More Notes on Directional Couplers for HF -- the Monimatch

I purchased my very first SWR meter at the local Radio Shack store back in 1970 when I was a young Novice.  Its main virtue was that it was inexpensive, which was very important to this high-school aged ham!

The meter movement broke sometime in the 70's and I replaced it with a 100 uA meter that someone gave to me, but I wasn't able to add the SWR scale to the meter face -- the meter itself was sealed and it was impossible to access the scale. But it worked fine, and after all, I didn't really need a scale -- I was just tuning for minimum Reflected power.

I've since graduated to fancier meters, but I still have that original one.  Here it is:

 (click on image to enlarge)

This is the meter I was thinking of when, back in college, my professor mentioned that one could measure SWR by first finding a voltage maxima along a transmission line and then moving lambda/4 from that point and measuring the voltage minima. The SWR would be the ratio of those two values.

Well, I'd been using my meter to measure SWR on 80 meters, and I was certain that it wasn't 20 meters long.  So how did it work, I wondered?

Fast forward about 40 years...and I finally decided to look into it.

Let's start with the construction.  Below are the guts of two SWR sensors with similar architectures.  The bottom one is my venerable Radio Shack meter.  The top one is a box I found some years ago at a surplus store in Silicon Valley.

  (click on image to enlarge)

This architecture, which consists of two pickup wires that run parallel to the center wire that connects the centers of the two SO-239 connectors, is known as the Monimatch. (The top unit in the photo actually has 3 parallel pickup wires to drive...3 different meters?)

Actually, this architecture should be called the "Monimatch, Mark II," which is title of the article published by Lewis McCoy back in the February, 1957 issue of QST in which this architecture of two parallel pickup lines is first described.

There was an a earlier article titled "The Monimatch" in the October, 1956 issue of QST, but this was a different design consisting of a single, long pickup wire with a single resistor connected to ground halfway along its length.  One end of this single wire was the Forward Voltage pickoff point, and the other end was the Reverse Voltage pickoff.

But I've never seen that original Monimatch design commercially produced, whereas the "Monimatch, Mark II" design was incorporated into a number of commercial products, including my Radio Shack SWR meter.

Because of its ubiquitous presence in ham shacks at the time, I will refer to all couplers of this type of topology as a "Monimatch" coupler, dropping the Mark II suffix.

Here's a schematic of the circuit (this one is from the manual for a Heathkit AM-2 "Reflected Power Meter and SWR Bridge," but it's identical to my Radio Shack unit):

(click on image to enlarge)

Note that the terminating resistors are each 150 ohms, which is the value necessary for coupler to give readings relative to 50 ohms.  This is the same value listed in the "Monimatch, Mark II" article by McCoy.  (For operation relative to 75 ohms, these resistors would need to be decreased to 100 ohms, per McCoy's original article and per the values listed in the schematic above).

You can see that are very few parts to this design, which is its virtue -- it was inexpensive to mass produce.  And there were no adjustments.  Convenience and affordability, it's small wonder that it found its way into many ham shacks.

Monimatch Principles of Operation:

I will first discuss Monimatch operation in the presence of Forward and Reflected waves, but before getting into that discussion, I'd like to make an important point:

The Monimatch, being made of "lumped elements" (in this case, the important components being two short wires and two resistors), is only looking at the voltage and current present at its output port.  It has no idea what the load is, or even how the load is connected to the port.  The load might be a resistor or other component simply clipped onto the output connector with test leads, or it might be a length of transmission line with a load (either known or unknown) at its other end.

Irrespective of what the load is (transmission line, clipped-on component, or whatever), the Monimatch gives us voltage readings that can be interpreted in terms of Forward and Reflected waves.  It is important to remember:  these readings should only be interpreted as representing actual Forward and Reflected waves when the Monimatch is connected in a transmission line with the same characteristic impedance, Zo, as the Monimatch's designed-for target impedance!

Therefore, for this discussion I will assume that the Monimatch is inserted into a transmission line of the designed-for (target) characteristic impedance.

OK -- on with the analysis!

If you've taken a look at my notes on the Bird Slug, you'll see that the Monimatch electrical design looks surprisingly similar to a Bird slug's sensor.  The main differences between the two is that the dimensions of the Bird slug's pickup is very small, thus the Mutual Inductive Coupling and Capacitive Coupling between the coax center-conductor and the sense wire are different.  The termination resistors are also different values, and the Bird unit has additional components to flatten its frequency response (over a frequency range of at least an octave).

The physical size of the Monimatch, although larger than the Bird Slug design, is still very small relative to a wavelength (e.g. 80 meters), so again we should be able to use straight-forward "lumped-element" circuit analysis.

It shouldn't be too surprising that the Monimatch design does not have frequency-flattening components.  After all, it's meant to be low cost.  So although its sensitivity increases with frequency, who cares -- it's an SWR meter.  We care about the ratio between the Forward and Reflected voltages, not their absolute values, so flatness over frequency is unimportant.

And the Monimatch, by virtue of its two sensors and potentiometer, makes determining SWR a snap:  put the meter in FWD mode, adjust the pot so that the meter's needle is at full scale, then flip the switch to REF and read the meter (with scale calibrated in SWR -- half-scale would be calibrated as 3:1, for example)

Compare this to the Bird Wattmeter, where one must place the slug in the Forward position, note the power, rotate the slug 180 degrees, again note the power, and then calculate SWR.

Given the similar electronic design and the small size relative to lambda, the same equations that we used for the Bird Sensor analysis should be applicable here, too.  So let's continue down that path...

Here's an equivalent circuit of the Monimatch.  I'll use this for my analysis.

 (click on image to enlarge)

 

Per the drawing above, I'll make the following assumptions and definitions:

• V is the voltage across the transmission line at the point of measurement, and I is the current along the transmission line (e.g. on the coax-cable center conductor) at the point of measurement.
• "jw" in the schematic above and the equations below represents j*omega, where omega = 2*pi*Frequency and "j" is the square root of negative one (just in case it isn't obvious).
• M is the Mutual Inductance between the coax center-conductor (carrying the RF current) and each pickups' wire.  It can be represented as an induced voltage source of value jw*M*I in each pickup wire.  Its value is determined by the length of a pickup wire and its spacing from the center conductor.
• C is the capacitive coupling between the coax center-conductor and a pickup loop wire.  It's actually a distributed capacitance along the entire length of the pickup wire, but for this analysis considering it as a lumped capacitance is fine.  Its value is determined by the length of the wires, their spacing from the center conductor, and their diameter.
• It's assumed that the meter circuit is of high enough impedance to ensure that there is negligible current draw by the metering circuit through the pickup wire -- that is, the current in either R1 or R2 due to the  jωM*I voltage sources (and thus its effect on Vc) is negligible:  the high-impedance detectors (used to measure Vref or Vfwd) are effectively in series with either R1 or R2, and their high impedance therefore should limit the current from the jωM*I voltage sources. through either R1 or R2. to negligible amounts.
• Also, the self-inductance (L) of each of the pickup wires is assumed to be negligible, that is, their impedance is so low, in conjunction with the current created by the jωM*I voltage sources, that these inductances can be ignored.

Forward with the analysis!

Using the assumptions and drawing above, the voltage at the junction of either C and R1 or C and R2 (call this voltage Vc) is easily calculated.  Remember, I am assuming that there is negligible current through either R1 or R2 from the jωM*I voltage sources, therefore the voltage at these two junctions can be calculated as simple voltage dividers dividing the voltage V (the voltage across the transmission line).  In other words:

Vc = V*R1 / ((1/jwC)+R1)
or
Vc = V*R2 / ((1/jwC)+R2)

And because each voltage divider has equivalent components, and thus voltage at either of these two nodes (junctions) should be the same.

The SWR meter  measures voltage at either the Vfwd or Vref points in the circuit diagram.  So let's calculate what these two voltages are.  Start by analyzing the sensor circuit for Vfwd.  If we assume that the impedance of the capacitor C is much larger than R2 (because it is a small capacitance and therefore should have a large impedance), then the equation above can be simplified to:

Vc = V*jw*C*R2

To calculate Vfwd we simply add our induced voltage, jw*M*I, to Vc (remember, we are assuming that the voltage source jw*M*I itself has negligible effect on the Vc, because the current that it induces in R1 or R2 is negligible due to the high-impendance of the "detector" measuring Vref or Vfwd (and that is a series-element in either loop).

   That is:

Vfwd = V*jw*C*R2 + jw*M*I

Rearranging:

Vfwd = jw*(V*R2*C + M*I)     (equation A) 

Which is exactly the same as Equation 2 in the Bird patent .  My analysis is tracking the Bird explanation.

We can do the same calculation for Vref.  The result is:

Vref = jw*(V*R1*C - M*I)     (equation B)

Note the minus sign!  This is because, although the voltage across R1 does not change polarity, the polarity of the induced-voltage source (jw*M*I) is now flipped with respect to the R1/C junction:  the "+" terminal of the induced voltage source is still to the left in the drawing because current on the coax center-conductor is still flowing from left-to right.  And if we now sum up these voltages around the loop from ground to the Vref pickup point, we find that they subtract, rather than sum together as they did for Vfwd.

Continuing on...

At any point along a transmission line (such as our measurement point), I = V/Zo, where V is the voltage across the line at that point and Zo is the characteristic impedance of the transmission line.  If we substitute this equality into equations A and B, we get:

Vfwd = V*jw*(R2*C + M/Zo)   (equation C)

Vref = V*jw*(R1*C - M/Zo)    (equation D)

If you take a look at Bird patent, you'll notice that the component values should selected to meet the patent's Equation 4, which is:

R*C = M/Zo = K

Where K is a designer-defined constant.

Let's use the same constraint for the Monimatch design.  For us, this means that

R1*C = R2*C = M/Zo = K

What happens if we substitute this equality for K into equations C and D?  Equations C and D become:

Vfwd = 2*V*jw*K  (equation E)

Vref = 0  (equation F)

In other words, if the wave were only moving from Left to Right and there were no wave moving from Right to Left (i.e. there's only a forward wave and no reflections from the load), then we get equations E and F above.

If we switched positions of load and source on the line in my drawing above (source now to right side, load to left side) so that current "flows" from right to left, then the polarities of the induced-voltage sources flip and equations E and F would become:

Vfwd = 0

Vref = 2*V*jw*K

So, with a wave only moving from Right to Left (no reflections from the left-side load), we read 0 volts at the Vfwd pickoff point when before we read 2*V*jw*K volts, and at the Vref pickoff point we now read 2*V*jw*K volts, when previously it had read 0 volts.

Continuing on...

We can express the equations for Vfwd and Vref in terms of Forward waves and Reverse (or reflected) waves that are simultaneously traveling on both directions on the line.

First let's bring back equations A and B:

Vfwd = jw*(V*R*C + M*I)     (equation A)

Vref = jw*(V*R*C - M*I)     (equation B)

Let's define the transmission line voltage V so that it includes both forward and reflected voltages.  And let's define the current on the line, I, so that it includes both forward and reflected currents. We will define Forward as a wave moving from Source to Load (left to right) and Reflected (or Reverse) as a wave moving from load to source, or right to left.

 (click on image to enlarge)

Note that because the reverse (reflected) current travels in the opposite direction of the forward current, they subtract, rather than add, at any point on the line.

I = Ifwd - Iref

But the forward and reverse voltages add to create V, the total voltage across any point on  the line.

V = Vfwd + Vref   (equation G)

Note, too, that on the transmission line Ifwd and Iref are defined as follows:

Ifwd = Vfwd/Zo

Iref = Vref/Zo

Where Zo is the characteristic impedance of the transmission line.

Therefore:

I = Vfwd/Zo - Vref/Zo    (equation H)

Substituting Equations G and H into A and B and keeping in mind that R1*C = R2*C = M/Zo = K, we get the following very important equations:

With Source to left and Load to right on the transmission line, per the drawing above:

Vfwd(measured) = Vfwd * 2 * K * jw     (equation I)

Vref(measured) = Vref * 2 * K * jw    (equation J)

So, our ports measure Vfwd and Vref, the voltages of the forward and reverse wave at the measuring point on the transmission line, and these measurements are isolated from each other (no Vref at the Vfwd(measured) port and no Vfwd at the Vref(measured) port).

This concludes our analysis using Forward and Reflected waves!  (Further below in this post I'll analyze the Monimatch circuit without resorting to Forward and Reflected waves.)

Of course, in reality these two ports are really not isolated.  Strays (inductive and capacitive) will limit the meter's Directivity.

And note that these equations for V(node B) contain the term "jw" (which is j*omega, where omega = 2*pi*F).  The omega term (2*pi*F) means that these voltages increase at 6 dB per octave (of frequency) and thus the meter is not flat across frequency.

A quick check of our analysis:

A quick check of our formulas should tell us if we've taken the correct analytical path.

We know that for a 50 ohm system, the terminating resistors R1 and R2 should be 150 ohms, and that for a 75 ohm system they should each be 100 ohms.  Let's see if we can derive 100 ohms for a 75 ohm system.

Let's use this equation. 

 R1*C = R2*C = M/Zo

Let's consider R1 (because the result for R2 will be the same) and rearrange the equality so that R1 and Zo are on one side of the equal sign and M and C are on the other:

M/C = R1*Zo

Now, we don't know either M or C, but we don't need to know these to do our check.  We know that R1 is 150 ohms and Zo is 50 ohms, so:

M/C = 150*50 = 7500

So what should R1 be if Zo is changed to 75 ohms?  Here's the calculation:

R1*Zo = M/C = 7500

Therefore:

R1*75 = 7500

Solving, we get:

R1 = 100 ohms

That's the value mentioned in the Heathkit AM-2 schematic and the "Monimatch, Mark II" QST article.

Check!


The Monimatch analyzed in a non-Transmission Line environment:

We don't need to use the Monimatch in a transmission line environment:  we can measure an impedance imbalance (relative to 50 ohms) at the Monimatch's "Antenna" port with no need to resort to the concepts of Forward and Reflected waves.  This illustrates my point (also made in my initial "Notes on Directional Couplers" post) that you don't need to resort to the concepts of Forward and Reflected waves to understand the operation of these sorts of "lumped-element" couplers.

Transmission line?  Reflections?

So instead of using forward and reflected waves, as we did above, let's just define V to be the source voltage, which is also the voltage across the load connected to the Monimatch's "Antenna" connector.  And "I" is the current being delivered to the load.  The load itself will be an unknown impedance, Zload.

(click on image to enlarge)

(For convenience I'm using the same measurement-port names, Vfwd and Vref, even though this analysis won't be using waves.)

So, given the definitions above for V, I, and Zload, we know that:

I = V / Zload

Recall equations A and B.  They still apply for this analysis:

Vfwd = jw*(V*R2*C + M*I)     (equation A)

Vref = jw*(V*R1*C - M*I)     (equation B)

From our previous analysis, we know that R1, R2, C and M were all chosen for operation with a 50 ohms system.  That is, the components were picked so that they satisfy the following equation:

K = R1*C = R2*C = M/Zo = M/50

From which we get the following equation for M:

M = 50 * K

So now let's substitute our equations for "I" and "M" into equations A and B.  The resulting equations for the voltages measured at the "FWD" and "REF" ports, are:

Vfwd = V*jw*K*(1 + 50/Zload)

Vref = V*jw*K*(1 - 50/Zload)

 
As a quick check, what happens if Zload  = 50 ohms?  We get:

Vfwd = V*jw*2*K

Vref = 0

Exactly what we expect.

OK, now to measure impedance imbalance from 50 ohms, we're going to follow that same procedure that we would use when measuring SWR.  That is.

1. Place the switch in the FWD position.
2. Adjust Potentiometer so that the meter needle is at full-scale.
3. Switch to the REF position.
4. Note meter reading.

For example, if the meter reading is 0, we know that the load is 50 ohms resistive.

When we do this, what we are really doing by first setting the needle to full-scale in the FWD position is that we are normalizing the magnitude of the Vref reading to the magnitude of the Vfwd reading. Why magnitude?  Because the SWR meter usually first rectifies Vfwd and Vref, thus, they are no longer vector quantities, but magnitudes only.

So, in the Vref position, we are really reading this :

Vref/Vfwd = |[V*jw*K*(1 - 50/Zload)]| / |[V*jw*K*(1 + 50/Zload)]|

If we define Vfwd to be "1", and:

Vref = |[V*jw*K*(1 - 50/Zload)]| / |[V*jw*K*(1 + 50/Zload)]|

Simplifying the equation:

Vref = |(1 - 50/Zload)| / |(1 + 50/Zload)|

Or, stated another way:

Vref = |(Zload - 50)| / |(Zload + 50)|

Which (because we are now dealing with magnitudes and not vectors) is the definition of rho, the magnitude of the Reflection Coefficient.

Let's do a quick check of this last equation.  What should I measure if I connect a 150 ohm resistor to the Antenna port of my Monimatch?

If Zload = 150 ohms, then, from the equation above, the meter should be at half-scale (when it is calibrated to read full-scale (i.e. "1") by setting the Vfwd reading to full-scale).  So, if Vfwd at full scale is considered to be "1", then Vref at half-scale would be 0.5 and thus the magnitude of the Reflection Coefficient is also 0.5.

Using the well-known formula for SWR (expressed in terms of the Reflection Coefficient):

SWR = (1 + |Reflection Coefficient|)  / (1 - |Reflection Coefficient|)

The result if we plug 0.5 for the magnitude of the Reflection Coefficient into this equation is:

 SWR = 3:1

And if we look at the meter scale on a typical Monimatch meter, we'll see that half-scale is marked as an SWR of 3:1.

Check!

Summing up:

Our typical "Monimatch" SWR meter is really just calculating a relationship between the load at its output port (Zload) and its own internal M and K design parameters.  And this relationship is equivalent to the Reflection Coefficient if M/K equals Zo of the Transmission Line and the meter is set up such that Vfwd drives the meter to Full Scale.

But it's important to note that Zload could be a load connected directly to the coupler's "OUT" port with a couple of wires, or it could be the impedance "presented" to the port by a long length of transmission line (an impedance determined, at that point, by the interaction of the Forward and Reflected waves).

The coupler doesn't care "how" the load is connected to its OUT port.  It's just looking at the relation between the voltage across the OUT port and the current through the OUT port.  It doesn't know anything else about the load except for this voltage and current relationship at its OUT port.  For example, if the OUT port happens to be connected to a transmission line, the coupler has no knowledge of the line's Zo. It doesn't even know if there's a transmission line attached, nor that the impedance it sees at its OUT port might be due to the interaction of Forward and Reflected waves.

For this reason, never assume that the a meter reading is reading the actual Γ or rho, or that the SWR reading is the actual SWR reading of the line.  It might not be.  We are really just measuring the relationship between Zload (as it appears at the OUT port) and the Monimatch's M and K values.  Only if M/K equals the actual characteristic impedance, Zo, of the transmission line would we truly be measuring rho and from that deriving SWR..


OK, that ends the analysis.  What follows are a list of references...


Links to my Directional Coupler blog posts:

Notes on the Bruene Coupler, Part 2

Notes on the Bruene Coupler, Part 1

Notes on HF Directional Couplers (Tandem Match)

Building an HF Directional Coupler

Notes on the Bird Wattmeter

Notes on the Monimatch

Notes on the Twin-lead "Twin-Lamp" SWR Indicator

Calculating Flux Density in Tandem-Match Transformers


And some related links from my Auto-Tuner and my HF PA posts:

Auto Tuner, Part 5:  Directional Coupler Design

Auto Tuner, Part 6:  Notes on Match Detection

Auto Tuner, Part 8:  The Build, Phase 2 (Integration of Match Detection)

HF PA, Part 5: T/R Switching and Output Directional Coupler


Monimatch references:

McCoy, Lewis, "The Monimatch," QST, Oct., 1956. Single "linear-inductor" pickup.  Design originally developed at the Naval Research Laboratory and described in:  Norgorden, "A Reflectometer for the H-F Band", NRL Report 3538.  I don't know any commercial products that use this design.

McCoy, Lewis, "Monimatch, Mark II," QST, Feb., 1957.  A smaller version of the original Monimatch.  Later, this design would be commercially mass produced (I bought mine from Radio Shack back in 1970).  Ubiquitous in ham shacks.

Shallon, S. C., "The Monimatch and S.W.R.," QST, Aug., 1964.  Good, but basic, description of how a Monimatch works.

http://www.g3ynh.info/zdocs/bridges/inline/part_1.html  Good discussion.  This might be useful for Monimatch analysis.

Microstrip and other Couplers:

http://kilyos.ee.bilkent.edu.tr/~microwave/programs/magnetic/dcoupler/theory.htm Detailed analysis of a Microstrip Directional Coupler.  Note that coupling is max when length is lambda/4.

Campbell, Rick, "Directional Coupler Project," PDF.  Good analysis of a Microstrip Directional Coupler.  Note similarities with Monimatch.

Wade, Paul, W1GHZ, "High Power Directional Couplers with Excellent Performance," PDF. Interesting high-power directional couplers for VHF/UHF and above.


Other references of generally interest:

http://www.g3ynh.info/zdocs/bridges/Xformers/part_1.html  great discussion on current-transformers for directional coupler applications

http://www.g3ynh.info/zdocs/bridges/Xformers/part_2.html Part 2 of current-transformers

http://www.g3ynh.info/zdocs/bridges/Xformers/part_3.html  And part 3, the last part, of current-transformers

http://www.g3ynh.info/circuits/diode_det/index.html Diode detectors!

http://www.g3ynh.info/zdocs/bridges/index.html  Indexes numerous topics.  Lots of great info to be found here!

http://www.richtek.com/assets/AppNote/AN008_EN/AN008_EN.jsp  Common-Mode choke model


Final Caveats:

As always, I might have made a mistake in my equations, assumptions, or interpretations.  If you see anything you believe to be in error, or if anything is confusing, please feel free to contact me.

More notes on Directional Couplers for HF -- the Bird Wattmeter

During a recent conversation with a fellow ham, my interest was piqued when he mentioned the physical construction of the Directional Couplers contained in the slugs used by Bird Wattmeters.

At the time, I didn't know their principle of operation and I wondered if they were similar to other types of Directional Couplers I'd investigated, such as the Bruene coupler or Tandem Match coupler.  That is, at any point along a transmission line, there is a voltage V across the transmission line and current I through that point, and these directional couplers use a "sample" of both this voltage and current to determine forward and reflected power.

And most importantly, given the small dimensions of the Bird slugs, I wondered if their operation could be analyzed with straight-forward lumped-element circuit analysis.

So I started poking around the web, looking for further information as to how the Bird slugs operate.  Here's one explanation that I found:

"The Bird directional coupler is a sample loop with a matched resistance at one end and a detector at the other end. Current flowing in one direction heats the resistance. Current flowing in the other direction deflects the meter."

Another explanation was a variation on the previous one, but with an induced traveling wave moving down a parallel transmission line (formed by the slug's pickup loop) either towards the meter or towards the resistor terminating this secondary, parallel transmission line.

I love the simplicity of these two explanations and they make intuitive sense.  But are they correct?

Note that they both state that the undesired wave (or current) flows towards the  resistor at the end of the pickup loop where it is dissipated.  And the desired wave (or current) flows in the opposite direction, towards the meter and deflecting it.

Therefore, if we want to measure the forward wave, the induced forward wave needs to travel towards the meter end of the loop.

It is critical to note that this induced wave must be moving in the same direction as the main wave.  So, if measuring forward power, the meter should be at the end of the sensing loop closest to the load, and the terminating resistor should be at the other end of the loop, closest to the source.

[If the induced forward wave were to travel in the opposite direction of the main wave, then there's a huge issue with causality.  Imagine this example:  the main transmission line is very very long (let's pick a length, say, several light-years), and we put next to this line a second transmission line of the same length that is going to be our "pickup sensor" line.  If the induced wave really traveled in the opposite direction, then, if we start a wave traveling down our main line from left to right, the induced wave would have to start simultaneously at the far end of the second "pickup" transmission line if it's going to be moving in the opposite direction, from right to left.]

So, to recap a requirement that must be satisfied if the "traveling wave" explanation were true, the meter end of the loop must be towards the load and the resistor end towards the source when measuring forward power.

But here's the problem.  In actuality, when measuring forward power, the meter end of the loop is towards the source and the resistor end is towards the load.   The termination resistor is actually at the opposite end of the loop from where it should be if the "induced traveling-wave" explanation were correct! 

And therefore, the "induced traveling-wave" explanation cannot be correct!

(You can verify the position of the resistor by taking a look at the resistor locations in a "Monimatch" type of coupler (which is similar to a Bird sensor but with larger dimensions and cost reduced).  You will see the termination resistors placed as I described -- towards the antenna for forward power and vice-versa for reflected power.)

So -- is there a better way to analyze the operation of a Bird slug?

Before I get to the meat of this blog post, I'll add my own philosophy, which is this:  if the dimensions of a circuit are very small compared to the wavelength of the frequencies over which it is to operate, then it can (and should) be analyzed using straight-forward lumped-element circuit analysis.

And I'll note that the dimensions of a bird slug are very much less than the wavelengths it's operating at, especially at HF.

I'll add this important note:

The Bird wattmeter, whose sensor can be considered a "lumped-element" device, is only looking at the voltage and current present at its output port.  It has no idea what the load is, or even how the load is connected to the port.  The load might be a resistor or other component simply clipped onto the output connector with test leads, or it might be a length of transmission line with a load (either known or unknown) at its other end.

Irrespective of what the load is (transmission line, clipped-on component, or whatever), the Bird Wattmeter gives us Power readings for what we assume is a Forward wave or, if the sensor is rotated, for the Reflected wave.  It is important to remember:  these Power readings should only be interpreted as representing actual Forward and Reflected Power when the Wattmeter is connected in a transmission line with the same characteristic impedance, Zo, as the Wattmeter's designed-for target impedance! 

Therefore, for this discussion I will assume that the Bird Wattmeter is inserted into a transmission line of the designed-for (target) characteristic impedance.


Analysis of the Bird Slug's Directional Coupler:

In understanding how the Bird circuit works, there's no better place to start than with the Bird patent itself:

Patent US2852741 Directional Wattmeter, J. R. Bird et al.  Granted 16 September 1958 

I'll start this discussion by noting that the patent is very readable, and I would recommend anyone interested in the subject to click on the link above to download it.

And let's also note that, regarding the analysis of the slug's operation, the patent states:

"Dimensions are kept to a minimum, much less than the wave length of the energy transmitted, and in considering the theory of operation it is satisfactory to refer to lumped impedances rather than evaluating the distributed parameters." [Emphasis mine, k6jca]

(I'll add that the patent then continues, "In practice, however, it has been necessary to supplement theoretical calculations with empirical methods of testing in making corrections for distributed capacitance and distributed inductance.") ["Strays" is my "official engineering term" for the latter.]

But lumped-element analysis is how Bird presents their operation, and we shall follow that line.  Note that I will use the concepts of Forward and Reflected waves for this analysis, but later in this post I will present an alternative analysis that does not use waves at all.

First, to get an idea of how a Bird slug is constructed, here are some illustrations from the patent.

(click on image to enlarge)

And, again from the patent, here's an equivalent-circuit schematic (Fig. 13) of the components.

 (click on image to enlarge)

For my analysis, let me simplify the patent's Figure 13 so that it looks like this:

(click on image to enlarge)

Before we start, some assumptions and definitions:

• V is the voltage across the transmission line at the point of measurement, and I is the current along the transmission line (e.g. on the coax-cable center conductor) at the point of measurement.
• "jw" in the equations below represents j*omega, where omega = 2*pi*Frequency (just in case it isn't obvious). 
• M is the Mutual Inductance between the coax center-conductor (carrying the RF current) and the pickup's loop-wire.  It can be represented by an induced voltage source in the loop wire of value jw*M*I.
• C is the capacitive coupling between the coax center-conductor and the pickup loop wire.  It's actually a distributed capacitance, but this distribution can be "biased" towards the resistor end of the loop with extra copper at that end (item 150 in Fig. 13).
• The induced-voltage source in the pickup wire creates a loop-current from the "+" terminal of the voltage source through C1 to ground, then up from ground through R, and then back along the loop wire to the "-" terminal of the voltage source.  For the equations in the patent to hold true, it is important that this loop current *not* create a significant voltage drop through R, compared to R's function as a voltage-divider in combination with C.  So we will assume C1 is very small Therefore C1 can be ignored because its impedance is very high.  (In reality this isn't the case, but we need to assume this to replicate the patent equations which do not contain any C1 terms).
• It's assumed that the self-inductance of the loop wire is negligible, that is, its impedance is so low that the voltage drop across it can be ignored.
• I'm ignoring the effect of the capacitive sleeve around the resistor R (see text further down).

Continuing on...

Assuming that the loop-current created by the induced-voltage source creates a negligible voltage drop across R, then the voltage at Node A (in the drawing above) is:

V(node A) = V*R / ((1/jwC)+R)

because it's a voltage divider.

If we assume that the impedance of the capacitor C is much larger than R (because it is a very small capacitance), then the equation can be simplified to:

V(node A) = V*jw*C*R

The wattmeter measures voltage at Node B.  Using the assumptions listed above, the voltage at Node B is simply the sum of the voltage at Node A plus the value of the induced-voltage source:

V(node B) = V*jw*C*R + jw*M*I

Rearranging:

V(node B) = jw*(V*R*C + M*I)     (equation A)

Which is exactly the same as Equation 2 in the patent (except I use of "V" in lieu of "E").  So my analysis tracks theirs.

Note that if the sensor (i.e. slug) is rotated 180 degrees so that R is now closest to the source side of the line, rather than the load side:

(click on image to enlarge)

Equation A now becomes:

V(node B) = jw*(V*R*C - M*I)     (equation B)

Note the minus sign!  This is because, although the voltage at Node A does not change polarity, the polarity of the induced-voltage source is now flipped with respect to Node A:  the "+" terminal of the induced voltage source is still to the left in the drawing because current on the coax center-conductor is still flowing from left-to right.  And if we now sum up these voltages to determine the voltage at Node B, we find that they subtract, rather than add.

Continuing on...

Note that, at any point along a transmission line (such as our measurement point), I = V/Zo, where V is the voltage across the line at that point and Zo is the characteristic impedance of the transmission line.  If we substitute this equality into equations A and B, we get:

V(node B) = V*jw*(R*C + M/Zo)   (equation C)

V(node B) = V*jw*(R*C - M/Zo)    (equation D)

If you take a look at the patent, you'll notice that the component values are selected to meet the patent's Equation 4, which is:

R*C = M/Zo = K

Where K is a designer-defined constant.

What happens if we substitute this equality for K into equations C and D?  Equation C (sensor in original position) becomes:

V(node B) = 2*V*jw*K  (equation E)

and Equation D (sensor rotated 180 degrees) becomes:

V(node B) = 0  (equation F)

In other words, if the wave is only moving from Left to Right and there is no wave moving from Right to Left (i.e. there's only a forward wave and no reflections from the load), then we get equations E and F above.

What happens if we now switch positions of load and source on the line in my drawing above (source now to right side, load to left side), then equations E and F would become:

V(node B) = 0  (equation E') 

V(node B) = 2*V*jw*K  (equation F')

Now, with a wave only moving from Right to Left (no reflections from the left-side load), we now read 0 volts when before we read 2*V*jw*K, and, when the sensor is rotated 180 degrees, it now reads 2*V*jw*K, when previously it had read 0 volts.

Continuing on...

We can express the equation for Node B (normal and rotated positions) in terms of Vfoward (Vfwd) and Vreverse (Vref) -- waves simultaneously traveling on both directions on the line.  E.g. source on left of drawing and unmatched load on right.

First let's bring back equations A and B (sensor in "normal" position, then sensor rotated 180 degrees):

V(node B) = jw*(V*R*C + M*I)     (equation A)

V(node B) = jw*(V*R*C - M*I)     (equation B)

Let's define the transmission line voltage V so that it includes both forward and reflected voltages.  And let's define the current on the line, I, so that it includes both forward and reflected currents.  Note that because the reflected current travels in the opposite direction of the forward current, it subtracts from that current:

V = Vfwd + Vref   (equation G)

I = Ifwd - Iref

Note, too, that on the transmission line Ifwd and Iref are defined as follows:

Ifwd = Vfwd/Zo

Iref = Vref/Zo

Where Zo is the characteristic impedance of the transmission line.

Therefore:

I = Vfwd/Zo - Vref/Zo    (equation H)

Substituting Equations G and H into A and B and keeping in mind that R*C = M/Z0 = K, we get the following very important equations:

When the sensor is rotated so that its resistor R is towards the load, we only measure Vfwd:

V(node B) = Vfwd * 2 * K * jw

And when the sensor is rotated so that its resistor R is towards the source, we only measure Vref:

V(node B) = Vref * 2 * K * jw

Also, because we know that power is related to the square of the voltage, if we know the voltage, we can easily calculate both forward and reflected powers.  Voila, we have a directional wattmeter!

Note that these equations for V(node B) contain the term "jw" (which is j*omega, where omega = 2*pi*F).  The omega term (2*pi*F) means that this voltage increases at 6 dB per octave and thus the sensor is not flat across frequency.  Bird's compensation techniques to flatten the response are discussed in the patent (see the text I've included below), but they are not part of Bird's analytical equations presented in the patent.


Analyzing the Bird Wattmeter in a "Non-Transmission Line" Environment:

We can actually analyze the operation of the Bird element without resorting to Forward and Reverse waves.  After all, the above analysis was done using lumped elements, and because of this we can also analyze operation in terms of simple voltages and currents in lieu of waves.

So instead of using forward and reflected waves, as we did above, let's just define V to be the source voltage, which is also the voltage across the load connected to the wattmeter's "output" connector. And "I" is the current being delivered to the load.

The load itself will be an unknown impedance, let's call it "Zload".  And we'll attach it to the output connector of the wattmeter with a couple of short clip leads haphazardly draped on the workbench -- no coax.

(click on image to enlarge)

 So, from the image above we know that:

I = V / Zload

Recall equations A and B.  They still apply for this analysis.  For the sensor oriented with R towards the load:

V(node B) = jw*(V*R2*C + M*I)     (equation A)

And for the sensor rotated 180 degrees (R towards source):

  V(node B) = jw*(V*R1*C - M*I)     (equation B)

From our previous analysis, we know that R1, R2, C and M were all chosen for operation with a 50 ohms system.  That is:

K = R1*C = R2*C = M/Zo = M/50

Which is to say that the design parameters were such that:

M = 50 * K

So now let's substitute into equations A and B our equations for "I" and "M".  The result, for the voltages measured at the "FWD" and "REF" ports, is:

Sensor with R towards load:   

V(node B) = V*jw*K*(1 + 50/Zload)  

Sensor rotated with R towards source:  

V(node B) = V*jw*K*(1 - 50/Zload)

 
As a quick check, what happens if Zload  = 50 ohms?  We get:

  V(node B, "forward" orientation) = V*jw*2*K

V(node B, rotated 180 degrees) = 0

Exactly what we expect.

One interesting conclusion from these equations:  The Bird Wattmeter will not accurately indicate forward power if the load is not 50 ohms.

Here's an example:

Suppose the meter is calibrated so that, when V(node B) = 2 volts, this represents 0.02 watts into 50 ohms.

In other words, for this example I'm defining the quantity "jw*K" to be equal to 1, and therefore a voltage "V" that is 1 volt, across a load of 50 ohms, generates a voltage of 2 volts at Node B.   That is, for this example our equation for the sensor in its normal (forward power) rotation is:

V(node B) = V*(1 + 50/Zload)

Now, let's terminate the meter with 150 ohms and adjust our source voltage so that V(node B) again reads 2 volts.  The meter will again show 0.02 watts.  But is this the power being dissipated by the load?

Let's first calculate the voltage "V" across the load.  From the equation above, we get:

2 = V*(1+50/150)

Therefore V = 1.5 volts

The actual power being dissipated across the load is calculated as P(load) = V²/Zload.  Given V = 1.5 and Zload = 150 ohms, resistive, then:

P(load) = 0.015 watts

So, our meter tells us that the "Forward" Power is 0.02 watts, but in fact the actual dissipation across the load (now 150 ohms) is 0.015 watts.

Interestingly, if the sensor is then rotated 180 degrees, we apply the equation

V(node B) = V*(1 - 50/Zload)

We know that "V" is 1.5 volts and Zload is 150 ohms, so V(node B) with the sensor in the "Reflected" Power orientation should now be 1 volt.

What power would 1 volt correspond to?  Well, it is one-half of 2 volts, which means that the power when V = 2 volts has been decreased by 6 dB.  So if 2 volts is calibrated to be 0.02 watts, then 1 volt would be a quarter of that, or 0.005 watts.

From these two measured power values, we can see that the actual power dissipated across our 150 ohm load is the measured P(forward) minus the measured P(reverse), which is 0.015 watts.

But there really isn't any power being reflected back.  Remember, at the start of this non-Transmission Line analysis I stated that the resistive load was connected to the meter with a couple of short wires routed willy-nilly from meter to load.  I'll quote G3YNH:

"[The bridge] can only infer the existence of reflected power from the difference between the actual load impedance and the target load impedance. To understand this point, consider an SWR bridge designed to balance when the load is 50+j0Ω. If we connect this bridge directly [emphasis mine, k6jca] to a 100Ω load resistor, it will declare an SWR of 2:1. The resistor is not reactive however, and so will absorb all of the power delivered to it and reflect none. The 2:1 SWR reading is only true when the bridge sees an impedance magnitude of 100Ω (or 25Ω) at the input to a 50Ω transmission line. The bridge is just an impedance bridge, it has no special psychic powers, and its readings are only true when it is inserted into a line having the same characteristic resistance." 

And with that, I'll end the post with the following notes...


Other notes on the circuit, from the patent:

Regarding the unlabeled inductor at the left end of the pickup wire in Figure 13, I didn't find any mention of it in the patent text (but I easily could have missed it).  I suspect this represents the self-inductance of the wire and that it is so small that, for this analysis, it is unimportant (and thus unlabeled).  But maybe it represents the Mutual inductance.  I don't know.

Patent text regarding capacitor C1:

"One of the features which characterizes the present invention is the supplementing of the sampling circuit of the loop and resistor of known instruments by a frequency compensating capacitor used in association with the diode contact rectifier and series connected in the resistor-loop circuit.  This supplemental capacitor is connected in parallel relation to the diode circuit which  includes the galvanometer or other indicator external to the high frequency components and is of much greater capacitance that the capacitance C coupling the loop and other components of the sampling circuit to the transmission line.  The effect of such compensating capacitor is to give broad frequency band operation to directional couplers and the like of the type referred to.  It is believe that, since the generated voltage in the loop resistor circuit is proportional to frequency (Eq. 2) and the impedance of the supplemental capacitor is inversely proportional to frequency, the output voltage across the capacitor can be made to remain constant, or substantially so, by suitable selection of values and provided the total impedance of the circuit remains constant."

Capacitor C1 "tunes or resonates the loop circuit in the frequency band and at the sensitivity for which the particular pickup unit is designed.  The loop circuit, thus heavily loaded by the capacitor C1, exhibits broadband characteristics by reason of the resistance R which flattens the response curve of the circuit."

And...

"This capacitive loading of the resistive loop circuit by the series capacitor C1 is one of the distinguishing characteristics of the present invention and provides wide frequency band operation."

Patent text regarding capacitor C4:

Capacitor C4 [also called C-4 in the patent -- k6jca] is a metal sleeve around resistor R (and insulated from it).  C-4 "functions to modify the loop-resistor circuit and obtain several beneficial results, chiefly improved directivity characteristics, but also so-called "flat" response over a wide frequency band."

And...

"Placing the modifying capacitance C-4 across the resistor R of the loop-resistor sensing combination in the manner described distributes the capacitance along the length of the resistor and has the effect of improving the balance and directivity of the instrument.  With this arrangement a directivity of over 40 decibels is obtained in the instrument described over a wide frequency range having a ratio of at least 2 1/2 to 1 and having satisfactory directivity over even wider frequency ranges, as wide as 5 to ratio being possible, whereas the same instrument without the modifying capacitor has less than about 25-35 decibels of directivity over the same range of frequencies."

Patent text regarding the selection of R and C1 (a.k.a. C-1 in the patent):

"In the selection of the resistor R of the loop-resistor combination and the supplemental or compensating resistor C-1 for these several units empirical methods must be used in conjunction with calculations to satisfy the requirements of Equation 4.  The compensating capacitor C-1 is not the "C" of this equation ["C" is the capacitive coupling between line and loop -- k6jca] but must be chosen in relation to the components concerned in Equation 4 to obtain the desired "flat" response of the meter over a wide frequency band."

And patent text regarding the loop and both "M" and "C," the mutual inductive coupling and capacitive coupling between line and loop:

"In balancing Equation 4 the size or diameter of the wire comprising the loop 105 is an influencing factor.  Increasing the wire size increases capacitance C between the loop and the inner conductor 10 [see patent figure 13 -- k6jca] of the transmission line, whereas decreasing the wire size decreases such capacitance, the mutual inductance M remaining substantially the same.  If desired, a plate 150 [patent figure 8 -- k6jca] of suitable area may be soldered to the straight portion 106 [patent figure 8 -- k6jca] of the loop wire in a plane parallel to the axis of the line to increase the capacitance coupling."

Other related Bird patents:

Patent US2891221,  Standing Wave Indicator, J. R. Bird et al.  Granted 16 June 1959

Patent 4080566A, RF Directional Wattmeter, Mecklenburg (assigned to Bird Electronic Corporation).  Granted 21 March 1978


Links to my Directional Coupler blog posts:

Notes on the Bruene Coupler, Part 2

Notes on the Bruene Coupler, Part 1

Notes on HF Directional Couplers (Tandem Match)

Building an HF Directional Coupler

Notes on the Bird Wattmeter

Notes on the Monimatch

Notes on the Twin-lead "Twin-Lamp" SWR Indicator

Calculating Flux Density in Tandem-Match Transformers


And some related links from my Auto-Tuner and my HF PA posts:

Auto Tuner, Part 5:  Directional Coupler Design

Auto Tuner, Part 6:  Notes on Match Detection

Auto Tuner, Part 8:  The Build, Phase 2 (Integration of Match Detection)

HF PA, Part 5: T/R Switching and Output Directional Coupler


Other references of generally interest:

http://www.g3ynh.info/zdocs/bridges/Xformers/part_1.html  great discussion on current-transformers for directional coupler applications

http://www.g3ynh.info/zdocs/bridges/Xformers/part_2.html Part 2 of current-transformers

http://www.g3ynh.info/zdocs/bridges/Xformers/part_3.html  And part 3, the last part, of current-transformers

http://www.g3ynh.info/circuits/diode_det/index.html Diode detectors!

http://www.g3ynh.info/zdocs/bridges/index.html  Indexes numerous topics.  Lots of great info to be found here!

http://www.richtek.com/assets/AppNote/AN008_EN/AN008_EN.jsp  Common-Mode choke model


Final Caveats:

As always, I might have made a mistake in my equations, assumptions, or interpretations.  If you see anything you believe to be in error, or if anything is confusing, please feel free to contact me.

Building an HF Directional Coupler

I previously discussed some of the theory underlying lumped-element (i.e. High Frequency) directional couplers here: http://k6jca.blogspot.com/2015/01/notes-on-directional-couplers-for-hf.html

Now I'm going to build one.

I'm using the Tandem Coupler topology (see previous post).  Here's what the circuit will look like:

Why 16 turns?

I want enough turns on the transformer to present a high impedance on 160 meters, but not so many turns that they effect performance on 6 meters.  So, I want to minimize the number of turns used and try to find a core with a high mu.  But too few turns also means that the terminations on the FWD and REF ports will need to dissipate higher power.

With this in mind, my goal for the Coupling-factor (coupling of Input port to Forward port) is -24 dB, which means 16 turns on a transformer whose primary is a single turn (i.e. 20log(16) = 24).

Note that if the coupling from IN port to FWD port is -24 dB, then the power at the FWD port will be P(in) * 0.004 (i.e 24 dB down).  So if power at the IN port is 100 watts, there will be 0.4 watts at the FWD port (important because the 50 ohm load on this port must be able to dissipate this power).

But what cores to use?  Let's go to the junkbox and see what I can dig up...

Here are some I dug up.  I believe these are primarily used for RFI mitigation applications, but they are made of type-43 material.  Let's see if they'll work. 

Note that they are ferrite, not powdered-iron (link to datasheet is at the end of this post).  Per N8LP's QEX article (see link at end), ferrite cores are more prone to saturation than are powdered-iron cores.  I don't know how much power these cores will tolerate -- I'll have to experiment.  [Update:  more info on applying these cores here: http://k6jca.blogspot.com/2015/07/antenna-auto-tuner-design-part-5.html and here: http://k6jca.blogspot.com/2015/12/antenna-auto-tuner-design-part-8-build.html]

I'll need sufficient inductance at 1.8 MHz to ensure that the voltage-sense transformer presents a high impedance compared to 50 ohms.  I wound test coils on two of these cores, each with 16 turns of wire, and then I measured their inductance (these are not the coils I'm actually building the coupler with).  They were 1.1mH and 0.7mH, respectively (measured on GenRad 1657 Digibridge, at 1 KHz).  I don't know why there's a difference in inductance, but I suspect it's due to a variation in the ferrite core mu.

Another important Directional Coupler parameter is Directivity.  Here, Directivity is defined as the coupling from the OUT-to-REF ports minus the coupling from IN-to-REF ports.  Directivity affects SWR accuracy -- poor directivity means that "forward" power is getting into the "reflected" power port and corrupting the reading.  So my goal is to have Directivity be at least -40 dB over the HF range (1-30 MHz, and ideally up to 54 MHz, but I'm also willing to sacrifice a bit at 6 meters if it gets me better performance at 30 MHz and below).

Some notes on construction:

1.  For the "one turn" winding I ran a straight piece of Thermax MIL-C-17 spec RGU-142 coax through each transformer.

• The Max Power specification of this coax is 2,400 watts at 100 MHz.  Not bad!
• This coax's max working voltage is 1400 V (not sure if that's a peak V or an RMS spec). Note that for an SWR of 1:1, 100 watts Forward Power into 50 ohms equals 100V peak, on the transmission line (if the SWR were infinite and Forward Power were still 100 watts, this peak voltage becomes 200V).  And at 2000 watts and 1:1 SWR, Peak V is 442 volts.  So at an infinite SWR peak voltage for 2000 watts of forward power would be 884 V, peak. 

2.  The outer sheathing of the coax has been left on, but trimmed back to expose the shield.  The shield is also trimmed back, but left slightly exposed at both ends (and tinned by me) so that I could experiment with which end of the coax shield should be grounded.  Do not ground both ends!

3.  I used insulated wire in lieu of enameled wire for the transformer secondary windings.  Insulation breakdown is especially important for the voltage-sense transformer, whose 16-turn secondary is across the coax.  So, if SWR were infinite and Forward Power were 100 watts, there will be 200V, peak, across the windings of this transformer.

4.  In the box I added a center-divider (made of PCB stock) between the two transformers.  I found through experimentation that this divider should fully contact the three sides of the case in which I was mounting it.  This was a problem because my case is aluminum; I can't solder to it.  So I lined the inside of the case with copper tape and soldered the divider to it.  Note:  all tape seams were soldered along their entire length.

Here's the result.  For my first tests, I'm going to call the lower-left port the IN port, the upper-left port is the OUT port (but this will later change, as you will discover further on...)

In the above image, the FWD port (relative to the IN port) is the lower-right port, and the REF port is the upper-right port.

Measuring and Improving Performance:

Let's make some measurements with a Vector Network Analyzer (VNA).  Here's my test setup with an HP 3577A and matching S-parameter unit.

Directivity will be all important, so I want to see what I can do to minimize the coupling between the IN port and the REF port (because the coupling from OUT-to-REF is fixed at -24 dB).

Before I start experimenting, let's get a baseline.  Here's a plot of Coupling, IN port to REF port, 0.1 - 100 MHz:

Directivity is the coupling shown above reduced by the forward coupling (-24 dB for 16 turns), so it will be 24 dB worse than the image above.

Can I improve Directivity?  Time to experiment (this is where the design becomes more art than science).  Here are some examples of what I tried...

If I move this wire closer to the case (using an insulated stick)...

There's an improvement.  The coupling is lower by about 5 dB at 30 MHz, for example.

So I incorporate this "gimmick" of wire routing.  Now, let's put cover on.  Here's the cover, screwed down.

 Note that the response has worsened.

 But, if I remove just one screw...

...there's an improvement!

Yikes!

This is why there's an art to RF -- it's difficult to simulate these types of effects.

Another example of stray and parasitic effects...as I move a copper plate over the top, touching one side of the case but not both sides of the case...

...performance improves!

But if I continue to move the copper across the case until it's also touching the opposite side (straddling the case)...

...performance worsens by 10 dB at 54 MHz!

Long story short...after spending much time trying to improve performance when the case was screwed on, I finally decided that I wasn't really advancing.  So, it was time to move on to the next step: characterizing the coupler's performance.

But, while making these characterization measurements I discovered that the ports are not quite symmetric in their performance.  Specifically, there's a difference in Directivity, depending upon which port we define to be our "IN" port.

With this new data, I redefined the port configuration to maximize Directivity performance from 1 to 30 MHz.  Here are the new port assignments:

And here's the Directional Coupler's characterization data for this new configuration.:

(click on image to enlarge)

Note that I've assigned the ports so that the Directivity data with the yellow background is appreciably better than the "Reverse Directivity."  This is because, in my applications, I will be applying power to the IN port, and thus I want to minimize any coupling of this power to the REF port.

(I don't know why there is a difference in directivity.  But if I want that additional performance at 54 MHz (about 2.5 dB improvement in Directivity), all I need to do is swap the In and Out connections and swap the FWD and REF connections).


Here's a drawing showing the construction connections in better detail:

(click on image to enlarge)

(Note the "gimmick" of routing one of the wires closer to the wall of the case.)

And some additional pictures...

Voltage-sense transformer on left (connected between REF (top) and FWD (bottom) ports):

Current-sense transformer on right (connected between OUT (top) and IN (bottom) ports):

Plots of the four coupling parameters (1 - 100 MHz)
(click on images to enlarge)

IN-port to FWD-port:

OUT-port to REF-port:

IN-port to REF-port and OUT-port to FWD-port:

Although they ought to be identical (or close to it), this image shows that the IN-port to REF-port coupling is noticeably different from the OUT-port to FWD-port coupling.  Note the difference at 30 MHz and below.  The IN-port to REF-port coupling is significantly lower (what we want!).

A plot showing actual Directivity (I'm measuring IN-to-REF, but after first normalizing the measurement of OUT-to-REF to 0 dB.  That normalization factor is then automatically applied to this new measurement).

For the sake of completeness, here is what the OUT-to-FWD coupling looks like over the range of 0.1 - 200 MHz (the full range of the 3577A Network Analyzer).  (Note that the IN-to-REF plot is about the same).  Horizontal divisions are 20 MHz.  Note that the hump just to the right of the middle of the plot is right around 144 MHz.  Therefore expect very poor performance (because of poor directivity) on 2 meters!

Here's an interesting photo.  This is what happens to the IN-port to REF-port coupling when the coupler's top cover is removed...

Here's the coupler, case screwed on.

Other Measurements

(Note that these were made before I reassigned the ports.  Never the less, they should be close to the values of the reassigned ports).

Let's take a look at S11 in the IN port with all other ports terminated in 50 ohms.  Here's the setup:

First, for reference, look at just S11 of the 50 ohm reference that I will attach to the coupler's "output" port (roughly -65 dB at 54 MHz).

And here's S11 of the terminated coupler.  Roughly -27 dB (apologies for the blurriness) at 54 MHz.

S11 of same configuration on Smith Chart:

S11 with all ports unterminated.  That is, S11 of just the coupler itself.

Measuring Self-Resonant-Frequency (SRF) of the 16-turn coil. Coil is paralleled with 50 ohm load, thus no cables, to minimize the effect of cable capacitance on SRF.  Look for dip in S11.

S11 plot.  And a nice dip at 10 MHz. That's the SRF (I don't know why there is a second dip).

Hmmm...I wonder if performance would improve if the SRF were higher...


Directivity and SWR Uncertainty:

Directivity has a direct effect upon VSWR error -- the poorer Directivity is, the more uncertain will be the VSWR reading (that is, the more uncertain will be the measured Return-Loss).

For example, if Directivity is -40 dB, VSWR uncertainty is fairly small for VSWRs under, say, 5, as shown in the graph below.  That is, if your VSWR measures 5:1 or better, the actual SWR will be close to that value.

Let's say the measured SWR is 3:1.  If our directivity is -40 dB, then the SWR might actually be somewhere between 2.9:1 and 3.1:1 -- in other words, VSWR will be within a narrow range that's essentially equal to 3:1.

But as Directivity worsens, uncertainty grows.  If Directivity = -30 dB, then a measured VSWR of  3:1 could, in reality, be a VSWR anywhere between 2.7:1 and 3.4:1.

Or let's say Directivity is only -20 dB.  Now, if we measure a VSWR of 3:1, the actual VSWR could be anywhere from 2.3:1 to 4.6:1.  And this spread widens significantly for VSWRs greater than 3:1, as seen in the graph below.

And for reference, here's the graph for -35dB Directivity (my Coupler at 54 MHz):

Note:  These graphs were each calculated using an EXCEL calculator, "VSWR Uncertainty versus Directivity, Return-Loss", which can be downloaded via a link in the "Links" section, below.  I'm assuming the equations in the spreadsheet are correct.


Other Notes and Comments:

1. Ground only one side of each coax cable that runs through the cores, not both sides!
2. Experiment with which ends of the transformer windings connect to ground and which ends connect to ports.  For example, the Voltage-sense transformer could connect to either the IN port or the OUT port, and also either end of the 16 turns of this transformer could go to this selected port.  These choices do affect performance.  You will need to experiment and discover which connections give the best response.
3. Experiment with grounding one side or the other of the shields of each of the "one turn" coax cables.
4. A Network Analyzer has been invaluable.  I don't know how I would have tested this coupler without one.
5. And many thanks to Dick Benson, W1QG, for his invaluable help and advice!!!

>>> Important Updates!!! <<<

For additional information on designing Direction Couplers, please see this later post:  http://k6jca.blogspot.com/2015/07/antenna-auto-tuner-design-part-5.html .

As part of the Directional Coupler design in this post I analyze core selection (among other things).  Serendipitously, my core choice (above),  Fair-Rite 2643625002, looks pretty good, per my spreadsheet below (see http://k6jca.blogspot.com/2015/07/antenna-auto-tuner-design-part-5.html for more details).

(click on image to enlarge)

(Note that peak voltage and peak current (at peak power, i.e. AM modulation) assume an infinite SWR on the transmission line.)

Also, I describe the build of another Directional Coupler here:  http://k6jca.blogspot.com/2015/12/antenna-auto-tuner-design-part-8-build.html


Links to my Directional Coupler blog posts:

Notes on the Bruene Coupler, Part 2

Notes on the Bruene Coupler, Part 1

Notes on HF Directional Couplers (Tandem Match)

Building an HF Directional Coupler

Notes on the Bird Wattmeter

Notes on the Monimatch

Notes on the Twin-lead "Twin-Lamp" SWR Indicator

Calculating Flux Density in Tandem-Match Transformers


And some related links from my Auto-Tuner and my HF PA posts:

Auto Tuner, Part 5:  Directional Coupler Design

Auto Tuner, Part 6:  Notes on Match Detection

Auto Tuner, Part 8:  The Build, Phase 2 (Integration of Match Detection)

HF PA, Part 5: T/R Switching and Output Directional Coupler


Useful Links:

Directivity and VSWR Measurements
Bird, Straight Talk about Directivity

Mini-circuits, Table, Return Loss vs VSWR
EXCEL Calculator, VSWR Uncertainty versus Directivity, Return-Loss

Fair-rite 2643625002 datasheet
Thermax RGU-142 Coax Datasheet

Philips, Design of HF Wideband Power Transformers, Part 1
Philips, Design of HF Wideband Power Transformers, Part 2

N8LP Wattmeter (QEX Article)
N2PK Power and Return-Loss Meter


And Finally, the Standard Caveat:
I could have easily made a mistake in any of the above, so please approach this material with a bit of skepticism -- don't assume it's correct.  And if you do find an error, or would like more detail, please feel free to contact me.