31MHz using the parts shown at centre of the pic. The fixture is shown with a 200Ω 1% DUT that measures 200.23Ω at DC.

NanoVNA-H v3.3 with NanoVNA-D v1.2.29

Above is a screenshot from the NanoVNA-H measuring the SMD resistor that measures 200.23Ω at DC. The red and green traces use the internal feature to transform an S21 measurement into series thru impedance. The measured value of 204.9-j2.042Ω is significantly different to the expected 200.23Ω.

Above is a plot of calculated DUT assuming the Zs+Zl=100Ω (as does the screenshot above).  The measured values are significantly different to the expected 200.23Ω.

NanoVNA-D v1.2.29 does not correct source and load mismatch, and that is probably the main cause of the apparent error.

Lets turn the measurement around, if we measure some known impedance Zk, we can calculate Zs+Zl:

\(Zs+Zl=\frac{Zu}{(\frac{1}{s_{21}}-1)}\).

#import the network
nws21k=rf.Network(name+'-S21k.s2p')
zu=(50+50)*(1/nws21k.s[:,1,0]-1)
zk=200.23 #precision measurement of DUT resistor at DC
#calculate zs+zl using zu=(zs+zl)(1/s21-1) and zu=zk
zs_zl=zk/(1/nws21k.s[:,1,0]-1)

Above is a snippet of code in Jupyter to import the network and calculate the value of zs_zl (Zs+Zl) inferred by the s21 measurement of the DUT.

Above is a plotting of calculated zs_zl impedance components, real and imaginary, or R,X.

NanoVNA-H4 v4.3 with NanoVNA-D v1.2.40 using ERC

NanoVNA-D v1.2.40 (released 07/09/2024) includes optional Enhanced Response Correction which corrects source mismatch. The feature is turned on for these measurements.

The instrument was calibrated with a LOAD that measured 50.17Ω at DC, this was specified in the calibration.

The NanoVNA-H4 v4.3 has better Port 2 input impedance than the NanoVNA-H used in the previous tests.

All of these measures improve the accuracy of s21 series through measurement of Z.

Above is a screenshot from the NanoVNA-H4 measuring the SMD resistor that measures 200.23Ω at DC. The red and green traces use the internal feature to transform an S21 measurement into series thru impedance. The measured value of 199+j0.594Ω is different to the expected 200.23Ω, about 0.5%.

Above is a plot of calculated DUT assuming the Zs+Zl=100Ω (as does the screenshot above).  The measured values are significantly different to the expected 200.23Ω.

NanoVNA-D v1.2.40 does not correct load mismatch, and that is probably the main cause of the apparent error.

Lets turn the measurement around, if we measure some known impedance Zk, we can calculate Zs+Zl:

\(Zs+Zl=\frac{Zu}{(\frac{1}{s_{21}}-1)}\).

#import the network
nws21k=rf.Network(name+'-S21k.s2p')
zu=(50+50)*(1/nws21k.s[:,1,0]-1)
zk=200.23 #precision measurement of DUT resistor at DC
#calculate zs+zl using zu=(zs+zl)(1/s21-1) and zu=zk
zs_zl=zk/(1/nws21k.s[:,1,0]-1)

Above is a snippet of code in Jupyter to import the network and calculate the value of zs_zl (Zs+Zl) inferred by the s21 measurement of the DUT.

Above is a plotting of calculated zs_zl impedance components, real and imaginary, or R,X. Zs+Zl is considerably closer to ideal (100+j0Ω) than the previous case.

Conclusions

• The analysis here is specific to a NanoVNA-H v3.3 running NanoVNA-D v1.2.29 and NanoVNA-H4 v4.3 running NanoVNA-D v1.2.40 configured as described.
• The formula often given and implemented for transformation of a series through s21 measurement to impedance depends on an assumption that source and load ports have zero mismatch error (eg that any mismatch is corrected).
• NanoVNA-D v1.2.29 does not correct source and load mismatch, the results are mediocre.
• NanoVNA-D v1.2.40 combined with the improved NanoVNA-H4 v4.3 hardware does not correct load mismatch, but other improvements improve the accuracy.

References

• Agilent. Feb 2009. Impedance Measurement 5989-9887EN.
• Agilent. Jul 2001. Advanced impedance measurement capability of the RF I-V method compared to the network analysis method 5988-0728EN.

Fox Flasher MkII and several follow on articles described an animal deterrent based on a Chinese 8051 architecture microcontroller, the STC15F104E.

Fox flasher MkII update 7/2019 documented a rebuild of the enclosure etc.

This is an update after five more years operation outside.

Above is a pic of the device. The polycarbonate case has yellowed a little. Importantly the cheap PVA has not crazed, it is kept dry by the outer enclosure, and a hydrophobic vent helps keeps the interior dry.

The battery is a pouch LiPo single cell, it is in good condition. A previous trial with 18650 LiIon cells showed they were unsuitable for the environmentals.

Two previous articles were desk studies of the the ARRL EFHW kit transformer, apparently made by hfkits.com:

• Thoughts on the ARRL EFHW antenna kit transformer; and
• Thoughts on the ARRL EFHW antenna kit transformer – improvements?

This article documents a build and bench measurement of the component transformer’s performance, but keep in mind that the end objective is an antenna SYSTEM and this is but a component of the system, a first step in understanding the system, particularly losses.

The prototype

Albert, KK7XO, purchased one of these kits from ARRL about 2021, and not satisfied with its performance, set about making some bench measurement of the transformer component.

Above is Albert’s build of the transformer.

The kit parts list is as follows:

Magnetics

The first point to note is that Amidon’s 43 product of recent years has published characteristics that are a copy of National Magnetics Group H material (though they changed the letterhead).

Above is a side by side comparison of the NMG H material datasheet and Amidon 43, the Amidon appears to be a Photoshop treatment of the NMG.

Fair-rite have been a long term manufacturer of a material they designate 43 (which has changed over time), and it has been resold as such by many sellers. NMG H material is somewhat similar, but to imply it is equivalent to Fair-rite 43 might be a reach.

Overall design

I might note at the offset that the design is not original, there are countless articles on the net describing a 2:14 turn on a ‘FT240-43’ transformer for an EFHW using exactly the same winding layout.  As discussed in other articles on this site, 2t is insufficient for operation down to 3.5MHz using Fair-rite #43, even worse for the National Magnetics H material published as Amidon 43.

Measurement

Measurements were made with a NanoVNA-H4. It is not a laboratory grade instrument, but well capable of qualifying this design and build.

Albert performed a two port measurement using the setup above. This places a nominal load on the transformer, and the voltage division of the series resistor and Port 2 input impedance is used to correct the measured s21 figure.

So let’s take the measurements and calibrate a SimNEC model of the transformer.

Above is the model using Fair-rite #43 material calibrated to measured leakage inductance and InsertionVSWR. The reconciliation of model (magenta) with measurement (green) is good. The equivalent Fair-rite part is 5943003801.

Let’s compare measurement to the same model but with Amidon 43 material (NMG-H):

Reconciliation is very poor at lower frequencies, the measured transformer appears to have significantly higher permeability.

Measure core complex permeability

Let’s take a diversion for a moment and put this question to bed.

Above is complex permeability calculated from measurement of a 1t winding on the core used above compared with the Fair-rite #43 2020 published data. Keep in mind that tolerances on ferrite are relatively wide, these two reconcile very very well, there is no doubt in my mind that the material is Fair-rite #43. This questions the seller’s specified parts list.

A similar plot against NMG-H shows a stark difference.

InsertionVSWR and ReturnLoss

So let’s return to the saved .s2p file from the two port measurement.

Above is a plot of bench measurement of ReturnLoss and (related) InsertionVSWR for the transformer with a nominal load.

The InsertionVSWR might look acceptable, but using InsertionVSWR as a single metric is a very limited view.

Above is a plot of InsertionLoss (-|s21|dB), and its components MismatchLoss and (Transmission) Loss. See Measurement of various loss quantities with a VNA for discussion of Loss terms.

Let’s dismiss performance below 7MHz, the plot shows it has insufficient turns.

Importantly, (Transmission) Loss is around 1dB at 7MHz, so 20% of the input power is converted to heat in the core and winding, mostly in the core. If you look back to the first SimNEC screenshot, the model predicts just under 1dB Loss, so measurement reconciles well with the prediction model.

Experience and measurement of Loss and thermographs informs that a transformer of this type in this type of enclosure is not capable of more than about 10W of continuous dissipation in typical deployments, less if it is in direct sun in a hot climate. That means the transformer is not likely to withstand more than about 50W average input power without damage or performance degradation.

Now that might be quite acceptable to some users, gauging by the number of web articles and Youtube videos recommending this, a lot of users apparently.

Credit

Credit to Albert for his interest in understanding these things, careful measurement of the prototype, and preparedness to dismantle the prototype for science.

Summary

So let’s end this article with the results of desk study and measurement:

• though the kit specifications state the core is Amidon #43, the sample kit is almost certain to contain a Fair-rite 43 core which is significantly different;
• two port measurement of the sample of one with nominal load showed around 1dB of Loss at 7MHz;
• MismatchLoss grows rapidly as frequency is reduced below 7MHz suggesting it has insufficient magnetising impedance, a result of insufficient turns;
• the winding configuration is not optimised for leakage inductance;
• popularity is not a good indicator of performance.

Where to from here?

These problems beg a redesign and measure of the transformer… more to follow.

It is often handy to have a reliable / known female UHF short and open circuit terminations when measuring using cables terminated in a UHF male connector.

This article describes a DIY solution.

Above is a diagram from Rosenberger showing the location of the ‘standard’ reference plane on UHF series connectors.

Above, the DIY short and open terminations. The short uses a M4x12 brass washer to short inner to outer at the connector body. This was measured using a VNA to have a one way propagation time of 50ps from the reference plane, and it is labelled for reference. The open termination simply has the pin cut off very close to the end of the dielectric, and again it measures 50ps.

These are not microwave standards, you are kidding yourself if you think you are making accurate measurements using UHF connectors above 100MHz, even less for demanding measurements.

You might wonder why you need an open termination. A UHF plug with a loose coupling sleeve and / or  exposed male pin is not a reliable open with known location.

An example application is measurement of the above transformer (though with nominal load of 2450Ω attached by very short wires) using a short cable from the VNA to the UHF(F) jack, If the cable + SC adapter described above is calibrated with an e-delay value that shows X=0 over a wide range of frequencies,  removing the short termination and connecting the cable to the transformer (with load) allows capture of the impedance as exists at the point that the (blue) compensation capacitor is attached, ie we want the reference plane to be the inboard end of the UHF connector. In this case, we ignore the 50ps offset.

One could take that s11 data and apply a small +ve or -ve capacitance in shunt to evaluate whether the optimal capacitor is larger or smaller and by how much.

Above is an example of measurement a correspondent’s build of a hfkits.com EFHW transformer (aka ARRL EFHW transformer) imported to the L element as a .s1p file with reference plane at the UHF connector, and Ccomp is an additional +/- adjustment dialled up and down to optimise the VSWR response. In this case an additional 20pF provided a small improvement to VSWR on the higher bands.

For this technique to be valid, it is essential that the reference plane be where the compensation capacitor will be applied.

You wanted a LOAD as well? See A check load for antenna analysers with UHF series socket. If you want a UHF(F) load, do the same thing but with a UHF(F)-SMA(F) adapter.

Derivation of the expression for the unknown impedance in an s21 series through measurement arrives at the following expression:

\(Zu=(Zs+Zl)(\frac{1}{s_{21}}-1)\).

The diagram above is from (Agilent 2009) and illustrates the configuration of a series-through impedance measurement.

It is commonly assumed that Zs+Zl=100Ω, as is done in (Agilent 2001). That might be a reasonable assumption if the VNA correction scheme corrects source and load mismatch, but let’s consider the NanoVNA-H running NanoVNA-D v1.2.29 (Apr 2024) firmware (the current release).

It is good practice to validate a measurement system by measuring a known component. Let’s measure a 200Ω 1% resistor that measures 200.23Ω at DC (it is actually 2 x 0806 100Ω 1% resistors in series.

Above is the test setup, the SDR-kits test board fixture was SOLIT calibrated 1-31MHz using the parts shown at centre of the pic. The fixture is shown with a 200Ω 1% DUT that measures 200.23Ω at DC.

Above is a screenshot from the NanoVNA-H measuring the SMD resistor that measures 200.23Ω at DC. The red and green traces use the internal feature to transform an S21 measurement into series thru impedance. The measured value of 204.9-j2.042Ω is significantly different to the expected 200.23Ω.

Above is a plot of calculated DUT assuming the Zs+Zl=100Ω (as does the screenshot above).  The measured values are significantly different to the expected 200.23Ω.

NanoVNA-D v1.2.29 does not correct source and load mismatch, and that is probably the main cause of the apparent error.

Lets turn the measurement around, if we measure some known impedance Zk, we can calculate Zs+Zl:

\(Zs+Zl=\frac{Zu}{(\frac{1}{s_{21}}-1)}\).

#import the network
nws21k=rf.Network(name+'-S21k.s2p')
zu=(50+50)*(1/nws21k.s[:,1,0]-1)
zk=200.23 #precision measurement of DUT resistor at DC
#calculate zs+zl using zu=(zs+zl)(1/s21-1) and zu=zk
zs_zl=zk/(1/nws21k.s[:,1,0]-1)

Above is a snippet of code in Jupyter to import the network and calculate the value of zs_zl (Zs+Zl) inferred by the s21 measurement of the DUT.

Above is a plotting of calculated zs_zl impedance components, real and imaginary, or R,X.

Conclusions

• The analysis here is specific to a NanoVNA-H v3.3 running NanoVNA-D v1.2.29.
• The formula often given and implemented for transformation of a series through s21 measurement to impedance depends on an assumption that source and load ports have zero mismatch error (eg that any mismatch is corrected).
• NanoVNA-D v1.2.29 does not correct source and load mismatch.

References

• Agilent. Feb 2009. Impedance Measurement 5989-9887EN.
• Agilent. Jul 2001. Advanced impedance measurement capability of the RF I-V method compared to the network analysis method 5988-0728EN.

This article is principally a short commendation for Jupyter or Interactive Python for ham radio related projects for the quantitative ham. Python is a cross platform programming language that has a very rich set of libraries to support scientific and engineering applications, and a good graph maker.

The exercise for this demonstration is to decompose three measurements of currents on a two wire transmission line at a point into the differential and common mode components at that point, and to plot a phasor diagram of a solution to the measurements. Remember that common mode current and differential current in an antenna system are usually standing waves.

Above is a diagram explaining the terms used, I1 and I2 are the magnitudes of currents in each conductor measured using a clamp on RF ammeter, and I12 is the magnitude of the current when both conductors are passed through the clamp on RF ammeter, i12 is the phasor sum of the underlying i1 and i2.

The solution to the problem lies in applying the Law of Cosines to find the angular relationship between the differential and common mode components, a high school trigonometry problem. In fact, we find the magnitude of the angle between ic and id.

Above is the solution, a phasor diagram taking id as the phase reference (ie 0°). Because we know only the magnitude of the angle between ic and id, there is a second possible solution as noted on the graphic.

Above is a screen capture of the Jupyter source cells and results.

When you look at the measurements that were taken, |i1| was within 2% of |i2| which many online experts would opine means there is nearly perfect balance. Measurement instruments based on simply comparing |i1| and |i2| indicating within the BalanceBar are deeply flawed… though very popular.

The decomposition shows that the magnitude of the differential current |id| is 25.7A and the magnitude of the total common mode current is 9.3A (4.65A per leg). It is not nearly balanced!

This demonstration uses high school mathematics applied to three measurements of current to drill down on the distribution of currents in a scenario that many would regard as balanced. Balanced means that the currents in each wire are equal but opposite in phase at any point along the line.

A quotation from Lord Kelvin:

When you can measure what you are speaking about, and express it in numbers, you know something about it. But when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind. It may be the beginning of knowledge but you have scarcely in your thoughts advanced to the state of science.

The most common problem of broadband ferrite cored transformer designs for RF is insufficient turns which results in:

• low magnetising impedance Zmag causing:
• high InsertionLoss at lower frequencies;
• excessive core loss at low frequencies, and
• high InsertionVSWR at low frequencies.

This article give a simple test for a transformer that will have a nominally 50Ω input or output winding

Without going into a lot of magnetic and transformer theory, a through test using a VNA of the core and just one winding configured as a 1:1 (50Ω:50Ω) autotransformer is revealing. If that combination of turns, core, frequency is not adequate, it is very unlikely any transformer

Above is a schematic of the test configuration, the DUT is the central element, everything else is supplied by the VNA.

Above is an example mystery core with 3t for the 50Ω winding, connected in shunt with the through connection using a SDR-kits test board.

The test board and NanoVNA-H4 was SOLIT calibrated for the test, the the DUT inserted. For this core, the question is whether there are sufficient turns for 3.5MHz and up, we will test to 11MHz as this test will not reveal the high frequency limit, you need the other winding… which you can put on having established whether 3t is enough.

Above is the scan on the NanoVNA. Here we note that |s21| @ 3.5MHz is -0.528dB, this has potential. The network is symmetric, and so only a scan in one direction is needed.

Let’s import the .s2p file into SimNEC and do some calcs. (Where the .s2p file contains zeros for the s22 and s12 columns, SimNEC assumes a symmetric network and silently copies the values… which is ok as this network is symmetric.)

Above is the SimNEC model. The plots include calculated:

• InsertionLoss;
• Loss; and
• InsertionVSWR.

//Plots
dcl pfwd=S1.P/(1-(Gamma(S1.Z).M)^2);
LossdB=10*Log10(S1.P/L.P);
Plot(LossdB,"dB");
InsLossdB=10*Log10(pfwd/L.P);
Plot(InsLossdB,"dB");

Above is the code for these calculations. See Measurement of various loss quantities with a VNA for meanings of the terms. In this source case of UseZo(), pfwd=1, but it may not be for other source cases.

InsertionLoss @ 3.5MHz is 0.523dB, depending on the applications requirements, that might be acceptable, you probably would not want any worse.

Loss tells us about conversion of input RF power to heat, and it is relatively low at 0.083dB.

InsertionVSWR is moderately high at 1.9dB, again it depends on the application requirements.

Overall, this 1:1 (50Ω:50Ω) is likely to be marginal to unsuitable for most applications and would require at least 4t all else equal to perform reasonably well.

Now increasing the step up ratio typically degrades these parameters a little, so this test really identifies the minimum core / turns / frequency configuration that may result in an acceptable transformer with a higher step up ratio.

The discussion has inferred that the final transformer will be an auto transformer, but the analysis is useful for a conventional transformer using a medium to high µ core, just that a little more departure from the measured performance is likely with a high ratio conventional transformer.

So if such a test of the 50Ω winding and core has a bit of margin, wind the other winding and test the transformer.

7MHz and up

There are articles on this site that use this core (LO1238) with 3t 50Ω winding in 1:64 and 1:49 transformer configurations for an EFHW antenna system for 7MHz and up.

Whilst the combination doesn’t really make the grade at 3.5MHz, it does look better at 7MHz, see the chart above. Built, tested, measured transformers based on 3t winding worked well 7-30MHz (which suits lots of portable uses).

This is a follow up to Thoughts on the ARRL EFHW antenna kit transformer.

The first point to note is that Amidon’s 43 product of recent years is specified identically to National Magnetics Group H material. It is significantly different to Fair-rite’s 43 mix.

Though the parts list specifies an Amidon #43 core, I note that W1VT posted recently:

The ARRL kits don’t use Amidon parts as specified in the Parts List.

That was done as a “service” to those who wanted to know where to get parts for building their own without buying the kit.

The parts are sourced by a European company and shipped as kits to ARRL HQ, which acts as the distributor.

ARRLHQ publishes a Youtube video which shows a label by hfkits.com, and their website also lists Amidon FT240-43. hfkits.com may use a ‘genuine’ Amidon FT240-43 in their kits… this article applies to ‘modern’ Amidon FT240-43.

Trusting hfkits.com and ARRL, lets take the core as a ‘modern’ Amidon FT240-43 (equivalent to NMG-H).

Estimate the power dissipated in the core magnetised to 50V applied

Let’s make a first estimate of the power dissipated in the core with 50V impressed on the nominal 50Ω input winding alone (ie no secondary winding on the core), equivalent to 50W in 50Ω.

We  will calculate the magnetising admittance Gm+jBm, and the power dissipated is given by \(P=V^2G_m\).

Amidon 43 / National Magnetics H case

The first point to note is that Amidon’s 43 product of recent years is sourced from National Magnetics Group, and is their H material. It is not a good equivalent to Fair-rite’s 43 mix.

Let’s make a first estimate of core loss at 3.5MHz.

We can estimate the complex permeability which is needed for the next calculation.

The real part of Y is the magnetising conductance Gm (the inverse of the equivalent parallel resistance).

\(P_{core}=V^2G_m=50^2 \cdot 0.00950=23.8 \text{ W} \).

Amidon 43 / National Magnetics H case with 4t primary

Let’s recalculate with a 4t primary.

The real part of Y is the magnetising conductance Gm (the inverse of the equivalent parallel resistance).

\(P_{core}=V^2G_m=50^2 \cdot 0.00232=5.8 \text{ W} \).

To me, 5.8W core heating due to 50W RF input is a lot more acceptable that the 23.8W with a 2t primary. It is not stunning by an means but borderline acceptable. This configuration might stand 100W FT-8 without overheating (depending on the enclosure, environment etc).

So, can you use too many turns?

Yes, increasing the turns will increase leakage inductance which is a very important, if not most important, constraint on high end Insertion VSWR.

Try it and measure it.

Oh, but I only want to use 40m and up

You can follow the same process and estimate the minimum primary turns that suits your own acceptable core loss criteria.

One sees analyser sweeps of EFHW measurements posted online quite frequently, and a trend is that posters are quite pleased with the results.

Above is an example, a ‘user’s’ MyAntennas.com EFHW-4010 antenna with 23m of unspecified coax. Unfortunately it is a bit narrow, ordered up by an online expert.

The responses to the post were inevitably a focus on the location of the VSWR minima, and the value of VSWR at those locations.

But before focussing on the location of the resonances, I was taken with the rather compressed VSWR range. Let’s present that as ReturnLoss.

Above is ReturnLoss from the same .s1p file. For a shortish antenna, we might usually expect that the ReturnLoss minima will be quite a lot lower. Yes, these are out of band, but should not be dismissed as irrelevant.

Let’s look at an NEC model of a 21m long InvertedL EFHW.

Above is magnitude of Reflection Coefficient or ρ at the feedpoint (Zref=2450Ω) for a native EFHW as an Inverted L, ReturnLoss=-ρ (the chart is upside down compared to the previous one). Note that the ReturnLoss minima are up to about 1.2dB (recall that this model has no transformer loss, feed line loss, counterpoise on the ground loss).

The loss that results in high minimum ReturnLoss is likely to be a broaband loss, ie to affect in-band performance as well as between desired bands.

This begs the question, does the user’s antenna system contain some broadband loss mechanism that masks the natural impedance variation of the native EFHW?

If so, is there perhaps 2dB or more of broadband system loss that degrades RadiationEfficiency by as much as 40%.

Note also that there are fewer minima and maxima in the NEC model. The OP’s antenna with 5 distinct peaks shows signs of being electrically longer… the notion that the counterpoise is not part of the antenna length is wrong. So before focus on the location of ReturnLoss maximum (ie the ‘tuning’) there is an issue with the number of maxima and minima… this antenna is not working like a simple 40m EFHW on harmonics.

Background

From time to time, ham radio operators may question whether a section of installed and used coax is still good or significantly below spec and needs replacement.

A very common defect in coax installed outside is ingress of water. The earliest symptoms of water ingress are the result of corrosion of braid and possibly centre conductor, increasing conductor loss and therefore matched line loss (MLL). Any test for this must expose increased MLL to be effective.

Introduction

This article describes a simple but effective test of MLL for coax of known Z0 and length using a suitable one port antenna analyser (or VNA such as the NanoVNA), the nominal Z0 is sufficient to demonstrate cable is good.

The test involves measuring the resistance looking into a resonant length of coax with either an open circuit or short circuit termination.

The concept is to measure MLL and compare it to specification. Defects that increase MLL are not usually narrowband, but will be evidenced over a very wide range of frequencies so measurement at the exact operating frequency is not necessary.

Analyser requirements

Frequency

The analyser will need to cover a suitable frequency range for measurement. For cables for use on HF, I would advise measurement above 10MHz as actual Z0 is closer to nominal Z0. For higher frequencies, choose a range near to the operating frequency.

The analyser needs to be able to measure R and X reasonably accurately at a low impedance or high impedance resonance of the line section with either SC or OC termination.

Access

Access is needed to one end for the analyser, and at the other end for a SC or OC termination (the cable has to be disconnected from the antenna). It is not necessary to connect the ‘far end’ back to the analyser as you would for a two port transmission test.

Connectors

If you use connectors with a loose coupling sleeve (UHF, SMA etc), do not use a loose male connector as OC, connect it to a F-F adapter so nothing is loose.

To get accurate results, all connectors must be secure, clean and properly tightened.

Got all that under control? Let’s measure…

A practical example

The DUT is 10m of quite old budget RG58A/U fitted with crimp BNC connectors. A sample of this cable has previously been measured for braid coverage, it is just 78% so we might expect it to be a little poorer than Belden 8259.

Above, the top is a sample of the cable under test, and lower is Belden 8259. One can see the poorer braid coverage of the test cable… but does that alone condemn it?

The analyser is an AA-600 which uses an N(F) connector so a N(M)-BNC(F) adapter is used. The AA-600 uses a 16bit ADC, so it gives very good accuracy of extreme impedances (which is the case for this test).

Taking my own advice to measure above 10MHz, the third low impedance resonance of the cable section with OC termination is about 15MHz… let’s measure that.

Using the AA-600’s measure All facility and scrolling frequency up and down with the arrow keys until X passes through zero, we get the above measurements. I have taken a screen shot for the article, but no USB connection is needed for a practical measurement, just write down the frequency and R when X=0.

Now using Calculate transmission line Matched Line Loss from Rin of o/c or s/c resonant section we will calculate MLL (see Measuring matched line loss).

So, now we know the frequency of measurement and MLL, we need to find the specification MLL at that frequency using a GOOD line loss calculator.

Specification MLL is 0.06dB/m, we measured 0.07dB/m, it is a little higher than spec, probably a result of the budget construction, and no reason to condemn it, it is probably as good as the day it was made.

Can you use a NanoVNA?

Yes, you can any instrument that can measure R and X at resonance. I have demonstrated the technique using a noise bridge, an antenna impedance bridge (GR1606B), and a NanoVNA.

Conclusions

The technique and formulas used gives a practical simple but effective method of measuring matched line loss using a one port analyser (or any instrument that can measure R and X at resonance).

Several recent articles examined the use of s11 port extension or e-delay in some scenarios that might have surprised.

Recall that s11 port extension adjusts the measured phase of s11 based on the e-delay value converted to an equivalent phase at the measurement frequency.

It is:

1. an exact correction for any length of lossless line of Z0=50+j0Ω transmission line;
2. an approximate correction for a very low loss length of approximately 50Ω transmission line; and
3. an approximate correction for some specific scenarios such as those discussed at Some useful equivalences of very short very mismatched transmission lines – a practical demonstration.

Of course 1. does not exist in the real world, but 2. can give measurement results of acceptable accuracy if used within bounds. Both departures mentioned in 2. occur in the real world, non-zero loss and departure from Z0=50+j0Ω. Provided these departures are small, port extension may give acceptable results.

Let’s analyse some example measurements based on a 10m length of ordinary RG58A/U from 1-11MHz.

Above, measurement of the first series resonance with SC termination.

Note that the curve is a spiral inwards from the outer circle, the line is not lossless.

A requirement for e-delay to work well is that phase of s11 is proportional to frequency. This plot wraps, but apart from that, the plot looks approximately linear… however scale prevents detailed analysis.

Above, measurement of the first series resonance with OC termination.

Note that the curve is a spiral inwards from the outer circle, the line is not lossless.

Again the plot wraps, but apart from that, the plot looks approximately linear… however scale prevents detailed analysis.

Let’s find a value for e-delay at 1MHz and analyse the result.

Above is adjustment of e-delay to 115ns for approximately s11 phase 180° at 1MHz with SC termination.

The phase is correct at 1MHz, but at higher frequencies, it departs. So, the assumption that this TL has phase delay proportional to frequency is invalid. If you look closely, it is not a perfectly straight line, there is a small oscillation superimposed which is a sign of Z0 error. For these reasons, e-delay correction will have error.

Above is adjustment of e-delay to 100ns for approximately s11 phase 180° at 1MHz with OC termination.

The phase is correct at 1MHz, but at higher frequencies, it departs. So, the assumption that this TL has phase delay proportional to frequency is invalid. If you look closely, it is not a perfectly straight line, there is quite an oscillation superimposed which is a sign of Z0 error. For these reasons, e-delay correction will have error.

Let’s proceed anyway and look at the error. We will connect the 50+j0Ω termination load to the end of the cable and measure with each of the e-delays above.

Above is measurement of a 50+j0Ω termination with e-delay calibrated using 100ns e-delay (calibrated to OC termination). Note that the curve is a small circle, a sign of Z0 error and a hint that actual Z0 is about the centre of the circle plotted. Note though that Z0 is frequency dependent at these frequencies for this cable, so you can’t pin a pin on the chart and say this is Z0.

Above is measurement of a 50+j0Ω termination with e-delay calibrated using 115ns e-delay (calibrated to SC termination). Note that the curve is a small circle, a sign of Z0 error and a hint that actual Z0 is about the centre of the circle plotted. Note though that Z0 is frequency dependent at these frequencies for this cable, so you can’t pin a pin on the chart and say this is Z0.

At 5.75MHz and:

• e-delay from the SC calibration, Z=45.01+1.25Ω; whereas
• e-delay from the OC calibration, Z=45.01-1.26Ω.

For some purposes, that might be sufficient accuracy, for others it might be unacceptable:

• Z0 departure is more significant for lossier cables below about 10MHz; and
• in any event loss of tenths of a dB leads to measurable error.

Conclusions

Port extension or e-delay can provide a convenient means of shifting the reference plane given suitable test fixtures, but it is subject to significant error if the underlying assumption of lossless 50Ω line is breached.

Since the widespread takeup of the NanoVNA, a measure of performance proposed by (Skelton 2010) has become very popular.

His measure, Common Mode Rejection Ratio (CMRR), is an adaptation of a measure used in other fields, he states that he thinks the application of it in the context of antenna systems and baluns is novel and that “CMRR should be the key figure of merit”.

Skelton talks of different ways to measure CMRR, but essentially CMRR is a measure of the magnitude of gain (|s21|) from Port 1 to Port 2 in common mode, with the common mode choke (or balun) in series from the inner pin of Port 1 to the inner pin of Port 2.

Note that this is the same connection as used for series through impedance measurement, but calculation of impedance depends on the complex value s21.

Above is capture of a measurement of a Guanella 1:1 common mode choke or balun. The red curve is |s21|, the blue and green curves are R and X components of the choke impedance Zcm calculated from s21.

Matched vs mismatched DUT

Case 1: impedance matched DUT

In this type of test, the DUT between Port 1 and Port 2 is a good match to both Port 1 and Port 2.

Lots of readers will understand that if they connected a long piece of 50Ω coax between Port 1 and Port 2, and measured |s21|=-6dB, that it is reasonable to say that the cable appears to have an attenuation or loss of 6dB for that length. Further, that the current into Port 2 is exactly half of that out of Port 1… the current has been “attenuated”.

If the DUT is deployed in another matched scenario, you would expect to observe similar behavior, including attenuation.

Case 2: impedance mismatched DUT

In this type of test, the DUT between Port 1 and Port 2 is not a good match to both Port 1 and Port 2.

For example, the matched DUT case does not apply if you made an electrically short connection between ports using a series resistor, the current from Port 1 to Port 2 is approximately uniform. If the DUT is a electrically short inductor, capacitor resistor, or combination with only two terminals, one connected to Port 1 inner and the other connected to Port 2 inner, the same thing applies, the current into Port 2 is approximately equal to the current out of Port 1, the current has NOT been “attenuated”.

If the DUT is deployed in another undefined mismatched scenario, you should not expect to predict behavior based on the simple |s21| measurement.

Interpretation of the |s21| plot above

The widespread interpretation of |s21| for the balun test described above is that it is a plot of the common mode current attenuation property of the balun.

That is deeply flawed, very popular, but deeply flawed. The measurement is of the type discussed under Case 2 above, and the two terminal DUT does not possess some intrinsic attenuation property independent of its measurement context.

Interpretation of the plotted series through R,X derived from the complex s21 measurement, so-called series through s21 impedance measurement

It is popularly held that it is valid to measure common mode impedance (Zcm) by this technique, superior even by many authors… but let’s stay with valid for the moment.

The calculation of series through impedance from s21 depends on an assumption that the current into Port 2 is exactly equal to that out of Port 1, there must NOT be any reduction or attenuation of current in the test setup, otherwise the results are invalid.

Properly executed, this IS a valid technique for measuring Zcm… and one of the necessary conditions is that there is no reduction in current from Port 1 to Port 2.

So, you cannot accept the common technique for series through s21 impedance measurement and at the same time entertain the concept of a matched attenuator DUT.

Bringing it all together

Let’s explore the system response using three terminal measurement of the antenna system impedance and the balun measured above.

Working a common mode scenario – VK2OMD – voltage balun solution reports a three terminal impedance measurement of an antenna system at 3.6MHz.

This following presents calculation of some interesting balun / drive scenarios based on those measurements and Zcm of the balun reported above, and repeated here for convenience.

Above, an identical balun was measured to find |s21| of the balun in common mode. Also shown is the s21 series through measurement of Zcm.

The oft touted CMRR is + or – |s21|, depending on the author and their self defining measurement. Let’s take Skelton’s definition and call CMRR for this balun 29.4dB.

Let’s list the key configuration parameters:

• frequency=3.6MHz;
• drive voltages V1 and V2 are not perfectly balanced as detailed in the table below;
• other key parameters are listed in the table.

Above is a table showing for each configuration, the magnitude of the total common mode current |2Ic|, |2Ic| relative to the No balun baseline configuration, differential current |Id|, and |2Ic/Id| as a percentage.

Note that these currents are potentially standing waves, and they are measured at the antenna entrance panel, about 11 m of two wire feed line from the dipole feed point.

You might ask in respect of the total common mode current:

1. is the no balun result surprising?
2. is the current balun performance surprising?
3. is the voltage balun performance surprising?
4. does the measured CMRR of 29.2dB imply the reduction in common mode current due to the current balun of 24.3dB?
5. what does the measured CMRR infer?
6. can the CMRR be used in an NEC model of the system scenario?
7. can Zcm be used in an NEC model of the system scenario?

References

• Agilent. Feb 2009. Impedance Measurement 5989-9887EN.
• Agilent. Jul 2001. Advanced impedance measurement capability of the RF I-V method compared to the network analysis method 5988-0728EN.
• Anaren. May 2005. Measurement Techniques for Baluns.
• Skelton, R. Nov 2010. Measuring HF balun performance in QEX Nov 2010.

This article presents a simple practical test of the concepts laid out at Some useful equivalences of very short very mismatched transmission lines.

Above is the DUT, it is a short circuit at the end of 102mm of two wire transmission line with VF=1, conductor diameter 0.47mm and 5mm spacing.

The transmission line is not perfectly uniform, but sufficiently good for this demonstration.

We are going to use port extension or e-delay to adjust the reference place to the short circuited end of the transmission line.

Let’s calculate Z0 and propagation time and phase length at 10MHz of the nominal transmission line. It is chosen for this example because it has a VF very close to 1, and is easily physically measured and parameters calculated.

RF Two Wire Transmission Line Loss Calculator

So, Z0=369Ω, and its propagation time is 340ps one way, two way is 680ps, βl=0.021ᶜ.

Using the theory set out in Some useful equivalences of very short very mismatched transmission lines, we can calculate the e-delay that should refer the reference plane from Port 1 connector to the end of the transmission line section.

\(\frac{\beta l Z_0}{50}=0.155\), so this is just above the limit of 0.1 radians for best accuracy, but the results should still be good enough visually.

\(edelay_{50}=edelay_{Z_0} \frac{Z_0}{50}=680 \frac{370}{50} \text{ ps}=5.03 \text{ ns}\\\)

Let’s estimate Z0 from the impedance of the short circuit stub.

\(Z_0=\frac{X}{\tan (\frac{2 \pi l f}{C_0})}=\frac{8.0}{\tan (\frac{2 \pi \cdot 0.102 \cdot 1e7}{299792458})}=374\), that measurement based value reconciles well with the calculation above.

Let’s plot the phase of s11 SOL calibrated at the Port 1 connector.

Above, phase looks fairly linear, but in fact it departs a little from linearity above about 6MHz, more so as frequency increases.

Above is application of e-delay adjusted to obtain an almost flat phase response to 10MHz. Never mind the phase wrap, but note there is a very slight upward slope in the upper part of the trace (obvious when the marker is swept over the area).

Above is the sweep from 1-11 MHz with e-delay adjusted to 5.05ns. The trace looks very flat, sliding the marker around shows it to be pretty good. This reconciles well with the calculated e-delay of 5.03ns.

Conclusions

Port extension within the limits discussed at at Some useful equivalences of very short very mismatched transmission lines. can provide an accurate, convenient and useful technique for referral of the reference plane without doing a full SOL calibration at that point.

NanoVNA-H4 radio remote trial #1 – HC-05 Bluetooth described intial tests on a Bluetooth remote connection to a NanoVNA-H4 using an inexpensive HC-05 adapter by hc01.com.

UART connector

For more convenient access to the UART pins, I installed a SIL 6w female header and cut a 3x18mm opening in the back for access.

I have seen reports that the Bluetooth module can be fitted inside the case. At this stage I am reluctant to do that for several reasons, EMC being one, and a convenient means of turning the power off to the Bluetooth module is another (it might be useful if one of the IO pins signaled that the UART interface was selected).

NanoVNA firmware changes

Dislord made changes to add compression of the screenshot data transfer using a run length encoded (RLE) compression scheme (the capture rle command). This reduced the size of the data transfer from 300kB to around 50kB depending on screen content, and made transfers over a 38400pbs link practical.

Data channel error analysis

The data channel is the path from the NanoVNA to the receiving application software.

NanoVNA UART

The NanoVNA’s UART port is a simple three wire serial port (GND, Tx, Rx) with ASYNC encoding. There is no hardware flow control, no error detection.

The prototype used a short unshielded connecting cable for GND, Tx, Rx, and Vcc.

If the connecting cable is short, there should be only a very small risk of bit errors. That may be worse if the system is subject to high intensity electromagnetic fields.

Simple bit errors that do not result in loss of an entire byte will corrupt the data, and those corruptions to some bytes of the encoded data may be detected as invalid values. Some bit errors will go undetected and be carried through as corruptions of the decoded image. This is no means provided in the data to detect the latter condition.

Bluetooth link

The Bluetooth link segment provides a reliable link at potentially very high air speed. I say potentially as it is a radio path subject to interference and loss of signal strength due to obstructions and excessive path length.

There should not be data corruptions over the Bluetooth link itself, but overrun of the input buffer is an issue.

Whilst the HC-05 appears to contain a sizeable input buffer, it is not sufficient to hold the entire screenshot transfer and so there is a risk of buffer overrun if the Bluetooth channel throughput slows. Buffer overruns would result in loss of complete bytes, one to many.

Loss of complete bytes will very likely result in failure to decode the RLE structure.

Receiving application

Because the end to end link is not a ‘reliable link’, the way in which the receiving application handles apparently lost or corrupted data is important, and there is no ‘standard’ way to do that.

Conclusions

The HC-05 Bluetooth solution is usable. Screenshots are practical with later firmware that supports compressed image files.

At the limits of radio coverage, communications timeouts will make the link unusable.

An online expert recently promoted this way of using a NanoVNA on 600Ω lines: Normalizing the NanoVNA for any characteristic impedance.

Essentially, he calls for SOL calibrating the VNA with the L or LOAD being a 600Ω resistor.

This does have the effect of ‘correcting’ all s11 measurements to be wrt Zref=600Ω, but most of the calculations of derived values like R, X, etc are wrong.

Above is an example where the NanoVNA-H4 was calibrated with LOAD=470Ω, and then that resistor measured. Note the |s11| is very small, it is correct. The Smith chart locus is a dot in the middle of the chart, it is correct… but the Smith chart marker legend shows Z=49.96-j0.0206Ω which is a gross error, it should be very close to 470Ω.

The instrument assumes that s11 measurements are wrt 50Ω, and this “trick” does not consistently transform the measurements to the desired reference impedance.

So, in summary, while this does centre the Smitch chart on the impedance used for the LOAD, and some other displayed data is correct, some displayed data is grossly wrong, and many available displays are grossly wrong.

There is a better way…

There are many variants of NanoVNA-H4 firmware, and each in many versions. Some may incorporate the “PORT-Z” transformation shown below, some may not.

Above is a NanoVNA-H4 using Dislord’s NanoVNA-D reporting v1.2.37. This version was downloaded as beta firmware and might not be generally available. Competetive variants might have the same feature.

The VNA was SOL calibrated with a LOAD=50Ω, and the PORT-Z set to 470 to change the reference Z for calculation of related displays.

Note the chart is centred on 470Ω (the DUT resistor), the marker legend shows 467-j5.057Ω.

So if you want to present the measurements wrt some impedance other than 50Ω, this is the better way to do it.

A similar feature exists in lots of one port antenna analysers, some allowing selection from a small set of alternative references.

One sees a lot of discussion on social media of 12VDC power supplies for ham radio equipment. Some of the recommendations are unsafe.  Bear in mind that the user could well be a young person with little knowledge and experience and unsafe equipment may put not just themselves at risk of electrocution, but other members of the family / household, people who might try to rescue them.

Firstly, before someone rushes to correct me on the matter of 230V:

The nominal mains input supply voltage in Australia in accordance with AS 60038 is now:

• 230 volts AC Single phase with a tolerance range of + 10% to – 6%
• 400 volts AC Three phase with a tolerance range of + 10% to – 6%

NSW has laws / regulations requiring approval of some electrical articles to protect end users and others. A quote from Explanatory Notes -For the approval and sale of electrical articles in New South  Wales July 2024:

2.1 Definition of ‘Sell’
“Sell” includes auction or exchange; offer, agree or attempt to sell; advertise, expose, send, forward or deliver for sale; cause or permit to be sold or offered for sale; hire or cause to be hired; and display for sale or hire. The laws apply to any person who sells an electrical article and includes the manufacturer or importer and any on-seller. The compliance requirements of electrical articles at the time of sale reflects the current applicable product standard as revised or amended. It’s important that traders effectively manage their
compliance obligations by ensuring that inventory is controlled and that the valid approval status and compliance of this stock is maintained. A person’s obligation under Section 8 of the Act is at the
time the article is sold (for example to a retailer). Once sold it is the obligation of the current holder of the stock for any further sales.
2.2 Declared articles
In order to sell declared articles in New South Wales, the articles must:
1. Be approved as compliant to use prior to sale, evidenced by a NSW Fair Trading Certificate of Approval (or by an accredited Recognised External Approval Scheme.)
2. The approval process must demonstrate that the electrical article meets all relevant Australian Standards and any further requirements that may apply. This process includes the testing of these articles by accredited laboratories.
3. Be marked with the NSW approval mark or an approved alternate mark (see 3.3.)
4. Definitions of declared articles and their associated safety standard/s are attached

Battery chargers and Extra Low Voltage supplies are declared articles.

States each make these regulations, this is NSW but similar regulations apply in other states.

Note that you do not have to be a commercial seller to be in scope of these regulations, read the definition of “sell” carefully.

Some equipment recommended by online experts is actually a power supply component intended to be incorporated into some larger piece of equipment, and enclosed in a way that prevents accidental contact with live conductors / terminals / parts, and they would never obtain the approval necessary to be sold as an ELV power supply article.

Online market places offer a wide range of battery chargers and ELV power supplies, many of which may not have the required approvals. Similarly Chinese online market places are likely to offer equipment that does not have the required approval.

There are retail sellers of approved ELV power supplies suited to ham radio equipment.

This article repeats some earlier tests on two competitive ESC firmwares for sensorless brushless DC motors.

The motor chosen for the tests, a 4822-690KV, is of a type that is very popular; a flat radial flux outrunner with high pole count. These are marketed as more suitable to multi-rotors that the barrel shaped motors developed for planes, but the claims are questionable, these motors are often at higher risk of sync loss due than the barrel shaped motors and used feature regularly in forum postings of de-sync problems.

The article Demagnetisation in a sensorless brushless DC drive givese a broad overview of demagnetisation in a sensorless brushless DC drives that depend on Zero Crossing (ZC) detection to synchronise the next commutation phase.

A Demagnetisation Risk Index for a sensorless brushless DC drive gives a quantitative measure that can be used to indicate high risk drives. In my own testing experience, motors unlikely to exhibit sync loss have DRI well less than 5, and those well over 5 are problem motors. High pole count increases DRI, and this is a 22 pole motor, high when compared to 11 pole barrel shaped motors.

DRI on 4S is 5.1, on 3S is 3.8.

On 3S sync loss could be excited with a hand servo tester using BLHeli, it was not observed with SimonK. Previous testing has shown this motor very prone to sync loss on 4S with either ESC and I dismiss it as impractical.

Above is a logged test run of SimonK (~2017) on 3s using script driven by asrg.

Above is a logged test run of BLHeli-16.7.14.9.0.3 (the latest) with default settings on 3s using script driven by asrg.

Importantly they both use default settings including Complementary PWM (though BLHeli calls it something else).

Superficially, they might look nearly identical, but there are some key differences:

• they are both stable, there is no significant sign of desync;
• BLHeli uses more current at all throttle settings (so reduced battery endurance); and
• BLHeli is less responsive to throttle, it is slower to accelerate, and even slower to decelerate (possibly a measure to avoid de-sync).

Lots of claims have been made of the superiority of the 48MHz Silabs based ESC used for the BLHeli test over the 16MHz AVR MCU used for the SimonK test… but it does not result in superior performance, rather the BLHeli ESC isn’t quite as good.

Overall, I would be happy with BLHeli, though it is slightly poorer than the old SimonK (tgy) firmware. BLHeli was taken up by the community, even when it had significant de-sync problems, and I can only guess that users liked the GUI and drives system performance was a lesser priority.

I have not tried the newer closed source BLHeli_32, and doubt that I will. The BLHeli pitch that a more powerful 32bit MCU will result in better performance is questioned by the above comparison of 8bit MCUs… and if it is the GUI one desires, it is already there in BLHeli_S.

I have an MFJ-264N which does not perform very well.

A measurement of the impedance at the inboard side of the N connector jack would be informative.

So, a NanoVNA-H4  (SOL calibrated at the Port 1 connector) with short SMA(M) to SMA(M) and SMA(F) to N(M) adapter are available, but how to set the reference plane to the inboard end of the N(F) connector?

Port extension, or e-delay is a means of correcting a lossless (ie short) ‘adapter’ where propagation time is independent of frequency, ie phase delay is proportional to frequency.

Above is a view of the inboard side of N(F) connector. If we can apply an effective short circuit centre pin to ground at that point, we can adjust e-delay to calibrate the ‘fixture’.

Above shows a small piece of kitchen foil scrunched up into a ball and pressed into the space to short the inner conductor to the connector body. The piece is held in place with moderate finger pressure whilst calibrating the e-delay value.

Above is the display after tweaking e-delay for approximately flat s11 phase over the frequency range (save the wrap from 180° to -180°), a necessary condition for validity of the technique.

The VNA is configured with VF=1, so the displayed distance is the two way free space electrical length which reconciles with the approximately 200mm cable length.

Having calibrated e-delay, we can now measure Z looking into the dummy load from the inboard end of the N(F) connector. There are two significant problems:

• R at low frequencies is close to 60Ω when ideally it would be 50Ω; and
• X rises linearly to 4.7Ω at 100MHz, suggesting there is about 7nH of series inductance when ideally X should be zero.

The main problem is the resistance of the carbon resistor. They tend to age high in value, and operation at high temperature accelerates aging. Given that these are rated at 1500W for intermittent operation and the derating curve suggests they are probably not good for more than about 50W continuously, users should keep in mind that every cycle to extreme temperature accelerates aging of the resistor and upwards creep in resistance.

This one has not been abused, abuse will exacerbate the problem.

Conclusions

Port extension or e-delay can provide a convenient means of shifting the reference plane given suitable test fixtures.