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 MFJ-264N 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 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 1.35 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.

This article presents some NEC-4.2 model results for a 7MHz λ/2 horizontal 2mm copper wire at height of λ/4 above average ground.

The model is impractical in a sense that it does not include unavoidable by-products of a practical way to supply RF power to the antenna, but it is useful in providing insight into the basic antenna.

The NEC model has 200 segments, and varying the feed segment gives insight to what happens to feed point impedance.

Above, it can be seen that as the wire is fed closer to the end (segment 1), feed point Z includes a rapidly increase capacitive reactance.

The very large series reactance close to the end makes feeding at those points impractical as any impedance transformation network needs to deliver power to a very reactive very high impedance load.

As the feed point approaches the end, the feed point reactance approaches -∞ and the feed point voltage approaches ∞.

Let’s analyse the antenna at a feed point that is close to the end, but a compromise for more practical feed point impedance. We will look at the case at segment 10 (1m from the end) which is 5% of the dipole length or 2.5% of wavelength.

Above is a 3D magnitude and phase current plot from 4NEC2. It can be seen that there is a significant change in phase near the feed point.

Above, the magnitude of current an phase are plotted.

Many authors insist that the behavior of a half wave dipole is independent of where it is fed, that the current distribution is exactly identical for all feed points, and often give the familiar sine current distribution to support their argument.

The chart above shows that the magnitude of current is close to a sinusoidal distribution, but there is a glitch near the feed point… but more importantly there is a significant variation in phase in the last quarter wavelength, culminating in a discontinuity at the feed point.

The current distribution is not the same as a centre fed half wave dipole, though it is somewhat similar.

The gain pattern at 10° elevation shows some asymmetry, not large, but evidence again that the thing is not exactly the same as a centre fed half wave dipole, but somewhat similar.

The radiation efficiency of the modeled system is 75%, it has no feed or impedance transformation losses factored in, just conductor loss (which is very small) and ground loss.

An NEC-4.2 model of a 7MHz λ/2 horizontal 2mm copper wire at height of λ/4 above average ground reveals:

- feed point impedance vs displacement for a somewhat idealised or ‘pure’ antenna, ‘pure’ in the sense of not including a feed line or other elements that would alter its operation; and
- current distribution (magnitude and phase) that are a little different to a centre fed dipole.

1 highlights the impractical nature of feeding such a ‘pure’ antenna very close to the end.

2 questions the assumption that underlies most discussions of an EFHW that it works identically to a centre fed dipole as even in this ‘pure’ form, the current distribution is not exactly the same.

Further articles will explore the effects of popular practical feed arrangements on the system.

]]>The article is ‘in-brief’ as technical stuff that will not interest most hams is published privately on a members-only page. This article is based on the information in the QST article alone (ie not on the private members only supplementary information).

The core has a modest price in North America, but shipping to other parts of the world may make it very expensive… IOW unobtainium to most parts of the world.

Above is the published InsertionLoss. The article states that they were half the value obtained in a back to back measurement, and it should be noted that is a compromised measurement, and secondly that InsertionLoss comprises two components, (dissipative) Loss and MismatchLoss.

The fact that InsertionLoss increases markedly at the lower frequencies is a hint that it has too few turns for those frequencies, and that InsertionVSWR and efficiency may suffer.

The transformer is intended to be used with a load such that the input impedance Zin is approximately 50+j0Ω, Gin=0.02S.

Analysis of a simple model of the transformer with a load such that input impedance is 50+j0Ω gives insight into likely core losses in that matched condition.

Let us calculate the magnetising admittance of the 4t primary at 1.8MHz. The core is a Laird 28B1540-000 ferrite toroid.

Above is a table of complex permeability for Laird 28 material. (I have seen online experts advise that this information is not available… but here it is.) The Laird #28 material is a medium μ NiZn ferrite, somewhat similar to Fair-rite #43 but different enough to not be equivalent.

Now lets model the 4t primary at 1.8MHz.

Gcore is the real part of Y, 0.000826S.

If Yin of the loaded transformer is 0.02S, we can calculate the core efficiency as 1-Gcore/Gin=1-0.000826/0.02=95.8%, core loss is 0.18dB. Note that this efficiency is in the matched condition, and could be higher or lower at other input impedances (η=1-Gcore/Gin). Ferrite materials have fairly wide tolerance, so measurements of actual cores may have some variation.

The balance of the measured InsertionLoss is likely to be MismatchLoss, but that information is not disclosed in the main article. MismatchLoss will include contributions from the shunt magnetising admittance (moderately low in this case) and effects of flux leakage.

- 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).

]]>

AIM915a was recently pulled from the distribution site and replaced by a new release, AIM916.

AIM916 chokes on some calibration files created with earlier versions, so again historical scan data is rendered worthless. Note the illogical diagnostic message… typical AIM quality.

I cannot recall ever finding a new release that did not have significant defects, commonly inconsistency between displayed values. In the common theme of one step forward, two steps backwards, this version has defects that were not present in AIM910B.

This problem existed in AIM915a, it persists in AIM916.

Let’s review the internal consistency of this part of the display screen.

Most of the values given above are calculated from a single measurement value, and should be internally consistent. That measurement value is translated to different quantities, many based on the stated Zref (50Ω in this case).

Let’s assume that the values given for Rs and Xs are the basis for the other quantities, and check the consistency of those other values with Rs, Xs based on Zref=50Ω as shown.

Above are various values calculated from Rs=49.720Ω, Xs=0.090Ω and Zref=50+j0Ω.

Working down from the top of the AIM results:

- SWR (1.508) is wrong, it should be 1.01;
- Rho Mag (0.2027) is wrong, it should be 0.002949;
- s11 (-0.0028+j0.0009) is ok;
- % refl power (4.1) is wrong, it should be 0.00087;
- Return Loss (13.86dB) is wrong, it should be 50.61B; and
- Cable Loss (6.93dB) is wrong, it should be 25.30dB.

What was fixed in AIM916? Well, that seems to be a secret… but some stuff that worked was broken (the cal file issue) and some stuff that was broken remains broken.

Does not inspire a lot of confidence, does it?

Will this internal error that has been in many released versions ever get fixed before the hardware is so dated as to be worthless anyway? Some might say that time has already passed… newer competitive hardware with greater ADC resolution obsoletes the AIMuhf.

]]>This article reviews the magnetics design of the -20dB / 25W coupler.

The coupler uses a type of Sontheimer coupler (Sontheimer 1966) and these are commonly poorly designed. The first question is whether the magnetising impedance of T2 which appears in shunt with the load is sufficiently high to not give rise to poor insertion VSWR.

The instructions specify a FT50-43 with 10t for 1MHz and up. Experience says this is probably low turns and worth reviewing.

Though rated down to 1MHz, this review is at 1.8MHz, the lowest ham band above 1MHz. (It has worse InsertionVSWR at 1MHz.)

Let’s calculate the expected magnetising admittance.

Magnetising Y=0.000598-j0.00241S, let’s calculate VSWR with 50Ω in shunt, so Yt=0.020598-j0.00241S.

Ok, 10t gives rise to an InsertionVSWR of 1.13 at 1.8MHz considering the core alone, which is on the poor side.

It is worth reviewing the expected dissipation of the T2 core as this is a failing of many designs.

At 25W in a 50Ω system, V=(25*50)^0.5=35V. The power dissipated in the T2 core is at Pfwd=25W is calculated as E^2*G=35^2*0.000598=0.73W. The core is likely to get quite warm, but in free air should dissipate that heat comfortably.

The performance may be better with a core with double the ΣA/l (or double Al).

The 30dB coupler can be analysed using the same method. It is left as an interesting exercise for the reader.

- Sontheimer,C & Frederick,RE. Apr 1966. Broadband directional coupler. US Patent 3,426,298.

AIM915 was recently pulled from the distribution site and replaced by a new release, AIM915a.

I cannot recall ever finding a new release that did not have significant defects, commonly inconsistency between displayed values. In the common theme of one step forward, two steps backwards, this version has defects that were not present in AIM910B.

This problem existed in AIM915, it persists in AIM915a.

Let’s review the internal consistency of this part of the display screen.

Most of the values given above are calculated from a single measurement value, and should be internally consistent. That measurement value is translated to different quantities, many based on the stated Zref (50Ω in this case).

Let’s assume that the values given for Rs and Xs are the basis for the other quantities, and check the consistency of those other values with Rs, Xs based on Zref=50Ω as shown.

Above are various values calculated from Rs=49.719Ω, Xs=0.090Ω and Zref=50+j0Ω.

Working down from the top of the AIM results:

- SWR (1.508) is wrong, it should be 1.01;
- Rho Mag (0.2027) is wrong, it should be 0.002959;
- s11 (-0.0028+j0.0009) is ok;
- % refl power (4.1) is wrong, it should be 0.00087;
- Return Loss (13.86dB) is wrong, it should be 50.58dB; and
- Cable Loss (6.93dB) is wrong, it should be 25.29dB.

Does not inspire a lot of confidence, does it?

]]>AIM914 was recently pulled from the distribution site and replaced by a new release, AIM915.

I cannot recall ever finding a new release that did not have significant defects, commonly inconsistency between displayed values. In the common theme of one step forward, two steps backwards, this version has defects that were not present in AIM910B.

Let’s review the internal consistency of this part of the display screen.

Most of the values given above are calculated from a single measurement value, and should be internally consistent. That measurement value is translated to different quantities, many based on the stated Zref (50Ω in this case).

Let’s assume that the values given for Rs and Xs are the basis for the other quantities, and check the consistency of those other values with Rs, Xs based on Zref=50Ω as shown.

Above are various values calculated from Rs=49.719Ω, Xs=0.090Ω and Zref=50+j0Ω.

Working down from the top of the AIM results:

- SWR (1.508) is wrong, it should be 1.01;
- Rho Mag (0.2027) is wrong, it should be 0.002959;
- s11 (-0.0028+j0.0009) is ok;
- % refl power (4.1) is wrong, it should be 0.00087;
- Return Loss (13.86dB) is wrong, it should be 50.58dB; and
- Cable Loss (6.93dB) is wrong, it should be 25.29dB.

Does not inspire a lot of confidence, does it?

]]>Of interest to European designers is inclusion of three common materials used for HF applications, Ferroxcube’s 4A11, 4B2, and 4C65.

]]>An online expert questioned the analysis and later measurements, and proposed his own transformer design as evidence.

Notably, his transformer uses #61 material and a larger binocular core, a Fair-rite 2861006802 with 2t for a nominal 50Ω primary, giving loss measurements at 7MHz of 0.08dB. Note that the confidence limits of that loss measurement because of the way in which it was obtained (eg a 1% error in the 1120Ω load resistor contributes 0.043dB error to the result), but the measurements do suggest that the loss is probably very low.

Though the loss is low and Return Loss is high at 7MHz, the limits for ReturnLoss>14dB (VSWR<1.5) is 5-18MHz. With compensation, that range may be changed.

Lets apply the method laid out at PD7MAA’s BN43-202 matching transformer for an EFHW.

The best Fair-rite data I can find quickly is a chart of the impedance of a one turn winding.

Scaling from this graph, Xs is close of 35Ω at 7MHz, so lets used that to derive some basic parameters for the core.

Firstly, lets find the permeability of #61 at 7MHz.

Freq (MHz) |
µ’ |
µ” |

7.000e+0 |
1.214e+2 | 1.159e+0 |

Using that in a calculator to iteratively find the value of ΣA/l that gives Xs=35Ω at 7MHz, we obtain ΣA/l=0.0054m, this captures the magnetic path geometry of the binocular core.

Let us now use that core characteristic to calculate the magnetising admittance of the 2t primary winding.

Gcore is the real part of Y, 0.0000421S.

If Yin of the loaded transformer is 0.02S, we can calculate the core efficiency as 1-Gcore/Gin=1-0.0000421/0.02=99.8%, core loss is 0.009dB.

The total loss of this type of transformer will be dominated by the core loss.

The posted measured results, though having wide confidence limits, fall quite in line with a theoretical prediction using the method laid out at PD7MAA’s BN43-202 matching transformer for an EFHW. The measurements are evidence that the design method works.

The superior efficiency of the tested transformer is due to a better magnetic design, better than the PD7MAA design.

- PD7MAA EFHW antenna for 40-10m qrp
- 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).

]]>