It explains in great detail how the antenna tuner at the input terminals of the feed line provides a conjugate match at the antenna terminals, and tunes a non-resonant antenna to resonance while also providing an impedance match for the output of the transceiver.

Walt Maxwell made much of conjugate matching, and wrote often of it as though at some optimal adjustment of an ATU there was a system wide state of conjugate match conferred, that at each and every point in an antenna system the impedance looking towards the source was the conjugate of the impedance looking towards the load.

This was recently cited in a discussion about techniques to measure high impedances with a VNA:

WHEN the L and C’s of the tuner are set to produce a high performance return loss as measured by the vna, then in essence, if the tuner were terminated (where the vna was positioned) with 50 ohms and we were to look into the TUNER where the antenna was connected, we would see the ANTENNA Z CONJUGATE. Wow, that’s a mouth full. The best was to see this is to do an example problem and a simulator like LT Spice is a nice tool to learn. Or there are other SMITH GRAPHIC programs that are quite helpful to assist in this process. Standby and I will see what I can assemble.

The example subsequently described set about demonstrating the effect. The example characterised a certain antenna as having an equivalent circuit of 500Ω resistance in series with 4.19µH of inductance and 120pF of capacitance (@ 7.1MHz, Z=500-j0.119, not quite resonant, but very close). A lossless L network (where do you get them?) was then found that gave a near perfect match to 50+j0Ω. The proposition is that if you now look into the L network from the load end, that you see the complex conjugate of the antenna, Z=500+j0.119.

I asked where do you get a lossless L network? Only in the imagination, they are not a thing of the real world.

So lets replicate the scenario matched with an L network where the inductor has a Q of 100, no other loss elements. (Quality real capacitor losses are very small, and the behavior will not change much, the inductor loss dominates.)

Above is a model in Simsmith where I have adjusted the lossy L network for a near perfect match. I have used a facility in Simsmith to calculate the impedance looking back from L1,the calculated L1_revZ on the form, (ie back into the L network) from the equivalent load.

The impedance looking back is 471.3-j0.1274Ω. The resistance element is quite different to the proposed 500Ω. The L network in this scenario lacks reciprocity.

Although the L network is conjugate matched at its input, it is not conjugate matched at its output.

This example is yet another that disproves Walt Maxwell’s simultaneous system wide conjugate matching nonsense.

None of this should be taken to suggest that when an ATU or other matching network is adjusted for an input VSWR(50) that it is conjugate matched to the source, much less that a typical ham transmitter is well represented by a Thevenin equivalent circuit or that the Jacobi Maximum Power Transfer Theorem applies.

- Duffy, O. Mar 2013. The failure of lossless line analysis in the real world. VK1OD.net (offline).
- Everitt, W L. 1937 Communications Engineering, 2nd ed. New York: McGraw-Hill Book Co.
- Everitt, W L, and Anner, G E. 1956 Communications Engineering, 3rd ed. New York: McGraw-Hill Book Co.
- Maxwell, Walter M. 2001. Reflections II. Sacramento: Worldradio books.

The AD8310 module was bought on eBay for about $10.

The module as supplied had a 100Ω resistor in shunt with the input, it needs to be 52.3Ω 1% 0805 resistor for a good match and was replaced with such.

I want to run this from a 3.7-5V supply so the on board 5V regulator was replaced with a NJM78L03UA 3V regulator (which has the SOT88 package with the same pinout as the original). The regulator chip is a little skewed as a result of poor solder mask layout and solder surface tension… but it will work fine.

Above is a sweep with a (modified) nanovna-H to 100MHz (this is for a HF current probe). Input VSWR would be more like 2 as supplied with the 100Ω input resistor… Chinese Quality.

]]>The update corrects an error in conversion between ENR and temperature where Tcold<>290K.

- Duffy, O. 2007. Noise Figure Meter software (NFM). https://owenduffy.net/software/nfm/index.htm (accessed 01/04/2014).

Some of the data is derived from manufacturer’s published complex permeability curves. The plot above shows the Ferroxcube’s published curve for 3C81 material, and points at which it was digitised to extract a table of µ’ and µ”.

The calculator result is a cubic spline interpolation of the tabulated data.

Some data is derived from manufacturer’s published complex permeability tables, most or all of the Fair-rite data is sourced in this way.

Above is a plot of Fair-rite’s published complex permeability table for #77 mix. Note that µ’ has negative values from 7-1140MHz which raises concern for the quality of the data, it may be the result of blind extrapolation.

Whilst I prefer to use data traceable to the manufacturer, I favor a solution that discards data that is on the face of it suspect.

So, in processing these tables data is discarded where µ'<0.95 or µ”<0. Only interpolation is done (ie no extrapolation). Note that this would include some data from the plot above that is probably extrapolated by Fair-rite, but not obviously wrong. It would be better if they published just what they measured. This change took effect on 07/09/2019.

The calculator result is a cubic spline interpolation of the tabulated data.

The calculator includes data for some cores for which published data could not be found. They are mostly characterised by my own measurement.

In fact, I did explore #73 as an option, this article presents some key comparisons. The two key statistics shown in this article provided the basis for selecting the design.

Note that the scales are different from plot to plot.

Where the magnetising impedance appears in shunt with an ideal transformer with Zin=50+j0Ω, Insertion VSWR can be calculated.

Where the magnetising impedance is a shunt component of total Zin=50+j0Ω, Core loss VSWR can be calculated.

Predictions of Insertion VSWR and core loss of the popular BN73-202 transformer with 2t primary for MF and my BN43-202 with 5t primary reveals that the BN43-202+5t is a better transformer for my intended application.

There is no need to follow the traditional design which anecdotally works, but is published without performance predictions or measurements… well that IS traditional.

]]>

Lets work through an example of a FT50-61 core with 10t primary at 3.5MHz.

Magnetic saturation is one limit on power handling capacity of such a transformer, and likely the most significant one for very low loss cores (#61 material losses are very low at 3.5MHz).

Let’s calculate the expected magnetising impedance @ 3.5MHz.

Above is the manufacturers B/H curve for #61 material. Lets take the saturation magnetising force conservatively as 2Oe=2*1000/(4*pi)=159A/m (or At/m for a multi turn coil).

The ID of a FT50 core is 7.15mm, so magnetic path length l=0.00715*pi=0.0225m.

So, we take saturation current as Is=Hs*l/t=159*0.0225/10=0.358A.

Saturation voltage magnitude at 3.5MHz=Is*|Zm|=0.358*144=51.6Vpk. This corresponds to about 25W in a 50Ω system.

Increasing the number of turns decreases Is for a given Hs, and increases Zm which reduces I for a given applied voltage. For example in this example, a 12t primary has |Z|=207, Is=0.298A, Vs=61.7Vpk which corresponds to a 43% 50Ω power increase.

Lets work through an example of a 2643625002 core with 3t primary at 3.6MHz (Small efficient matching transformer for an EFHW).

Magnetic saturation is one limit on power handling capacity of such a transformer. For lossier materials, heat dissipation is likely to be the practical limit in all but low duty cycle applications, but lets calculate the saturation limit.

Let’s calculate the expected magnetising impedance @ 3.6MHz.

Zm=94.1+j197Ω, |Zm|=218Ω.

Above is the manufacturers B/H curve for #43 material. Lets take the saturation magnetising force conservatively as 1Oe=1*1000/(4*pi)=79.6A/m (or At/m for a multi turn coil).

The ID of a 2643625002 core is 7.29mm, so magnetic path length l=0.00729*pi=0.0229m.

So, we take saturation current as Is=Hs*l/t=79.6*0.0229/3=0.607A.

Saturation voltage magnitude at 3.5MHz=Is*|Zm|=0.607*218=132Vpk. This corresponds to about 175W in a 50Ω system. This transformer would not withstand such high power continuously, but pulses or bursts to that level would remain in the substantially linear range of the material characteristic.

- Magnetic saturation is one limit on power handling capacity of ferrite inductors and transformers.
- For very loss cores, magnetic saturation is likely to be the significant limit on power handling.

Read widely, and analyse critically what you read.

]]>In a process of designing a transformer, we often start with an approximate low frequency equivalent circuit. “Low frequency” is a relative term, it means at frequencies where each winding current phase is uniform, and the effects of distributed capacitance are insignificant.

Above is a commonly used low frequency equivalent of a transformer. Z1 and Z2 represent leakage impedances (ie the effect of magnetic flux leakage) and winding conductor loss. Zm is the magnetising impedance and represents the self inductance of the primary winding and core losses (hysteresis and eddy current losses).

For 50/60Hz power transformers, Z1 and Z2 are mainly inductive and small (eg as would account for around 5% voltage sag under full load). Zm varies, it is large and mainly inductive for conservative designs using sufficient and good core material, and less so for designs that drive core magnetic flux into saturation.

For broadband RF transformers, Z1 and Z2 need to be small as they tend to be quite inductive and since inductive reactance is proportional to frequency, they tend to spoil broadband performance.

Zm shunts the input, so it spoils nominal impedance transformation (Zin=Zload/n^2) if it is relatively low. For powdered iron cores Zm is mainly inductive; and for ferrite cores Zm is a combination of inductive reactance and resistance depending on frequency and ferrite type.

Keep in mind that if Zm is sufficiently high, Im is low, and even though Zm may contain a large Rm component, Im^2*Rm may be acceptably low.

There are scores of articles on this website about ferrites, many of which show how to measure or calculate Zm from datasheets.

Proponents of powdered iron will claim that large Im does not create much loss because Rm is small, but large Im destroys broadband nominal impedance transformation (ie Insertion VSWR). Powdered iron tends to be low µ which increases leakage impedance and also destroys broadband nominal impedance transformation.

An online expert on the unsuitability of #43 for HF UNUNs discussed the stuff that masquerades as science in the name of ham radio, and gives one example which questions the exptert’s opinion. Lets work through some examples, calculating and plotting two key metrics that should be considered right up front when designing an efficient broadband RF transformer with close to ideal impedance transformation (ie low InsertionVSWR).

The following analyses are of expected core loss due to the magnetising impedance of the primary winding when the transformer is loaded to present an input impedance of 50+j0Ω. The magnetising impedance can be measured with only that primary winding on the core, the presence of a secondary winding, even if disconnected, may disturb the results.

Note that there is a quite wide tolerance on ferrite materials, and measured results my differ from the predictions based on published datasheets. Designs based on measurements of a single core are exposed to risks of being atypical.

Graph Y axes are not identically scaled.

This configuration is very popular in ham radio. I am not sure who originated the design, PA3HHO’s web article is a commonly cited reference.

Above is the percentage core loss when input impedance of the loaded transformer is 50+j0Ω.

Above is the Insertion VSWR caused by the magnetising impedance in shunt with 50+j0Ω. Note that this is not exactly the same configuration as for the previous chart.

Above is the percentage core loss when input impedance of the loaded transformer is 50+j0Ω.

Above is the Insertion VSWR caused by the magnetising impedance in shunt with 50+j0Ω. Note that this is not exactly the same configuration as for the previous chart.

This is a small #43 core as used in Small efficient matching transformer for an EFHW.

Above is the percentage core loss when input impedance of the loaded transformer is 50+j0Ω.

Above is the Insertion VSWR caused by the magnetising impedance in shunt with 50+j0Ω. Note that this is not exactly the same configuration as for the previous chart.

The Jaycar LO1238 is readily available in Australia, a medium size core of medium to high initial permeability (µi=1500) that seems overlooked by Australian hams in favor of harder to procure products.

Above is the percentage core loss when input impedance of the loaded transformer is 50+j0Ω.

It seems many hams have a “favorite mix”, and many spurn #43, nominating others (#31, #61 often for this application).

All are possibilities that for a given core geometry and mix will require a certain minimum number of turns on the nominal 50Ω primary to meet the designer’s loss and Insertion VSWR criteria. #61 is a lower loss material compared to #43, and it will require more turns to meet Insertion VSWR criteria at low frequencies, the length of the winding may limit the useful upper frequency.

- The context of the article is HF broadband transformers with close to ideal nominal impedance transformation, and does not necessarily apply to other contexts.
- Three of the examples use #43 material, two of those designs have core loss less than 10% at 3.5MHz and lower on higher bands demonstrating that it is possible to design a broadband RF transformer for HF using #43 material.
- The PA3HHO example shows that insufficient turns leads to appalling core loss.
- Traditional wisdom is that higher µ cores will be even worse than #43, but the LO1238 design shows that a low cost core readily available in Australia is a worthy candidate for Australian hams.
- There is more to designing a transformer than presented here, this article describes a first analysis to screen likely candidates and find minimum primary turns for a given core to meet the design loss and InsertionVSWR criteria.
- Successful designs are almost always a compromise to meet sometimes competing / conflicting design criteria.

Read widely, and analyse critically what you read.

]]>…The spec for type 43 makes it clear that it should never be used for HF unun construction. It is specifically engineered with a complex permeability that makes the core lossy on most HF frequencies. Since an unun is not a TLT (transmission line transformer) but rather an autotransformer, a low loss core is essential for efficient operation….

Now it contains the very common FUD (fear, uncertainty and doubt) that masquerades as science in ham radio, but without being specific enough to prove it categorically wrong. To a certain extent, the discussion goes to the meaning of efficient operation

.

At Small efficient matching transformer for an EFHW I described an ‘unun’ using #43 material, and gave design calcs and measured loss over HF.

I will concede that making loss measurements by that technique becomes less accurate at the high end of HF where the distributed inductance and capacitance of the combined load become significant… but good figures can be obtained below say 10MHz. In most cases, the core losses are greatest at the lowest operating frequencies, so that works well.

Back to the transformer, designs are typically a compromise of a lot of factors such as size, mass, loss, bandwidth etc. In the example case, it is a transformer intended for low power portable operation (eg SOTA) and efficiency is traded for size and mass to name a couple.

Nevertheless, the core efficiency is 90% at the lowest design frequency, 3.6MHz, and is higher at higher frequencies.

This example questions the impression that the online expert tries to leave in readers minds that #43… should never be used for HF unun construction

.

Read widely, and analyse critically what you read.

]]>Some of us use a resistor as a load for testing a transmitter or other RF source. In this application they are often rated for quite high power and commonly called a dummy load. In that role, they usually do not need to be of highly accurate impedance, and commercial dummy loads will often be specified to have maximum VSWR in the range 1.1 to 1.5 (Return Loss (RL) from 26 to 14dB) over a specified frequency range.

We also use a known value resistor for measurement purposes, and often relatively low power rating but higher impedance accuracy. They are commonly caused terminations, and will often be specified to have maximum VSWR in the range 1.01 to 1.1 (RL from 46 to 26dB) over a specified frequency range.

It is more logical to discuss this subject in terms of Return Loss rather than VSWR.

Return Loss is defined as the ratio of incident to reflected power at a reference plane of a network. It is expressed in dB as 20*log(Vfwd/Vref).

Calibration of directional couplers often uses a termination of known value, and the accuracy of the termination naturally rolls into the accuracy of the calibration and the measurement results.

A simple example is that of a Return Loss Bridge (RLB) where a known reference termination is compared to an open circuit and then an unknown load to find the Return Loss (being the difference between them).

Let use look at three examples of RF load resistors at hand and consider their performance as a calibration reference. The discussion uses datasheet VSWR or RL figures which are the best one can rely upon unless high accuracy measurements of made of the device.

The MFJ-264N is a high power ‘dummy load’ with max VSWR specified as 1.3 to 650MHz, which is equivalent to RL>17.6dB. In a very good RLB, the directivity will approach the reference termination’s RL, so we can regard the RLB directivity in this case to be 18dB in round numbers.

We can calculate the uncertainty in measuring a given VSWR given the minimum directivity of the RLB.

Let’s say we wanted to measure VSWR down to 1.5, and we wish to know the uncertainty (error bounds).

Above is a calculation of the scenario. It can be seen that with a true VSWR=1.5 load, the RLB may indicate anywhere between VSWR 1.16 and 1.97.

The Bird 6150 is a high power ‘dummy load’ with max VSWR specified as 1.1 from 30 to 500MHz, which is equivalent to RL>26.4dB. In a very good RLB, the directivity will approach the reference termination’s RL, so we can regard the RLB directivity in this case to be 26dB in round numbers.

We can calculate the uncertainty in measuring a given VSWR given the minimum directivity of the RLB.

Let’s say we wanted to measure VSWR down to 1.5, and we wish to know the uncertainty (error bounds).

Above is a calculation of the scenario. It can be seen that with a true VSWR=1.5 load, the RLB may indicate anywhere between VSWR 1.35 and 1.67.

Definitely better than the MFJ-264N.

The KARN-50-18+ is a low power ‘termination’ with RL specified on the chart above. In a very good RLB, the directivity will approach the reference termination’s RL, so we can regard the RLB directivity in this case to be >46dB in round numbers up to 1000MHz.

We can calculate the uncertainty in measuring a given VSWR given the minimum directivity of the RLB.

Let’s say we wanted to measure VSWR down to 1.5, and we wish to know the uncertainty (error bounds).

Above is a calculation of the scenario. It can be seen that with a true VSWR=1.5 load, the RLB may indicate anywhere between VSWR 1.48 and 1.52.

Much better than either of the previous examples, but it is only rated for 2W so it unsuitable as a load for a high power device.

High power RF resistors tend to have poor RL, yet a high RL high power resistor is needed for checking or calibrating high power directional wattmeters.

A possible solution is to use a good RLB with good reference termination to ‘calibrate’ a high power load via an ATU, and use the latter for high power measurements. This typically is a single frequency technique, and there is unavoidable uncertainty introduce in this calibration process.

Another technique is to use an ATU + high power load on the directional coupler, adjusting the ATU for null reflection indication. Then move the cable from the directional coupler to a VNA or analyser and measure the impedance seen by the DUT. Again, being an indirect method, uncertainty flows from cascading measurements.

Resistor loads of lower RL lead to high uncertainty of measurements using them as a reference (directly or indirectly).

The uncertainty is worse as measured RL of the unknown approaches the RL of the reference used.

Depending on the accuracy needed of measurements, RL of the reference typically needs to be 10dB or more better than the intended measurement.

Watch the blog for continuing postings in the series Exploiting your antenna analyser. See also Exploiting your antenna analyser – contents.

]]>The EFHW can be deployed in a miriad of topologies, this article goes on to explore three popular practical means of feeding such a dipole.

The models are of the antenna system over average ground, and do not include conductive support structures (eg towers / masts), other conductors (power lines, antennas, conductors on or in buildings). Note that the model results apply to the exact scenarios, and extrapolation to other scenarios may introduce significant error.

A very old end fed antenna system is the End Fed Zepp. In this example, a half wave dipole at λ/4 height is driven with a λ/4 600Ω vertical feed line driven by a balanced current source (ie an effective current balun).

Above is a plot of the current magnitudes. The currents on the feed line conductor are almost exactly antiphase, and the plot of magnitude shows that they are equal at the bottom but not so at the top. The difference between the currents is the total common mode current, and it is maximum at the top and tapers down to zero at the bottom. Icm at the top is about one third of the current at the middle of the dipole.

End fed Zepp deals in more detail with the common mode current on the EFZ.

One manufacturer of a popular EFHW antenna system that uses a 2/3 terminal matching device recommends that where the fed end of the dipole is elevated, that the match device be installed there and that the coax be grounded where it reaches ground. In this model, a 2m driven ground electrode is used to ground the coax.

Above, the plot of current magnitudes shows substantial common mode current on the feed line, with a maximum at the lower end approximately the same as the current in the middle of the dipole.

The relatively high common mode current on the feed line, and particularly at lower height is a distinct disadvantage bring risk of higher rx noise and transmitter interference to nearby electronics. The magic of End Fed Half Waves (EFHW) gives further information on the common mode current in this configuration.

This antenna is advertised as “no counterpoise needed” by at least one seller, which questions the term “counterpoise”: https://owenduffy.net/files/Counterpoise.pdf.

One popular author recommends a “0.05λ counterpoise” as he calls it. Again a 2/3 terminal matching device is used the coax is grounded where it reaches ground. In this model, a 2m driven ground electrode is used to ground the coax. This is essentially the same as the previous model but with the dipole fed 0.05λ from end.

Above, the plot of current magnitudes shows substantial common mode current on the feed line, with a maximum at the lower end approximately the same as the current in the middle of the dipole.

The relatively high common mode current on the feed line, and particularly at lower height is a distinct disadvantage bring risk of higher rx noise and transmitter interference to nearby electronics.

This is almost the same as the previous model, the so-called “counterpoise” has done little for the relatively high common mode current.

The three scenarios modeled are quite similar configurations, but the detail of the feed arrangement results in the first being significantly different to the later two.

The third model shows that the so-called “counterpoise” variation to the second model has negligible effect, and questions the credibility of sources suggesting otherwise.

Relatively high feed line common mode current is a risk, again dependent on implementation.

The concept of a “no counterpoise” EFHW as commonly used is questionable.

Because of the sensitivity to implementation detail, the term End Fed Half Wave is not very descriptive.

You might like: more articles on EFHW.

- Duffy, O. Oct 2010. Counterpoise. https://owenduffy.net/files/Counterpoise.pdf.