Common-mode Chokes (Baluns), Power Dissipation versus Effectiveness

Apropos my 80 meter loop, some notes I've made while thinking about common-mode chokes and feedline radiation...


One question I had -- how can I use EZNEC to model feedline radiation of a coax-cable feeding an antenna?

Let start by looking at a dipole fed with coax...


Feedline Radiation, Example 1: Coax-fed 80 Meter Dipole.

I'm going to start with an explanation that is also discussed elsewhere in excellent articles by the following authors (click on a callsign to be routed to their link): W0IVJ, W7EL, W2DU.


Let's take a look a a standard half-wave dipole up in the air, fed via coax from a grounded transmitter.  Like this:

(Note: dipole and coax drawn sideways for convenience)

The tight coupling between coax shield and coax center conductor forces the currents to and from the source to be equal and opposite while they are within the coax, with the current returning to the source flowing on the inner surface of the shield.

In other words, the coax itself acts as a very good common-mode choke (in the sense that it forces differential currents to return via the coax, rather than via a less desirable path). (For more information, please refer to: Noise Reduction Techniques in Electronic Systems, 2nd Ed., by Henry W Ott, page 51.)

But this common-mode choke behavior of coax stops at the ends of the coax, outside of which we can then have currents flowing on the outside surface of the coax, as shown below.

Note that I1 on the inner-surface of the coax (returning to the source) is composed of I2, the desired current-path in the dipole element, and I3, the undesired path on the coax shield's outer surface.  And note, too, that I1 flowing on the inner-surface of the coax shield is equal and opposite I1 flowing on the coax center conductor.

Given the currents, as drawn, above no current flows from ground directly to the source.  This lets us redraw the model without the source tied directly to ground:

Now the source only connects to the coax, and I have added a conductor (representing the outer-surface of the coax shield, with the shield's length and dimensions) that runs from the antenna-feedpoint end of the coax to back to ground near the source.

As long as we do not change the length of this conductor (representing the coax shield), we can move the source towards or away from the antenna feedpoint with no change in performance (assuming ideal, lossless, coax).  Like this:

Reducing the length of the coax in the above illustration to zero, our model reduces to:

Let's add our currents back in...

To minimize feedline radiation, we want to minimize I3, and the best way to do this is to add an impedance in the coax-shield-to-ground path at the source, which is actually the antenna feedpoint, not the original location of the source (at the other end of the coax), as shown below:

Let's assume we are inserting a large resistance as a choke (rather than a reactance, which could worsen I3 current if it series-resonates with the impedance of the coax-shield-to-ground).  How large does this resistance need to be to reduce I3 to an acceptable level?

Let's look at a worst-case model using EZNEC...


Feedline Radiation, EZNEC Model, 80-meter Dipole Fed with 1/2 Lambda Length of Coax:

This dipole's elements has been tuned to resonate at 3.5 MHz.  I will examine its currents and choking requirements at resonance (3.5 MHz) and at the other end of the 80-meter band (4.0 MHz).

The feedline length is 144 feet which, when represented by a conductor connecting one end of the dipole's feedpoint to ground (wire 5 in the EZNEC model, representing the coax shield's outer surface), results in maximum current flowing on this conductor.

(I did mention that this was a worst-case model, didn't I?)

Let's look more closely at the model.  Here's how the antenna is driven, at ground level:

...and here is how its feedpoint looks:

Notes:

1. The transmission line (ideal, Zo = 50 ohms, Vf = 0.66) runs from the center of wire 4 to the center of wire 2).
2. Note that one side of wire 4 connects to ground (via wire 7).  This will let me check if any currents flow from ground back to the source.
3. Wire 5 (and wire 6, which is in series with it down at the ground-end) represents the outer-surface of the coax shield (and thus the unwanted radiating path).
4. The little red square in wire 5 (up near wire 2) represents a choke in wire 5 at the dipole's feedpoint whose impedance I can vary to model its effect upon current in wire 5, as well as its power dissipation.

Here are the antenna's currents:

Note that very little current flows on the dipole arm represented by wire 3; it instead flows on the coax shield.

Not good!

But we can improve upon this by inserting a choke (represented by a resistance-only impedance) into wire 5 up at the antenna's feedpoint (near wire 2).

Here's the impedance I will insert:

And here is its effect on the antenna system's currents:

Much better!

(A quick sidebar...

What would happen if we were to place a choke at the source-end of a feedline, when the feedline is 1/4 lambda long?

First, let's examine the currents with no choke: 

Looks good!  (Note that the current for wire 7 (from one end of the source to ground) is shown to demonstrate that, within the limits of the EZNEC model, essentially no current flows from ground to the source)

Now let's add the choke (5000 ohms in wire 6)...

Now we have feedline radiation!

So the point is:  When in doubt, with an antenna system in which the antenna is fed with coax, choke at the antenna's feedpoint, NOT at the transmitter.

...end of sidebar).

Let's look at how different values of choking resistance affect wire 5's current, and how much power is dissipated by this resistance.

If we use G3TXQ's criteria of reducing the unwanted current by 30 dB, then a choke with 800 ohms resistance is sufficient to achieve this goal (note that, given the EZNEC source amplitude of 1.0 Amps, a 30 dB reduction would be 0.03 amps).

Here is a table summarizing the results of different choke impedances at 3.5 MHz:

Note that if I have an ineffective choke (e.g. 20 ohms, resistive), it could dissipate quite a bit of power!


What happens to currents if we tune our transmitter to the other band edge at 4.0 MHz?

Without any CM choke inserted, here are the antenna system's currents at 4 MHz:

There is some feedline radiation, but not as bad as the antenna system at 3.5 MHz.  But this isn't surprising, because the feedline length is no longer 1/2 lambda long, so the impedance it presents at the antenna's feedpoint will be higher.

But, my goal is to look at currents in the worst-case scenario.  So let's say that we were to add, at the dipole feedpoint, a choke whose reactance series-resonates with wire 5's reactance.

Also -- to more easily determine when the common-mode current is 30 dB down from the source current, I'm going to move the source up to wire 2 (the antenna's feedpoint) and eliminate the transmission line.  We can do this because EZNEC's transmission line is perfect and does not radiate -- we are using wire 5 to represent the "imperfect" part of the transmission line which radiates.  To illustrate this point, note that the current distribution of the "source-at-top" (i.e. in wire 2) antenna system, shown below, is essentially the same as the current distribution of the "source-at-ground" (i.e. in wire 4) antenna system, shown above.

With the source now at the top (wire 2), the source's current at that point is 1.0 A, rather than some other value with a phase angle.  And so to meet the G3TXQ criteria, I simply need to increase the choke's resistance in wire 5 until the current through the choke is 30 dB down from the source's current in wire 2.

But first, let's force the current in wire 5 (representing the radiating feedline) to be maximum (it's a worst-case analysis, after all).

If I add some reactance (-j350 ohms) as the series-load in wire 5 and adjust its value for maximum feedline current,  the current through the choke is maximized, and the antenna currents become:

Note the increase in feedline (wire 5) current!.

Here's a summary of different choke impedances for the off-resonance dipole:

Notes:

1. 90 ohms resistance exhibits max power dissipation.  And it is a LOT of power!
2. Even at 1000 ohms of resistance, 14 percent of the transmitter power is dissipated in the choke.  That is a lot.
3. The choke's resistance must be at least 4000 ohms to reduce the unwanted feedline current to 30 dB below the transmit current.  At this level, the power dissipated in the choke is 4.2 percent of the total power.

And again, I want to stress -- I am looking at worst-case scenarios!


Next, let's look at a full-wave coax-fed loop...


Feedline Radiation, Example 2: 80 Meter Full-Wave Loop.

Let's look at a Full-Wave 80 meter loop, cut to be resonant at 3.5 MHz and again (like the dipole) feed from a grounded source with 144 feet of coax.

From my discussion, above, the source itself is effectively isolated from ground due to the common-mode choke behavior of the coax cable, itself.  So I can simplify my model (just as I did when examining dipole currents at 4 MHz, above), and move my source to wire 6 at the loop's feedpoint.

Below is the loop.  Note that wire 5 simulates the coax shield's outer-surface that connects one side of the loop feedpoint to ground, below:

Here's a closeup of the feedpoint, as well as data on the source and data on the series-load (which will be used to mimic a choke) in the first segment of wire 5.

And here are the currents:

Note the huge difference in at-resonance (3.5 MHz) currents from the dipole (earlier, above).  Even though this loop has the same feedline path to ground as the dipole (simulated by the 144 foot conductor to ground), it has very little feedline current.

You can see that this feedline current is already 34 dB below the source's current (compared to 1 Amp), so: no choke is needed when the loop is operated at resonance.

Let's see what happens if we move the transmit frequency to the other side of the band (4 MHz)...


What happens to currents if we tune our transmitter to the other band edge at 4.0 MHz?

Now there are common-mode currents:

The magnitude of the current on the coax shield, near where it attaches to the feedpoint (and at the point where I will insert a choke), is 1.44A.

I can simulate worst-case feedline current by inserting  +j110 ohms (inductive) in series into the feedline common-mode current path (inserted close to the loop's feedpoint).  In this case, the current is 1.716 Amps.

To continue examining this worst-case scenario, let's keep this reactance of +j110 ohms, and add to it different values of resistance while examining how this resistance lowers the common-mode current as well as its power dissipation.

This table summarizes the results:

Notes:

1.  When operated off-resonance, the choke's resistance must be 10,000 ohms to reduce the worst-case common-mode current down to a level at least 30 dB below the transmit current of 1 amp (per G3TXQ criteria).

2.  Significant power dissipation can occur even at fairly large values of resistance.  Note that with a choke resistance of 4000 ohms, the power dissipation is 10 percent of total power.


So my conclusions, comparing worst-case Common-Mode radiation scenarios on Dipole and Loop coax feedlines, are:

1.  An 80 meter loop, at resonance, requires little common-mode choking.  The 80 meter dipole will require a choke.

2.  A loop, off resonance, can require significantly more common-mode choking (at least twice as much) than a dipole fed with the same length of coax.

3.  More power dissipation will occur in a loop's choke compared to a dipole's choke of similar resistance and worst-case reactance values.

My Balun (and 80-Meter Loop) posts:

80 Meter Loop, Part 1:  http://k6jca.blogspot.com/2018/05/adventures-with-80-meter-loop-antenna.html

80 Meter Loop, Part 2:  http://k6jca.blogspot.com/2018/05/adventures-with-80-meter-loop-antenna_30.html

Balun Power Dissipation:  http://k6jca.blogspot.com/2018/06/common-mode-chokes-baluns-power.html

Notes on 1:1 Baluns:  http://k6jca.blogspot.com/2018/06/transmit-common-mode-chokes-11-current.html

Notes on Common-Mode Currents:  http://k6jca.blogspot.com/2018/07/thoughts-and-notes-common-mode-current.html

Y21 Method of Measuring Common-Mode Impedance:  https://k6jca.blogspot.com/2020/07/the-y21-method-of-measuring-common-mode.html

A 3-Port Method for Characterizing Baluns:  http://k6jca.blogspot.com/2020/06/another-method-to-characterize-baluns.html

Standard Caveat:

I might have made a mistake in my designs, equations, schematics, models, etc.  If anything looks confusing or wrong to you, please feel free to comment below or send me an email.

Also, I will note:

This design and any associated information is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Adventures with an 80 Meter Loop Antenna, Part 2: Adding a 1:4 Current Balun (Guanella Balun)

In my previous 80-meter loop post, I showed that the measured SWR and the predicted power loss for the (roughly) 100 foot coax-only feed looks like this:

The coax performance is satisfactory, but in some ways underwhelming: very narrow SWR dips on the low bands and poor minimum SWR on the high bands.  Plus, there is significant power loss in the coax when the SWR is high (keep in mind that 3 dB of loss in the coax means that half your power is being lost there).

Could I do better?

The Case for Adding a 1:4 Balun:

As I mentioned in my previous post, Dick Benson, W1QG, thought the addition of a 1:4 balun (50:200 ohms) would improve performance.

I used SimSmith to model the concept and calculate loss, assuming an ideal 1:4 transformer in conjunction with the measured coax s-parameters.  Here's a table from that previous post summarizing the performance improvement:

From that post, my conclusions were:

1. The coax-only feedline beats the ladder-line/coax combination feedline on 80 through 20 meters.
2. Above 17 meters, the ladder-line/coax combo beats the coax-only feedline.
3. If we add a 1:4 transformer (in this case, lossless) to the coax-only feedline (attached at the loop), the coax-with-transformer combo beats all (although there can be an additional 0.4 to 0.5 dB loss on 80 and 40 meters, worst case). 
4. At the band edges on 10 meters, almost half the power is lost in the feedline, best case (with coax and 1:4 transformer)!

(A quick note on the above table: I used SimSmith to model the antenna system and calculate loss for the table, above, but this is a labor intensive process because, for each frequency, I needed to calculate the appropriate values for a matching network in my previous blog post.  In this post (further below) I will use a Matlab function, "powergain()" to greatly simplify the process of determining loss).

So that next step was clearly to build a 1:4 balun.  This post describes that process.

But before I get to that, first, a note on test equipment...

Test Equipment:

Good equipment takes the guess work out of design and verification.  I will be using the following equipment:

·  HP 4191A RF Impedance Analyzer, with 16093A Test Fixture.

The 16093A fixture is rated to 250 MHz.  It has 1.8 pF of stray capacitance and 1.8 nH of residual inductance.

Note that the 4191A is actually a one-port Vector Network Analyzer that measures S11.  Its directional coupler is temperature-controlled via a heater and temperature-control circuit.  It is recommended that the unit warm up for at least 40 minutes before calibrating it.

Although HP recommends calibrating the 4191A at its APC-7 connector and then applying 0.34 cm electrical length to compensate for the 16093A fixture, I prefer to calibrate the 4191A at the 16093A's terminals.  This procedure does not require expensive APC-7 calibration standards, and at frequencies up to 30 MHz (i.e. my testing range), it seems to better remove the effect of the fixture's stray capacitance of 1.8 pF.

·  HP 3557A Network Analyzer, HP 35677A S-Parameter Test Set.

This is the network analyzer at my wife's QTH (where this loop antenna is installed).  The 3577A only allows minimal calibration, and, unfortunately, a full 2-port calibration (open,short, reference-load on each port, plus through) must be done to get accurate results, as I've proven to myself during this testing.

To get around the device's calibration limitations, I use two Matlab applications written by Dick Benson, W1QG.  These applications are vna_s11.m and vna_gui_1.m, and they capture, display, and store the VNA's measurement data.  But they also allow full 2-port calibration data for the 3577A to be created and stored externally and then applied to the measurements.  I can testify that this is a great feature!

(Note -- this calibration uses a "12 term" correction algorithm.  As Dick points out (after much testing and simulation with Simulink) of an 8 term correction algorithm, "the 8 term algorithm works perfectly as long as the hardware requirements are satisfied.The 3577a / 8753x do not meet the requirements, but the HP 8510x,  and no doubt other VNAs, do.  The 12 term is the right choice for what we have."

·  HP 8753C Network Analyzer and HP 85046A S-Parameter Test Set.

(At my home QTH.)

Note:  All of this equipment has GPIB interfaces.  These interfaces allow me to connect the test equipment to my computer and use Matlab routines to download, plot, and analyze measurement data.  (Note:  I use an inexpensive Agilent 82357B USB-GPIB Interface dongle to connect my computer the the test equipment).


OK.  Back to baluns...


1:4 Balun Goals:

There should be a 1:4 Impedance Transformation: with 200 ohms at the output, the input should look like 50 ohms.

The balun should be low loss for both differential and common-mode signals.

The balun should have a high common-mode impedance, if possible.  And this impedance should have a large resistive component (because the reactive component could series-resonant with the existing common-mode impedance, in which case it is only the resistive component that will limit common-mode current).  Read more on the topic here:  G3TXQ Common-mode Chokes.)

Note that the Impedance Transformation is this balun's primary function.  High Common-Mode (CM) impedance would be nice, but not at the expense of the 1:4 transformation.  After all, if more CM choking is required, CM chokes (e.g. 1:1 current baluns) can be added in series.


Designing the Balun:

The next questions for design are:

• What winding topology?
• What Ferrite Mix and core size?
• What size wire?

The three topology choices were Guenella (current-balun), Ruthroff (voltage balun), and Trask.  After much reading (refer to links at the end of this post), I decided upon the Guenella topology, its advantage being that it provides some degree of common-mode choking in addition to the 1:4 impedance transformation.

Note the note in the drawing above!  Often, schematics of this balun do not show the winding "polarity" dots.  They are especially important if winding on a single core, as can be easily shown with a SPICE model.

Jerry Sevick, W2FMI, has a design for a 1:4 Guenella balun in my copy of the 2nd edition of his book, Transmission Line Transformers.

His design used a single Mix K FT-240 core, and each transformer consists of 6 windings on this common core.  (Note:  FT-240 Mix K cores available from Amidon).

(Note too that, for common-mode signal rejection, the two transformers, each wound on a separate core, is preferable to the two transformers wound on a common core.  Refer to the links at the end of this post).

From other experiments I determined that Mix 31 gave great common-mode choking, and I initially constructed a balun consisting of 10 turns on each of two FT-240 cores.  But this seemed to have more loss than I deemed acceptable. (Note: this loss might have been measured incorrectly (without sufficient common-mode choking on the Vector Network Analyzer's (VNA) S-Parameter Test Set's ports) -- so don't nix the idea based solely on my experience).

So I thought I would give Sevick's design a try, but with a separate core for each transformer.  In other words, the balun would consist of two FT-240 Mix K cores, each with a 6-turn transformer wound on it.  It is the balun on the upper-right in the image, below (the lower balun is the Mix 31 balun):

Building the 1:4 Balun:

The transmission line used for the balun's windings should have a characteristic impedance that is the geometric mean of the input and output impedances.  In this case, they are 50 and 200 ohms, which results in a Zo of 100 ohms.

I know that Cat 5 twisted-pair has a characteristic impedance of 100 ohms. But the gauge of Cat 5 twisted-pair, in my opinion, is insufficient for a transmitting balun.  Could I make my own 100-ohm twisted-pair transmission line with thicker wires?

Selecting the wire:

A popular wire selection for transmit baluns seems to be common THHN wire (usually available at hardware stores).

THHN insulation is rated at 600V breakdown between the conductor and external conduit.  So two pieces of THHN wire, side-by-side, should have a 1200V breakdown (given that there is now 2 layers of insulation between the two conductors).

(Note:  I am assuming that the 600V rating is PEAK VOLTAGE, not RMS).

Measuring characteristic impedance:

What would be the impedance of a twisted-pair transmission line made with 14 AWG THHN solid wire?  (Note:  from my experience, solid wire can be twisted into a twisted-pair much more easily than stranded wire).

Easy enough to check with my network analyzer.  Here's how I did it:

I made the length of twisted pair about 5 to 6 feet long.  I then connected one end of the twisted-pair to my network analyzer and to its other end I attach a 50 ohm load, as shown in the drawing, below.

The frequency span should be from the VNA's lowest frequency to a frequency that gives an intersection with the X axis of the Smith Chart (reactance = 0).  Adjust the Stop frequency until you see this second intersection (the first one being the start, at 50 ohms, assuming your start frequency is low enough).  As frequency increases from the lowest frequency to highest you will see a half circle (or more) traced on the Smith Chart.  The center of the circle (which should lie on  the real-axis of the Smith Chart) will be the transmission line's characteristic impedance, Zo.

So:  at very low frequency, the circle should start at 50 ohms.  As frequency increases, the trace will follow a circular pattern and will eventually intersect the real-axis (imaginary component = 0) again.  (This is when the transmission-line is a quarter-wavelength of the frequency when it intersects this axis.).

Note the resistance value at this upper frequency.  Let's call it Rupper.  Zo can then be calculated from the following formula:

Zo = SQRT(50 * Rupper)

Here's an example:

For demonstration purposes I twisted together about five feet of 12 AWG THHN stranded wire (note: solid wire twists together much more easily than stranded -- the stranded wire has a tendency to want to unravel or kink).

Turns per inch were roughly 1 turn per 2 inches.

I then connected it to my VNA per the diagram, above:

Here's the S11 plot:

In this example, Zo calculates to be 109 ohms, which is close enough to 100 ohms for my purposes.  Note that for twisted-pair made from 14 AWG THHN solid wire, I measured a Zo of about 93 ohms.  Again, close enough.


Winding Technique:

Here are two examples of 1:4 baluns (with twisted-pair made from 14 AWG THHN solid wire), using different number of turns and ferrite mixes.

The balun on the lower left consists of 10 turns of twisted-pair on each of two FT-240 Mix 31 cores.  The balun on the upper right consists of 6 turns of twisted-pair on each of two FT-240 Mix K cores.

Note that I use the winding technique that I will call "crossover (from "Simple and Efficient Broadband Balun", by Joe Reisert, W1JR, in the September, 1978 issue of Ham Radio magazine):

A Note on the Crossover Winding Technique:

I'll note that W8JI does not like this technique, as he points out here.  From my own measurements, though, I see little difference, and sometimes impedance and range can even seem to be increased using the "crossover" technique.  Below are some comparisons I made with my HP 4191A RF Impedance Analyzer (data captured via GPIB and plotted with a Matlab script I wrote):

First, some small-gauge wire (20 AWG) tests...

12 and 11 turns, normal winding technique, versus 12 turns "crossover" technique (Mix 43 FT-240).

12 and 11 turns, normal winding technique, versus 12 turns "crossover" technique (Mix 43 FT-240).

Now 12 AWG wire.  Normal versus crossover, 8 turns, on two FT-240 cores: one Mix 31, one Mix 43:

Finally, 12 turns of 12 AWG wire on one FT-240 core...

...and the winding styles for the plots in the figure, above:

As you can see, for the most part there isn't much difference between normal and crossover winding techniques.  For smaller AWG wires, perhaps the crossover technique is a bit better.  For larger AWG wires, the techniques are roughly the same (and in one example, above, the crossover is slightly worse), at least with the examples I've shown, above.

Additional testing would provide more conclusive results -- one of my old bosses would recommend that at least 30 different coils be wound for each of the four winding techniques pictured above (i.e. 120 coils, total), as 30 was the minimum number required to get statistically significant results.

Not something I want to do for this "one-off" design.  But I invite others to experiment!

Update, June 10, 2018.  I have discovered that the HP 4191A is not a great device for measuring the impedance of components with large amounts of conductive material (such as the four chokes, above).  Parallel capacitance effects due to coupling-to-ground of this material will lower resonant frequencies.

I repeated my winding tests using a different impedance measurement technique, as described in this blogpost.  My conclusion is still the same, but hopefully the results are more accurate.


Preliminary Testing:

Zin when Zload = 200 ohms:

On bench with an 0805 chip 200 ohm load on the back of a female SMA connector.

Same load, but balun now in case.  (Load is further away, though, due to N connector and adapters...)

You can see that there is some difference in the balun's input impedance (with 200 ohm termination) after it was installed in the plastic case.  Part of this difference is surely due to the long extension added between the 200-ohm port of the balun and the 200 ohm test load (and note that the adapters do not have a characteristic impedance of 200 ohms).

But it's close enough to 50 ohms for this application.


Common-Mode Impedance:

I typically measure a device's common-mode impedance by first shorting a device's input port, shorting its output port, and then measuring the impedance between the two ports, as shown in  the following diagram from TDK:

For this particular balun, here's how I connect it to measure its common-mode impedance with my HP 4191A:

And here's an actual measurement...

(The holes in the case are to provide convection cooling).

...and the results:

Resistance drops off at lower frequencies, so additional common-mode chokes should be added to the feedline to minimize common-mode radiation by increasing the resistive component of the series choking impedance (should common-mode radiation be an issue).


Predicted Power-Loss based upon Bench Measurements:

I first tried to determine balun loss by measuring its S11, S12, S21, and S22 parameters of the balun, stand-alone on the bench.

This s-parameter data (stored in an S2P file) can be combined with the coax S2P file (captured for the loop coax) and the Loop's S11 data to predict balun loss, in dB:

However, regarding these curves, please note:

1. Coax two-port s-parameters were measured without 3577A calibration (I did not have Dick Benson's latest and greatest program at the time) -- so it is probably inaccurate to some extent.
2. Also -- there was probably insufficient common-mode choking on my 8753C's S-Parameter Test Set's ports when I measured balun two-port s-parameters.

After I arrived in Nevada City with my balun (see below), I decided that my bench testing of the balun with the 8753C was not sufficient, for the reasons above.  Additional loss testing is described, below.


Installing the Balun:

Return to Nevada City, connect the 1:4 balun case, add additional Common-mode chokes (1:1 current baluns), and raise...

Ready to Raise!

Note the 1:1 CM chokes in the coax cable: 3 turns through Mix 31 Clamp.  5 turns through 2 Mix 43 and 2 Mix 31.  5 turns through 4 Mix 43.

(Note:  these may be poorly designed chokes -- I slapped them together because they were what I had in hand.  I need to do more experimentation...)



Measurements, with Antenna:

First, let me note:  all measurements were made with a full 2-port calibrated 3577A Network Analyzer (unlike the earlier measurements shown in the plots and table at the start of this blog post).  So you will see some differences if you compare earlier measurements to these measurements.


SWR:

SWR can be derived from S11 data (This S11 data is also stored in S1P file format.)

As part of my testing, I made the following three S11 measurements:

Measuring S11 of the Loop with coax-only feed:

Measuring S11 of the Loop with 1:4 Balun at its Feedpoint and coax feed:

Measuring S11 of the Loop's Feedpoint at the antenna-end of the coax:

These three S11 measurements are converted to SWR and plotted using Matlab.  Note the y-axis log scale!

Let's look more closely at the two curves representing the SWR a transmitter would see with and without the 1:4 balun:

The 1:4 balun has slightly worse SWR at resonance on 80 and 40 meters, but this is offset by a broadening of the SWR dips.

And on the higher bands, SWR at resonance, and the breadth of its dip, is improved by the 1:4 balun.

So, if SWR is the important metric, the 1:4 balun provides a noticeable improvement!

But I can get a great SWR with a 50 ohm resistor.  How do I know if RF energy is being effectively sent to the antenna, rather than lost through heat?  How do I know that I haven't gained the SWR improvement through the balun acting as a dummy load?

Fortunately, with s-parameter measurements of the feedline, balun, and load, we can calculate power loss...


Determining Power Loss:

These are the losses I want to determine:

We can use S-parameters to calculate Coax and Balun power losses.  To do this, I will calculate the "Operating Power Gain", Gp, for the following 2-port networks:

• Coax Feedline
• Coax Feedline-plus-Balun

Because these networks are both passive, there will only be loss, not gain.  We can then calculate the Balun loss by simply taking the difference between Coax+Balun loss and Coax loss.

Note:  Balun loss could also be determined for the balun itself as a stand-alone 2-port network.  But, because my specific 1:4 balun has a "balanced" output, additional Common-Mode choking is required to sufficiently isolate the balun from the VNA's Test Set ports (which are both unbalanced with a solid ground connection between the two connectors.

When I made these measurements I felt I did not have a sufficient supply of Common-Mode chokes to adequately isolate the 1:4 balun, itself, from the S-Parameter Test Set's ports (most of my spare FT-240 Ferrite cores were already used as 1:1 baluns on my RG-8 feedline's coax), and so I thought it best to leave the balun connected to the coax feedline (because there were already common-mode chokes on this feedline coax) and determine balun loss by taking the difference between Coax+Balun loss and Coax Loss.

Using Matlab to Calculate Loss:

I use Matlab's powergain function (in Matlab's "RF Toolbox") to calculate Gp.  Specifically,

g = powergain(s_params,z0,zl,'Gp') calculates the operating power gain of the 2-port network.

where: s_params are the 2-port network's s parameters (S11, S21, S12, S22), z0 is the Reference Impedance (50 ohms, for these calculations), zl is the Load Impedance seen by the 2-port network (e.g. the input impedance of the Balun+Loop if the 2-port network being analyzed is the coax), and 'Gp' identifies that "Operating Power Gain" will be calculated.

In addition to the S11 captures described above, the following diagrams describe how s-parameter data is captured for my two-port networks (S11, S21, S12, S22, all stored in S2P file format), and one additional single-port network (i.e. "load") s-parameter data (S11 data, stored in S1P file format).

Single-Port S11 data (stored in .S1P file):

This is a single-port measurement of the Loop-plus-balun's S11, measured at the balun's 50-ohm input port.

Two-Port S11, S21, S12, S22 data (stored in .S2P file):

The following diagrams show the connections and procedures for capturing the 2-port s-parameter data for five different 2-port networks:

· 2-Port Network = Coax-only:

· 2-Port Network = Coax-and-Balun:

(Note:  The coax feedline in the diagram above has a number of common-mode chokes integrated into it by winding coax through FT-240 Ferrite cores.)

· 2-Port Network = Coax-and-Balun (with Common-Mode Choke) -- note change in Test Set Port 2's Reference Plane:

(Note:  The coax feedline in the diagram above has a number of common-mode chokes integrated into it by winding coax through FT-240 Ferrite cores.)

· 2-Port Network = Coax (with Common-Mode Choke) -- note change in Test Set Port 2's Reference Plane:

(Note:  The coax feedline in the diagram above has a number of common-mode chokes integrated into it by winding coax through FT-240 Ferrite cores.)


Estimating Measurement Accuracy:

Why did I measure so many different feedline configurations?

I wanted to ensure that I could make an accurate loss estimate for the balun, but how would I know if my data was accurate?

So I measured s-parameters with and without a common-mode choke on port 2 of the S Parameter Test Set.

With these various S2P files, combined with appropriate S1P files representing the load impedance for a particular test case (i.e. loop with balun, or loop without balun), I could predict the SWR with and without the 1:4 balun.

If a prediction was very close to the actual measured SWR, I could feel fairly comfortable that the S1P and S2P files used to create this prediction accurately reflected the physical antenna and feedline, and that, therefore, any loss I calculated with these files would probably accurately reflect actual system loss.

Here are the two measured SWR curves (with and without 1:4 balun), and six predictions (using the S2P files from the configurations, above):

For the Loop with coax-only feedline, to me it's a toss-up between the two SWR predictions.  I've chosen to use the "yellow" line (w/o common-mode choke), but I could just as easily make a case for the purple line.

But the SWR of the loop with coax-only feedline is really just for reference.  As long as the prediction is close to the actual measurement, I'm satisfied.  I'm much more interested in the accuracy of the SWR prediction when the 1:4 balun is part of the system...

Let's look more closely at the SWR and the SWR predictions with the 1:4 balun as part of the system:

Three predictions are very close to the actual measurement.  But there is one that deviates significantly more, and that's the coax-and-balun s-parameter measurement without the common-mode choke on the S Parameter's Test Set Port 2 (which highlights the point:  you have to be careful when measuring balun s-parameters on a VNA.)


The Matlab Loss Results:

Using the deemed "accurately predictive" S1P and S2P files, I could then calculate coax and coax-plus-balun losses, and then take the difference of these two values to determine balun loss.  (Keep in mind, I'm not measuring the loss of the balun itself as a stand-alone 2-port network because I'm concerned I don't have sufficient common-mode chokes at my S-parameter test set ports to properly isolate it from the Test Set).

For example, the Matlab equations to calculate coax loss (Gcoax) for the "coax-only" feed case (no 1:4 balun) are:

% Get S1P and S2P file data:
s= '180528 3577A NC Loop, Loop-only, cal at Loop end (no balun).s1p'; 
[Loop_Obj,Antenna_Notes,Antenna_State]         = spar_read(path,s);

s= '180528 3577A NC Loop -- Coax-Only.s2p';                   

[Coax-only_Obj,Coax_Notes,Coax_State]            = spar_read(path,s);

% Get Zo (assumed 50 ohms for all s-parameter files)

Zo = Loop_Obj.Z0;  

% Calculate the impedance at the loop's feedpoint from its Gamma:

Z_Antenna_no_Balun = gamma2z(Loop_Obj.S_Parameters,Zo);

% Calculate coax loss with the antenna as its load

Gcoax = powergain(Coax-only_Obj.S_Parameters,Zo,Z_Antenna_no_Balun,'Gp'); 

And that's all there is to it!

Below are the losses, plotted:

The plots, above, visually show trends.  The table below shows the actual calculated values at the ham-band edges (and at the SWR minimum, if this minimum occurs within a ham band):

(Note that the colors of the colored columns match, roughly, the colors of the plot-lines in the plot, above, with which they are associated).


Calculating Balun Peak Voltages versus Drive Power:

As mentioned earlier, the THHN wire's voltage rating of 600 Volts means that the twisted-pairs breakdown voltage should be 1200 Volts, peak.  I should verify that the voltages on each transformer's winding is within this range for likely drive powers (e.g. 200 watts).

To make this calculation, first consider that the balun input with the loop as its load is a complex impedance, as is the loop's feedpoint.  Assume that in the "matched" condition all power from a source (i.e. Transmitter) is delivered to a load (e.g. the load can be either the loop's feedpoint impedance or the balun-with-loop-as-load input impedance (at its 50 ohm port)).  This "delivered-power" must be completely dissipated by the load's resistive component (the reactive component dissipates no power).

So, given the measured impedance of either the Loop's feedpoint or the balun input, calculating peak voltage across either should be straightforward.  All of the power must be dissipated by the resistive component of that impedance.  That will determine the voltage across this resistance and the current through it (V = sqrt(P*R), I=V/R).  The reactance, because it is in series with the resistance, sees the same current and thus we can calculate its voltage.  Finally, the total voltage across the load is simply the sum of these two series-voltages.

Here's my Matlab calculation for peak voltage at the loop feedpoint (i.e. balun output):

% Matlab calculation of 
% Peak voltage at Loop Feedpoint,
% given a drive power of 200 watts:

P200 = 200; % Watts
% Loop Impedance Real component:
resistance = real(Z_Antenna_no_Balun);
% Loop Impedance Imaginary component:
reactance = imag(Z_Antenna_no_Balun);  
% For the given power, calculate 
% voltage-across and current-through
% the load's resistance:
vr200 = sqrt(resistance.*P200);        
ir200 = vr200./resistance;
% Reactance is in series with resistance,
% so use current to calculate Voltage
% across reactance.
vx200 = ir200.*reactance;
% total voltage is the addition
% of these two voltages.  And 
% because one is only real and the
% other is only complex, creating
% the complex number effectively
% adds them together (i.e. = vr + jvx).
vdrive200 = complex(vr200,vx200);
% Calculate magnitude and peak of voltage.
vabs200 = abs(vdrive200);              
vpeak200 = squeeze(vabs200*1.414);     

Here's the calculated voltage at the balun's input, plotted for 200, 800, and 1500 watts:

To satisfy the THHN wire insulation rating, peak voltage should be less than 1200 volts.  Per the plots, above, this condition is met for all ham-bands, except 60 meters, for 1500 watts of drive power.

And here's the calculated voltage at the Balun's output (i.e. the loop feedpoint):

Assuming that the balun output voltage is equally divided between the two transformers, then the total peak voltage across the balun's output should be less than 2400 volts, peak (i.e. 1200 volts, peak, across each transformer), to satisfy the THHN rating of 600 Volts.

Per the plots, above, this condition is met for all ham-bands, except 60 meters, for 1500 watts of drive power.

Important note:  this 2400-volt rating assumes that the windings of one transformer do not touch the windings of the other transformer.  If these windings touch (especially the high-end output to the low-end output), then the maximum rating at the balun's output reverts back to 1200 volts, peak, and there is the possibility of arcing at high powers.

So make sure you provide an air gap, or insert an insulator, between the two transformers!

Conclusions:

· Compared to the loop with a coax-only feedline, the measured results of the loop with the 1:4 Balun look good!

To summarize:  below are graphs of performance in the ham bands from 80 through 10 meters. (excluding 60 meters), Note that the end-points of each curve actually extends slightly past a band's edges, because the frequency steps of the VNA's sweep did not align with band-edge frequencies.  So I have plotted the curves using the closest frequencies to the band edges that are outside each band.

SWR:

Losses:

Peak Voltage at Balun Input and Output, for 1500 watts drive power:

· Actual common-mode impedance (with CM chokes in coax) is unknown.

· Note that this design is probably not an optimal design -- it would be interesting to experiement with other ferrite mixes and core sizes.

And finally, I want to stress:  my conclusions are applicable to this balun used with this loop antenna.  Results should be similar if applied to other full-wave 80 meter loops (whose feedpoint impedances should be in the same ballpark as mine), but please do not assume that these results will apply to other antennas!

Sidebar:  A Matter of Nomenclature...

Anyone searching the web for balun information will quickly discover that the terms "1:4" and "4:1" seem to be used interchangeably when describing a balun that converts 200 ohms to 50 ohms.  Which is the correct term?

Should it be 1:4 or 4:1 if the goal is to transform a 200 ohm load to 50 ohms?

Input-to-output impedance is the common form that has been used for years for impedance matching transformer, such as a "10:1" audio transformer that might be used to transform a low-impedance speaker into a high impedance for a tube amplifier.  Which would mean that a transforming a 200 ohm load to 50 ohms would require a 1:4 transformer.

And this is the form used by Jerry Sevick, W2FMI, in his book "Transmission Line Transformers" -- it can also be found in the ARRL Handbook (e.g. the "Guenella 1:4 Transformer" shown in figure 20.21 of the 2017 ARRL Handbook.

But others use it to define the "balanced" side to the "unbalanced" side ratio.  So, in the case of 200 ohms on the balanced side and 50 ohms on the unbalanced side, the ratio is 4:1 instead of 1:4.

Personally, I prefer 1:4.  But, à chacun son goût!

Useful Choke and Balun Links:

These are links I have found useful.  I've added notes, where appropriate.

Common-Mode Choke Basics (as applied in switching power supplies):

ST Common Mode Filter App Note, AN4511 (Good): http://www.st.com/content/ccc/resource/technical/document/application_note/d2/4d/6f/9d/bc/80/4d/97/DM00119609.pdf/files/DM00119609.pdf/jcr:content/translations/en.DM00119609.pdf

Keysight (Model): http://powersupply.blogs.keysight.com/2011/11/should-i-use-switching-or-linear-dc_29.html

·         Note model of Common Mode Noise Current and Path.

Balun Basics:

DX Engineering (W8JI):  Choosing the correct balun

Ruthroff, C.L.: Some Broad-Band Transformers. Proceedings of the IRE, Vol 47, No. 8, August 1959, pp. 1337-1342.

·         The classic article on broad-band transformers.

W7EL, “Baluns: What They Do and How They Do it”:  http://www.arrl.org/files/file/History/History%20of%20QST%20Volume%201%20-%20Technology/AntComp1-Lewallen%281%29.pdf

Good primer.

W2DU, “Some Aspects of the Balun Problem”:  http://rfcec.com/RFCEC/Section-3%20-%20Fundamentals%20of%20RF%20Communication-Electronics/08%20-%20BALUN/01A%20Balun%20-%20Reflections%203rd%20Edition%20Chapter%2021%20-%20Some%20Aspects%20of%20the%20Balun%20Problem%20(By%20Walter%20Maxwell%20W2DU).pdf

Good discussion of balun basics as well as the W2DU bead balun.

W2FMI (Sevick), “More on the 1:1 Balun”:https://www.nonstopsystems.com/radio/pdf-ant/balun-sevick.pdf

Good review of 1:1 balun articles.

DX Engineering (W8JI?): 

 https://www.dxengineering.com/techarticles/balunsandfeedlinechokes/balun-basics-common-mode-vs-differential-mode

·         Discussion of the basics.

·         Myth:  equal conductor currents (if measuring only current magnitude) mean a feedline is balanced, because does not include phase info. 

·         Better to measure current sum by placing a current-sensing clamp over both conductors.

·         Check at two points 1/8 lambda apart.

·         Common rule of thumb of 10-to-one CM impedance to DM impedance is not always correct.

Marki Microwave: Balun Basics Primer

Introductory PPT presentation: http://www.hbphoto.com/Radio/Baluns_101.pdf

·        States that a 4:1 Guanella Current Balun should be made with 2 cores, but note that his 4:1 Ganella Current Balun schematics (pages 18 and 19) show the polarity dots of the two 1:1 transformers on different ends of each transformer, which is what they would need to be IF WOUND ON A SINGLE CORE.  (If wound on 2 cores, don’t really care which end the two dots are on, as long as each dot within a transformer is on  the same end as its other dot).

·        Also describes the Trask single-core 4:1 Current Balun.

Transmission-Line Transformers:

Philips xfrmr app note.   https://www.radio-kits.co.uk/radio-related/Linear_PA/ECO6907.pdf

·         Good App Note on “Design of HFWideband Power Transformers.

·         Section 6.3 describes a 1:4 Impedance Transformer (note that it is 1:4, NOT 4:1).  But wound on a single core, not two cores.

·         Note that Fig. 24 shows a 1:4 transformer (12.5 to 50 ohm) with an additional 1:1 common-mode choke.

K5TRA transmission line xfrmrs: http://k5tra.net/tech%20library/RF%20transformers/Transmission-Line%20Transformers.pdf

·         An informative power-point presentation of Transmission-Line Transformers, including overview as well as PA applications.

Trask, transmission line xfrmrs: http://home.earthlink.net/~christrask/TraskTLTTutorial.pdf

·         Tutorial on Transmission Line Transformers.

Measuring an Antenna System's Common-Mode Impedance:

W8JI, Links for Common-Mode Impdedance:

·         https://www.w8ji.com/common_mode_current.htm (Note: short feed line terminals and feed the antenna system as a single wire antenna)

·         https://www.w8ji.com/balun_single_core_41_analysis.htm (part of 4:1 balun discussion)

W9CF “Putting a Balun and a Tuner Together:  http://fermi.la.asu.edu/w9cf/articles/balun/balun.html

·         Modeling a 2-wire transmission line as a 3-terminal device and measuring the three values of that model (Zd, Zc, and Zu).

·         Note analysis of the effectiveness of a balun!

Common-Mode Choke and Balun Implementations:

K9YC Chokes:  http://audiosystemsgroup.com/CoaxChokesPPT.pdf

1.       Excellent power-point presentation.

2.       Resistance always reduces current.  Can get current increases via series resonances.

3.       W2DU choke uses #73 mix beads (#73 a very good choice).

4.       Prefers W2DU bead-choke (mix 73) to W0IYH bead-choke (mix 43).

5.       Choking Z: If well matched and balanced, 5K ohms is plenty, but if severe imbalance, 10K ohms may not be enough (chokes on Windom antennas notorious for failing).  See ppt pages 101 and 102.

6.       Heating of chokes wound with THHN wire: at 1.5 KW they barely got warm:  but no heating of the core itself, all dissipation was in the wire. (Note, this app had no common-mode current).

7.       14 turns of #14 THHN on #31 toroid.  Add second choke for higher power.

8.       Note that DX Engineering 1:4 baluns look like they use two xfrmrs, each made with 6 of the smaller cores and 4 turns each.  But measurements show Z about 1.5K at 4 MHz and 600 ohms at 7 MHz.

…and here: http://audiosystemsgroup.com/NCDXACoaxChokesPPT.pdf

·         (Essentially a shorter version of the above power-point presentation).

…and here: http://k9yc.com/RFI-Ham.pdf

·         K9YC’s excellent paper on understanding and solving RFI problems.  Note that chapter 6 (page 24) describes baluns and has LOTS of info.  Chapter 7 (page 36) is his Choke Cookbook (manly 1:1 chokes, but good info – e.g. 80/40 meters use 6 turns coax through 5 2.4” #31 cores as well as construction info.

W1HIS Chokes: 

http://www.yccc.org/Articles/W1HIS/CommonModeChokesW1HIS2006Apr06.pdf

·         |Z| should be t least 1K ohms for noise/RFI issues.

·         Prefers W0IYH choke to W2DU choke (page 12).

·         In an antenna application, you could need much more than one 1000 ohm choke (page 13).

·         Discusses how to identify ferrites at swapmeets.

·         Uses “4:1” turn (secondary to primary step-up of 2).  Page 29

·         His 1:4 current balun uses 6 (FT-240?) toroids, mix 61, with 7 turns through each.  Note that the cores are not stacked 3 high, rather, each transformer in the balun consists of 3 toroids in series.

G3TXQ’s page on chokes: http://www.karinya.net/g3txq/chokes/

·         43 or 31 mix for 80 meters?.  17T on 1x or 2xFT240-43 best?

·         Best CM Impedance:  > 8K. (>4K light green, >2k yellow)

·         Want Rs>|XS| -- don’t want reactive resonance.

·         Significant core heating can result if resistance is not sufficient to reduce CM current.

·         Measures Choke impedance via S21

Trask 1:4 Balun:  http://home.earthlink.net/~christrask/Trask4to1Balun.pdf

·         Discusses Guenella and Ruthroff 1:4 baluns (called 4:1 here).

·         Introduces his design for an improved 1:4 current balun.

·         Note this design is on a single core, and my simple SPICE simulations do not show it to be better than a 2-transformer implementation.

G3TXQ’s page on baluns:  http://www.karinya.net/g3txq/baluns/baluns.pdf

·         Analysis and discussion of some common balun topologies.

·         Analysis and discussion of the Trask balun.

W8JI, 4:1 baluns:  http://www.w8ji.com/balun_single_core_41_analysis.htm

·         Discussion why 4:1 balun should be on 2 cores, not 1.

·         Towards the end he seems to state that the Trask 4:1 xfrmr is NOT operating in TEM  mode.

·         Note 80 meter dipole example in which 5000 ohms common-mode impedance would not be enough at 1KW operation.

·         Another stressful load:  80 meter doublet on 40 meters.

·         Myth that the only requirement for a balanced transmission line not to radiate is to have equal and opposite currents at one point in the system.  Instead, for a balanced transmission line not to radiate, “line currents have to be exactly equal and opposite and voltage with respect to the outside world has to be exactly equal and opposite at any and all points along the system.”  

·         The 2-core current balun can have uneven heating in the two cores.

·         To minimize balun heating:  CM impedance should be as high as possible on the balun output, and DM impedance should be as low as possible across the balun output.

·         Most antenna systems are probably 1000 ohms or less common mode impedance.

W8JI, Core material section:  http://www.w8ji.com/core_selection.htm

·         Note his recommendation of 65, 61, or (in extreme cases) 43 mix.

W8JI,  parallel winding vs. split winding (this is what I call "crossover-winding") of toroids:  http://w8ji.com/balun_test.htm

·         Makes case that split winding not as good as parallel winding for CM impedance.

·         (Note: Joe Reiser, W1JR, describes the “split” or “crossover” technique of winding a 1:1 balun in “Simple and Efficient Broadband Balun”, Ham Radio, Sept 1978)

QRZ Thread http://forums.qrz.com/index.php?threads/4-1-balun-uses.267842/

·         Interesting discussion of 4:1 Baluns.

Eham: https://www.eham.net/articles/24502

·         Discussion of 1:4 baluns.

VK1HW:  https://sites.google.com/site/vkonehw/home/homebrew/common-mode-choke

·         Describes some his 1:1 common-mode chokes

VK6YSF, building a 1:4 balun: https://vk6ysf.com/balun_guanella_current_1-4.htm

·         Describes construction of a 1:4 Guanella Current Balun.

·         Note that he uses 2 cores.

 G8JNJ: http://www.g8jnj.net/balunsandtuners.htm

·         1:1 CM balun (12 turns on T240-K core) had loss above 10 MHz.  Impedance increases from 50 ohms.

·         If high impedance loads (and thus high voltages), coax outer insulator may not have sufficient voltage isolation – arcing.

·         With 100 watts uses eight turns of 100 ohm line on 5xFT240-31 cores.

·         Should have at least 1K ohm common mode rejection.

·         For a 4:1 Current Balun use type 61 or type K material, otherwise can have “a   noticeable shunt resistance which restricts the maximum impedance transformation   ratio that can be obtained.”

·         Measure loss using 2 baluns (preferred) or using ATU to tune to max power.

·         Discusses how to identify ferrites at swapmeets.

  

Biggins, Paul, Widband Balun Design with Ferrite Cores, (Cal Poly Senior Project).

VK2OMD (Owen Duffy):  https://www.owenduffy.net/balun/index.htm

·         A good collection of Balun posts! 

VK2OMD: https://owenduffy.net/blog/?p=3738. 

·         Comments on the Trask balun topology.

Taranovich, Steve, EDN Series reviewing excerpts from the the fifth edition of Sevick’s Transmission Line Transformers  (2014, Authored by Raymond Mack and Jerry Sevick).

·         Part 2 of the series:   https://www.edn.com/design/analog/4433174/Book-Excerpt--Sevick-s-Transmission-Line-Transformers--Chapter-9-Baluns--Part-2.  

·         Discusses Ruthroff and Guenella 1:4 topologies.

·         Note the recommendation that the Guenella topology use 2 cores if Rload is center-tapped to ground.

·         Part 2.1 of the series:   https://www.edn.com/design/analog/4433174/Book-Excerpt--Sevick-s-Transmission-Line-Transformers--Chapter-9-Baluns--Part-2.  

·         Taranovich builds a Guenella and a Ruthroff 1:4 baluns and tests them.

·         Note that 9 bifilar turns on the Mix 61 FT-240 core.  And only one core (not two) is used.

EA1DDO: http://www.ea1ddo.es/Balun_Guanella_4_1.php  

·         Quanella 4:1 Balun, analysis and construction.

N4SPP: Baluns, Ununs, Chokes, etc.

Palomar Engineers: Ferrite Mix Selection.

·         Good discussion of the best applications for various ferrite mixes.  Note:

·         Mix 31 excellent for CM suppression between 1-10 MHz, then about the same as 43 to 250 MHz.

·         Mix 31 not recommended for multi-ratio impedance transformers.

·         Mix 43 excellent for CM chokes from 2-300 MHz.

·         Mix 61 will withstand high power on multi-ratio impedance transformers

Measuring Balun Performance:

Johanson Technology, Balun Parameter Definitions and Measurement

Anaren, Measurement Techniques for Baluns

Skelton, Ron, W6WO: Measuring HF Balun Performance, QEX, Nov/Dec. 2010

·         Interesting article on measuring balun CMRR.

W8JI, Balun Testing: http://w8ji.com/balun_test.htm

·         Note poor balance for a single-core 4:1 current balun.

VK2OMD (Owen Duffy): https://owenduffy.net/blog/?p=12474

·         Comments on |S21| measurements of common-mode chokes (he does not agree with this technique).

G3TXQ, http://www.karinya.net/g3txq/chokes/s21.pdf

·         Use S21 amplitude and phase to derive the complex impedance of a two-terminal device.  See applied here: http://www.karinya.net/g3txq/chokes/#measurement

My Balun (and 80-Meter Loop) posts:

80 Meter Loop, Part 1:  http://k6jca.blogspot.com/2018/05/adventures-with-80-meter-loop-antenna.html

80 Meter Loop, Part 2:  http://k6jca.blogspot.com/2018/05/adventures-with-80-meter-loop-antenna_30.html

Balun Power Dissipation:  http://k6jca.blogspot.com/2018/06/common-mode-chokes-baluns-power.html

Notes on 1:1 Baluns:  http://k6jca.blogspot.com/2018/06/transmit-common-mode-chokes-11-current.html

Notes on Common-Mode Currents:  http://k6jca.blogspot.com/2018/07/thoughts-and-notes-common-mode-current.html

Y21 Method of Measuring Common-Mode Impedance:  https://k6jca.blogspot.com/2020/07/the-y21-method-of-measuring-common-mode.html

A 3-Port Method for Characterizing Baluns:  http://k6jca.blogspot.com/2020/06/another-method-to-characterize-baluns.html

Standard Caveat:

I might have made a mistake in my designs, equations, schematics, models, etc.  If anything looks confusing or wrong to you, please feel free to comment below or send me an email.

Also, I will note:

This design and any associated information is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.