Tuesday, February 3, 2015

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

Building an HF Directional Coupler

Notes on the Bird Wattmeter

Notes on the Monimatch

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


And some related links from my Auto-Tuner posts:

Part 5:  Directional Coupler Design

Part 6:  Notes on Match Detection

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


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.


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