Mornhinweg ferrite core measurements – #31 discussed his measurements of a #31 suppression sleeve.

Above are his measurements of a FB-61-6873 sleeve. Essentially there are two measurements at each frequency, and the expected flux density B is in the ratio of approximately 2:1. He has fitted a straight line on a log/log graph to the measurements at each frequency. The similarity of the slopes is not unexpected, and is a tribute to his experiment design, execution and calculations.

The first thing to consider is the slope of the the fitted line.

If the material was linear in its characteristic, we might expect the core heating to increase as the square of B. The blue line has such a slope and can be used to compare the slope of the red lines. By eye, the measurements show slightly higher slope, and no conclusions can be drawn about linearity as there are only two points for each frequency.

Lets estimate the core loss of a 2 turn inductor (ignoring conductor loss) using complex permeability from the datasheet.

We should keep in mind that suppression sleeves are not controlled principally for permeability in manufacture (they are controlled for Z at some frequency, see Using complex permeability to design with Fair-rite suppression products), so predictions based on published permeability curves have additional uncertainty.

Above is a plot of calculated core loss vs frequency, and Mornhinweg’s measurements at 21V impressed. The nature of the responses are somewhat similar, importantly the dip around 7MHz exists in both measured and calculated responses.

Though #61 is a low loss material at 1MHz, the loss turns upwards at the low end in the above plot simply because there is not much magnetising impedance Zm, and so magnetising current Im is high, and Im^2R grows quickly with decreasing frequency.

Above is a chart comparing calculated core loss for 2t and 4t on the core, it can be seen that increased Zm leads to lower core loss. The 4t case has 50% the volts/turn, 50% the flux density, 25% of the loss.

The matter of control of suppression product parameters has been mentioned and could be one of the factors giving rise to a difference to the datasheet.

However, there are other issues with #61 operated at high power.

Above is the B-H curve for the material, and at 100° saturation is above 1000gauss (100mT). The measurements at 21V have B ranging from 11mT @ 1.8MHz to 0.4mT @ 50MHz, it is always well under saturation.

Whilst we might then think that small signal analysis applies, lets look at the temperature sensitivity of the material.

We can see from the chart above that the loss increases with core temperature, more so at the lower frequency / higher B range. The DUT temperature varied from 21.5 to 29.4° @ 1.8MHz, not a very great range but enough to cause a 10% increase in loss at the end of the test. This issue is more relevant to the final application where the core might well operate at higher temperatures.

Another factor is that of conductor loss which is captured in the measurements. Though we might dismiss conductor loss out of hand, at the lowest frequency the real component of Zm (ie the equivalent core loss resistance) is very low and wire RF resistance may be significant.

- Mornhinweg, M. 2019. Ferrite core loss in HF power applications.

- Ferrite permeability interpolations
- Inductance of RF cored inductors and transformers
- Calculate ferrite cored inductor – rectangular cross section
- Calculate ferrite cored inductor – circular cross section
- Calculate ferrite cored inductor (from Al)
- Calculate ferrite cored inductor – ΣA/l or Σl/A
- Ferrite permeability interpolations

- inductive; and
- suppression.

Sometimes the same dimensioned cores are available in both categories with different part numbers and possibly different prices, implying some real difference in behavior, eg 5943003801 and 2643803802 are both FT240-43 sized cores.

Material datasheets often contain a note like this from the #43 datasheet:

Characteristic curves are measured on standard Toroids (18/10/6 mm) at 25°C and 10 kHz unless otherwise indicated. Impedance characteristics are measured on standard shield beads (3.5/1.3/6.0 mm) unless otherwise indicated.

I sought to clarify my interpretation of this clause by asking Fair-rite …whether the published material permeability curves / tables apply to suppression product. Can I use the published permeability curves / tables to predict inductor impedance reliably for suppression products?

Fair-rite’s Michael Arasim advised…

Yes the published permeability curve can be used to predict impedance. There will be some variance in the shape of the curve due to individual part size as well as process and material variation. The level of this variance will change depending on the individual material but, the curves themselves are all produced using the same sized toroidal core for each material. One thing of note; Inductive rated parts in theory will be controlled more tightly to adhere to the complex permeability curve since their acceptance criteria is generally going to be inductance and loss factor based. Impedance rated parts are accepted based on a minimum impedance at select test frequencies. Since the impedance is a complex value influenced by both the inductive and resistive components of the complex permeability; In theory you could see more variance in each component and still hit the impedance rating. Prior to production, all lots of our materials are screened to ensure that they will adhere (within a tolerance) to the published material data.

So, the following notes and tools are applicable to Fair-rite inductive and suppression products, but one might expect more variation in the real and imaginary components of impedance with suppression products, and loss in cores used for transformers.

- Inductance of RF cored inductors and transformers
- Calculate ferrite cored inductor – rectangular cross section
- Calculate ferrite cored inductor – circular cross section
- Calculate ferrite cored inductor (from Al)
- Calculate ferrite cored inductor – ΣA/l or Σl/A
- Ferrite permeability interpolations

My own experience is that the difference is not huge, but it explains the somewhat wider variation observed with suppression products and the need to verify designs by measurement.

]]>I have been asked several times recently about the assumed emissivity and the accuracy questioned, I assume this has been discussed online somewhere.

When first measuring ferrites with non-contact thermometers, I performed some experiments to discover whether the default emissivity ε=0.95 applied. It would be convenient if it did, and permit use of some instruments that do not allow adjustment of ε.

In the past, I have compared the reading of non-contact thermometers with several K thermocouple meters and a Thermomelt indicator, and observed insignificant difference (ie less than the variance of repeated measurements).

The following experiment is a thermal pic of a FT240-43 core on the black plastic case of the instrument. The setup has had hours to stabilise thermally.

Above is a combined thermal image and faint visual image. This instrument has only one readout point, and by moving it around, only 0.1° variation was observed between the background and the core.

The shape of the core cannot be reliably discerned in the thermal image, the variation is mostly measurement noise… but lets assume there was 0.1° difference between the black plastic case and the core when they are both at 23° and calculate the implied ε that would account for that indication.

Above, the calculated actual ε that would account for 0.1° error is 0.949. Such an error in ε does not translate to the same error in T at different T.

Above, calculating the actual temperature of a measurement when the actual ε is 0.949 and the instrument is calibrated for 0.95 gives 100°, the error is not significant in a three digit precision answer.

If we find what value of ε is required to cause a -1° error at 100°, it is 0.940… well below the estimated 0.949.

I sleep easy that the thermographs I have presented of ferrite cored inductors and transformers do not have significant error due to the assumed black body emissivity of the ferrite.

]]>The calculator has been revised to include 45° chamfers of a specified length on all four corners. If the chamfer angle differs, the error is very small in the range 30-60°. If the corners are radiused, use the radius as the chamfer length, the error is very small.

We do not need to obsess over these errors as they will usually be dwarfed by manufacturing tolerances.

The calculation of ΣA/l for the sharp corner model is fairly simple.

\(\int _{ir}^{or}\frac{w}{2 \pi r}dr\)

\(=\frac{w}{2 \pi }\left(\ln \left(or\right)-\ln \left(ir\right)\right)\)

To implement the chamfer adjustment, the ΣA/l component of the missing material is calculated.

Firstly the inner chamfers (which are simpler).

\(\int _{ir}^{ir+cr}\:\frac{r-ir}{2 \pi r}dr\)

\(=\frac{1}{2\pi}\left(cr-ir\left(\ln \left(ir+cr\right)-\ln \left(ir\right)\right)\right)\)

Then the outer chamfers are calculated.

\(\int _{or-cr}^{or} \frac{\left(r-\left(or-cr\right)\right)}{2 \pi r}dr\)

\(=\frac{1}{2\pi }\left(cr\left(\ln \left(or\right)-\ln \left(-cr+or\right)\right)-or\left(\ln \left(or\right)-\ln \left(-cr+or\right)\right)+cr\right)\)

The final ΣA/l is the first quantity less the two missing components.

Implemented in javascript in the calculator…

aol=width/2/pi*Math.log(od/id)*1e-3; aol=aol-(cr-ir*(Math.log(ir+cr)-Math.log(ir)))/(2*pi)*1e-3*2; aol=aol-(cr*(Math.log(or)-Math.log(-cr+or))-or*(Math.log(or)-Math.log(-cr+or))+cr)/(2*pi)*1e-3*2;

Let’s look at some examples.

Above is a calculation for the popular FT240-43. Without the chamfer adjustment, ΣA/l would be 0.001091 (which is the value given by Fair-rite in the datasheet), adjusting for chamfer the reduction is 2.5%.

Above is an example calculation of ΣA/l and Al. the calculated ΣA/l is less than 1% less than if the chamfer were ignored. The difference may be greater on some cores, especially very small cores.

Above is an example calculation for a very small core with radiused corners. The chamfer approximation reduces ΣA/l and Al by about 2%… again the manufacturing tolerances dwarf the adjustment.

]]>Above, the core is 35x21x13mm, a mid sized core, two used in my redesign of a commercial balun and implemented by VK4MQ . The mid size limits dissipation, but compactness can be an advantage. The cores sell for less than $4.00 per core and are readily available in Australia.

The core is almost certainly made in China, and Jaycar does not publish complex permeability curves for the material, but above are my measured characteristics over HF. The Chinese factor does raise questions about continued supply of consistent quality product.

Above is a plot of Fair-rite’s complex permeability for #31 ferrite material.

If you compare the two, they are not identical, but are very similar and you could conclude that applications where #31 is a good material selection would be well served by L15. Notably #31 is a MnZn ferrite and the L15 appears to be a NiZn ferrite based on its very high resistivity.

It is interesting to observe the fashions in online discussions of the best balun material

that the current fashion amongst online experts is #31. #31 is certainly a good candidate for applications with emphasis on lower HF, but its suitability for a specific applications needs also to consider other factors like its loss.

For the same reason, Jaycar’s LO1238 using L15 material may be quite suitable to those type of applications.

]]>Above are his measurements of a FB-31-6873 sleeve. Essentially there are two measurements at each frequency, and the expected flux density B is in the ratio of approximately 2:1. He has fitted a straight line on a log/log graph to the measurements at each frequency. The similarity of the slopes is not unexpected, and is a tribute to his experiment design, execution and calculations.

The first thing to consider is the slope of the the fitted line.

If the material was linear in its characteristic, we might expect the core heating to increase as the square of B. The blue line has such a slope and can be used to compare the slope of the red lines. By eye, they appear similar in slope, and no conclusions can be drawn about linearity as there are only two points for each frequency.

The other interesting this is B relative to the critical numbers given in Amidon’s advice. The table is in gauss, and 1 tesla (1T)=10000gauss.

The sparse points are a bit limiting… so lets explore whether there is a likely curve fit, whether they appear based on a simple relationship.

When plotted on log/log axes, the points fall roughly on a straight line. Considering that the table numbers are rounded, we cannot do better than to say Bcrit=f^2*15.1 where f is in MHz.

So, lets plot them on the chart.

Above, the magenta X is at Amidons Bcrit value. It can be seen that both measurements at 1.8MHz were above Bcrit, and one of the measurements at 3.5MHz was well above Bcrit. Nevertheless each pair of measurements appear to be on approximately the same slope as the blue line, linear material. There is little evidence of saturation.

Nor should there be, 23mT (230gauss) @ 1.8MHz is way below saturation.

Mornhinweg performed thermal analysis to estimate the core loss, and at 1.8MHz, the graph indicates the two data points were (0.0114,0.216), (0.023,1.000).

Lets estimate the core loss of a 1 turn inductor using complex permeability.

We should keep in mind that suppression sleeves are not controlled for permeability in manufacture (they are controlled for Z at some frequency), so predictions based on published permeability curves have additional uncertainty.

The key figure is the real part of Y, G which is 0.0109S.

To be able to calculate the core loss, we need to know the voltage impressed on the winding at each of the test flux densities using the expression \(E=\frac{4.44 B A_e N F}{1e8}\).

Power dissipated is given by \(P=E^2 G_m\).

We can then divide that by the core volume to obtain the core loss in W/cm^3 to compare to the plotted measurements.

The calculated result is (0.0114,0.242), (0.023,1.010) which reconciles very well considering the tolerances of ferrite cores and the uncertainty of measurements.

The core loss could also be calculating by finding the magnitude of magnetising current \(Im=\frac{V}{Z_m)\) and calculating \(P=I^2R_m\). It reconciles with \(P=E^2 G_m\).

- Mornhinweg, M. 2019. Ferrite core loss in HF power applications.

- Ferrite permeability interpolations
- Inductance of RF cored inductors and transformers
- Calculate ferrite cored inductor – rectangular cross section
- Calculate ferrite cored inductor – circular cross section
- Calculate ferrite cored inductor (from Al)
- Calculate ferrite cored inductor – ΣA/l or Σl/A
- Ferrite permeability interpolations

]]>

W0QE’s video #80: High Power Balun with #31 Ferrite Material gives some measurements and simulations of a FT240-31 inductor with 11 and 14 turns.

In the video he states:

It turns out that the heating effects in the coil are related to the voltage across the coil only, not the current through the it or anything else.

In fact, there is current flowing through the inductor and that develops a voltage difference across the ends. When we are talking about the self inductance properties, then we are talking about the voltage induced in the inductor as a direct result of the current flowing through the inductance.

Let’s look at his own figures to demonstrate,

Above is his Simsmith model. Let us focus on just the left hand two elements L and R1 (for the 11t inductor) as it is a quite complicated model. L was derived from a measurement of the inductor in a fixture, and to some extent the fixture is captured.

The voltage applied to both L and R is given as 272.2V, this is around the voltage that would be applied to a 50+j0Ω load at 1500W, so his experiment to to simulate the conditions if that inductor was the 50Ω winding of a 50Ω transformer at 1500W.

The impedance of R1 is given as 4134-j328.1Ω (interpolated possibly) from his measurement of Z.

From V and Z, we can calculate \(Y=\frac1Z\) and \(I=\frac{V}Z\), and powers \(P_i=I^2R\) and \(P_v=V^2G\) (R and G being the real parts of Z and Y respectively).

Let’s use Python as a complex number calculator to make the maths easy.

>>> import math >>> import cmath >>> z=4134-328.1j >>> y=1/z >>> y (0.00024038230052189223+1.907823725235434e-05j) >>> v=272.2 >>> v 272.2 >>> p50=v**2/50 >>> p50 1481.8568 >>> pv=v**2*y.real >>> pv 17.810607331400476 >>> i=v/z >>> i (0.06543206220205906+0.005193096180090851j) >>> pi=abs(i)**2*z.real >>> pi 17.81060733140048

We can see there is current flowing, and that calculated pv and pi reconcile (and they reconcile with Simsmith)… so the power dissipated (ie converted to heat) in the inductor can be calculated from current or voltage, his statement quoted earlier is plainly wrong.

So, if either current or voltage can be used, is one better?

This is more a question of whether voltage or current can be measured reasonably accurately and conveniently.

Whilst in W0QE’s test configuration it is fairly easy to make a valid voltage measurement of the inductor shunted by the 50Ω dummy load at the T (the test was designed for that), measurement of a ‘floating’ common mode choke is not so easy as the instrument may significantly disturb the thing being measured (it doesn’t have the 50Ω shunt load, circuit impedance is now much higher and the effect of the instrument leads etc is much greater).

A better approach for the common mode choke might be to use a clamp on RF ammeter and use measured Z of the choke to obtain \(P_{choke}=I^2 \mathbb{R}(Z_{choke})\) or \(P_{choke}=I^2 Real(Z_{choke})\).

I make the observation that many hams write about common mode current, but it is rare to see valid measurement of common mode current.

Another question that arises is the accuracy of measurement of Z. In this instance, the choke in fixture is very close to self resonant (evidenced by the smallish magnitude of X) and the real part of Z is quite sensitive to layout and shunt capacitance such as the fixture… giving rise to significant uncertainty or R around the resonant frequency. You might question whether the fixture actually represents the intended deployment scenario.

He also calculates the expected flux level as 50.7 gauss and mutters that they are rated for 57 gauss… yes, rated for 57 gauss

.

Above is from the Fair-rite datasheet for #31 material. It is easy to see that saturation flux density is of the order of 1000 gauss (0.1T), so operating at 50 gauss is way way below saturation. Like many if not most ferrite ham applications at HF, loss becomes a problem way before saturation.

Nothing in the Fair-rite #31 datasheet relates core loss to flux density.

I could not see where he used this magic 57 or 50.7 gauss in any power calculation, all of his power calculation is based on a small signal measurement of the inductor magnetising impedance. 57 gauss may have been sourced from Amidon… but keep in mind that Amidon is not a manufacturer, Fair-rite is a manufacturer. So much for the claim that loss is dependent on voltage and not current.

In this application, the power dissipated in an inductor can be calculated from Z and either current through it, or voltage across it.

If you want to estimate the core loss in a common mode choke, carefully measure the common mode impedance and the common mode current and calculate the core loss.

Uncertainty in Z can be significant, especially near the inductor’s self resonant frequency.

]]>Is this Segal’s law at play?

There are several common contributors including:

- faulty, dirty, or not properly mated connectors and cables;
- VSWR meters that are not accurate at low power levels; and
- influence of the common mode current path on VSWR.

The first and obvious question is, are all the cables and connectors sound and properly tightened? Some types of connector (eg UHF series, SMA) depend on tightness of the screw ring / nut for proper electrical contact of the outer conductor. An aerosol can of Isopropyl Alcohol (IPA) and some cleaning swabs / brushes are very handy to ensure connectors are clean.

Should you trust your VSWR meter – detector linearity discusses the second issue.

To the third issue mentioned, if you truly want to compare the two instruments, you must measure EXACTLY the same thing… and that means that when you disconnect the coax from the back of the radio and connect it to the analyser, you must RESTORE the common mode current path. I usually do this by holding the analyser coax connector (with antenna cable attached) firmly against the transceiver connector outer threads, and preferably isolating my fingers from the metal using an insulating sheet.

Above, an example of the nanoVNA with minimal adapters to UHF series, antenna patch lead attached and the shell of the connector held in good contact with the transceiver connector at far left. The white sheet is a silicone sheet to insulate my hand from the other stuff so that it is as close to the operating configuration as reasonably possible.

In this case, the minimum VSWR reconciles very well with the IC-7300 VSWR meter, provided the tx power is more than 60W.

]]>Section 1-36 states explicitly that it is applicable to Iron Powder and Ferrite, which is interesting because they are very different materials from a loss point of view.

Basically, their method depends on a maximum safe value for peak flux density.

They give an expression for peak flux density \(B_{max}=\frac{10^8E }{4.44 A_e N F}\) and the following table of design limits for Bmax.

Note that the table and formula are independent of ferrite mix type (though they do mention that “these figures may vary slightly according to the type of material being used.”

So, lets work some examples being a 3t primary at 7MHz on FT240 cores of #43 and #61 material. The two material types are very popular for HF RF inductors and transformers, and were chosen for that reason rather than designing an example that shows extreme difference.

Using VK1SV’s online calculator of Amidon’s method, we get…

By trial and error, it is found that 83V is just ‘safe’ for this transformer, irrespective of material.

At around 60gauss (0.006T), flux density is way way below saturation (>1000gauss (0.1T))

Now lets do a permeability based calculation of magnetising admittance and then power lost in the core Pcore at 83V applied for the #43 core.

\(P_{core}=V^2 G_{core}=83^2 \cdot 0.00232=16.0 \; W\) 16W is on the high side for this core in free air, more so if it is enclosed.

Note, this is a small signal analysis, but as explained, flux density is way way below saturation.

Now lets do a permeability based calculation of magnetising admittance and then power lost in the core Pcore at 83V applied for the #61 core. The Amidon method is probably unsafe.

\(P_{core}=V^2 G_{core}=83^2 \cdot 0.000147=1.013 \; W\) 1W is on the low side for this core in free air, it can probably dissipate more like 10W in free air, somewhat less enclosed. The Amidon method is unduly safe.

There is a huge difference, the core loss with #43 material is 1600% of that with #61.

Note, this is a small signal analysis, but as explained, flux density is way way below saturation.

The simplest way is to make a measurement of the magnetising admittance (or impedance from which you can calculate admittance).

One method is to put three turns onto each of the cores and sweep in with your calibrated nanoVNA. Find Z from s11 at 7MHz, and invert it to find G and B (Some hammy tools might give you Rp||XP, so G=1/Rp). Then calculate \(P_{core}=V^2 G_{core}=83^2 G_{core} \; W\).

Now keep in mind that the tolerance of ferrite are fairly wide, so your measured results won’t exactly reconcile with the calculations above, but you should find a wide disparity in the core loss for the two materials and question the usefulness of Amidon’s method.

So, before you accept online expert’s advice on either side of this argument… make some measurements and develop trust in the tools you use.

Amidon’s method is manifestly poor. People who recommend it have probably not tested its validity, and both damages their credibility.

For ferrites at RF (and zero DC current), operation is more likely to be limited by dissipation than magnetic saturation, and in that case, the flux density is not usually very interesting.

]]>Let’s work an example using Simsmith to do some of the calculations.

Scenario:

- 20m ground mounted vertical base fed against a 2.4m driven earth electrode @ 0.5MHz;
- 10m RG58A/U coax; and
- Receiver with 500+j0Ω ohms input impedance and Noise Figure 20dB.

An NEC-4.2 model of the antenna gives a feed point impedance of 146-j4714Ω and radiation efficiency of 0.043%, so radiation resistance \(Rr=146 \cdot 0.00043=0.0063\).

Above, the NEC antenna model summary.

Above is a Simsmith model of the system scenario.

R1 and G model the antenna, G uses Rr for Zo, and R1 contains the balance of the feed point impedance.

With the useZo source type, the source would deliver 1W or 0dBW to a conjugate matched load.

The next important figure is the power into the 500Ω load L. it is -58.3dBW. Simsmith has calculated the solution to the antenna loss elements, mismatches and coax loss under standing waves. Effectively, the average gain of the antenna system (everything to the right of L) is -58.3dB. Such an antenna is likely to have a Directivity of around 4dB, in fact the NEC model calculates 4.8dB. So the maximum gain is -58+4.8=-53.2dB.

The burning question is whether it is sufficiently good to hear most signals. Well, a better question is how much does it degrade off-air signal to noise ratio (S/N). All receivers degrade S/N, but how much degradation occurs in this scenario.

We need to think about the ambient noise. Lets use ITU-R P.372 for guidance on the expected median noise in a rural precint.

Above, ambient noise figure @ 0.5MHz is 75.54dB.

Now lets calculate the Signal to Noise Degradation (SND).

At 4.58 dB it is not wonderful, the weakest signals (ie those with low S/N) we be degraded significantly, stronger signals (those with high S/N) will be degraded by the SAME amount, but for instance reducing S/N from 20 to 15dB is not so significant.

Applying this to your own scenario

The information fed into the calculations included:

- Rr;
- feed point impedance;
- transmission line details;
- Rx input impedance and NF; and
- Ambient noise expectation.

To calculate your own scenario, you need to find these quantities with some accuracy.

Tools:

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