I see online discussion of specification bending radius for coax cables, and their application to ferrite cored common mode chokes.

A low Insertion VSWR high Zcm Guanella 1:1 balun for HF and follow on articles described a balun with focus on InsertionLoss.

Let’s remind ourselves of the internal layout of the uncompensated balun.

The coax is quality RG58A/U with solid polythene dielectric. The coax is wound with a bending radius of about 10mm, way less than Belden’s specified minimum bending radius of 50mm.

So, the question is does this cause significant centre conductor migration that will ruin the characteristic impedance:

• when it was first constructed; and
• through life.

Note the pigtails at each coax connector, they are a departure from Zo of the coax and the N type connectors. They can be seen as short sections of transmission line with Zo perhaps 200Ω or more. The effect of these is to transform impedance and so cause the input VSWR to depart from ideal.

When first constructed

Above is a chart from the original construction articles. InsertionVSWR @ 30MHz is about 1.15.

Note the pigtails at each coax connector, they are a departure from Zo of the coax and connectors. They can be seen as short sections of transmission line with Zo perhaps 200Ω or more. The effect of these is to transform impedance and so cause the input VSWR to depart from ideal.

After 5 years of service

This article presents measurement of the balun 5 years after it was made, 5 years in use, but not operated at temperatures above datasheet maximum.

As mentioned, the pigtails are the main contribution to InsertionVSWR. The balun was compensated using 10pF shunt capacitors at both coax connectors. (Possible compensation solutions were discussed at A low Insertion VSWR high Zcm Guanella 1:1 balun for HF – more detail #3).

Above is a NanoVNA screenshot of measurement of the compensated balun using the calibration LOAD, a couple of SMA(F)-N(M) adapters and a short SMA(M)-SMA(M) cable.

InsertionVSWR is highest at 1.01 @ 16MHz, at the limits of accuracy with this equipment. These 3kV 10pF ceramic capacitors have measured Q around 500 at 30MHz, expected loss is less than 200mW @ 1kW through.

The InsertionVSWR is not significantly affected by the quite small bending radius.

Voltage withstand

Does tight bending of this cable degrade voltage withstand of the balun?

Experience Hipot testing lots of baluns with this type of coax winding shows that the voltage withstand weakness is over the surface of the dielectric from braid to centre conductor, and pigtails of less than 15mm will flash over before internal flashover.

Alternative coax types

Coax with a solid PTFE dielectric is more suitable as the dielectric is harder and withstands higher temperatures before deformation.

Foamed dielectric cables are much more prone to migration of the centre conductor on tight bends, even at room temperature and are probably unsuitable for tight wraps.

Small diameter cables might seem the obvious answer, but they are higher in loss and will run at higher temperature.

Conclusions

Though the coax bend radius is substantially smaller than specification minimum bend radius:

• when first constructed, there was little evidence that the coax characteristic impedance was altered by the winding radius, and that the pigtails were the main contribution to InsertionVSWR; and
• after five years of service, the InsertionVSWR of the compensated balun is excellent, at the limits of accuracy of the test equipment and again, little evidence that the coax characteristic impedance was altered by the winding radius.

Solid dielectric coax may be quite satisfactory at static tight bend radius, subject to the temperature of operation and applied forces.

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.

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.

I have found you can never have enough of these things. It is very convenient to leave some measurement projects set up while work continues on some parallel projects.

Above is the kit as supplied (~$8 on Aliexpress). Note that it does not contain any male turned pin header… more on that later.

I was critical of Alixpress four years ago when I purchased the last one, but things have improved greatly in that time, to the point they are often faster delivery that eBay’s “Australian stock” sellers.

Carefully break off 7 x 7 way pieces of the turned pin female header and ‘dry’ fit them to the board, Now get two more pieces of header that are at least 7 way, and plug them at right angles to the ones already placed to set the spacing. Now solder them to the board (hint: liquid flux makes this job easier.) The ‘donuts’ are quite small, use a tip that gives contact to the donut so that heat is applied to the pin and the ‘tube’ for a good solder joint.

Test the coax connectors on a good male connector to be sure they are not defective… quality of these is poor. I tighten them to 0.8Nm to seat and form the female connector. If the threads bind, chuck them now rather than after you have soldered them in place.

I installed only the mid connectors on this board, I have another which has all the connectors and I have never used the other four. Carefully position and solder the connectors, again liquid flux helps.

The clear plinth does not come in the kit, it is my addition.

Above, the plinths designed in Freecad were cut out of 3mm clear PVC.

They are cut using a single flute 2mm carbide cutter.

You could easily make them with hand tools and a drill. M2.5×6 nylon screws are used to attach the plinth to the hex spacers (supplied), giving the assembly four non-scratch feet.

Now the kit is incomplete. You are going to need some parts you see above built on male turned pin header strip. The kit does contain some 49.9Ω resistors you can use for a LOAD, you will also need an OPEN (centre left) and a SHORT (lower right). Others are for connecting the sections of the test board and THROUGH calibration.

The SMA connector at left is another test fixture which uses the same calibration parts. It can be used directly on the NanoVNA or at the end of a convenient length of cable. I originally made it to use on a Rigexpert AA600, either on a N(M)-SMA(F) adapter, or a short N(M)-SMA(F) cable.

It is bit hard to see the connections on the board when it is populated, so I have made the graphic above, printed it and laminated it for handy reference.

Note that the connections are a little different to the SDR-Kits jig (that they probably copied), in particular C2, C6, E2 and E6 are each not connected to anything.

I have some custom made 300mm long RG400 cables that I use with these, labelled for calibration purposes. IIRC they cost about $30 per pair from RFSupplier.com.

The Airspy YouLoop is a no tune, broadband, small footprint, affordable LF to HF receive antenna that works indoors. Its modular construction facilitates experiments to understand where the Möbius inspired electrical design provides benefit.

The post Airspy YouLoop LF/MF/HF Möbius Receive Antenna appeared first on Ham Radio . Magnum Experimentum.

 Well,

Lots of discussions about my baluns and the test setup, a common question seems to be how to measure the output impedance.

Here's my way:

Fun, dont you think?

 How about this for a bit of bonkersness?

Fun, dont you think?