500 Watt Antenna Tuner - Part 5 - Directional Coupler

As I outlined in section 2, Analytical Model, I will measure the phase and gain of the reflection coefficient and from that, calculate the exact matching solution.

I will use the Analog Devices AD8302 to measure the magnitude and phase of the reflection coefficient.  Its phase comparator is a multiplier so it will produce the same output voltage if the phase of one of the signals (let's assume this is the forward signal) is leading or lagging by the same amount relative to the second signal (which would be the reflected signal).  This can be seen from the following diagram from the data sheet.  

My original intention was to measure the magnitude and the phase of the reflection coefficient and arrive at the answer in one step using this Analog Devices app note (https://ez.analog.com/cfs-file/__key/communityserver-wikis-components-files/00-00-00-01-03/UsetwoAD8302tomeasure360degrees_2D00_RevA.pdf).  After going down many blind allies, I have concluded that I can only directly measure the phase angle to within 180 degrees and not to the full 360 degrees (the same output for negative and positive phase angles in the -180 to +180 degrees range).   The problem that I could not solve was building a broadband 90 degree phase shift circuit.

In conversation with Joe Taylor, K1JT, he suggested varying the frequency and looking at the change in the phase to select between the two results.  A great idea.  It would require me to control the frequency of the rig from the tuner, but that is a problem that is much easier to solve (I am beginning to think that I need to link the Raspberry Pi running my Stationmaster software, and the tuner and the amp under development using the home network - Stationmaster running on a Raspberry Pi is already on the home network.

Here is a little summary of the Smith Chart characteristics.  The reflection coefficient from a (normalized) complex impedance of r + jx is measured on its real (horizontal) and imaginary (vertical) axis.  Values of r and x are plotted on the constant resistance and constant reactance circles and arcs.  Points above the horizontal axis have an inductive component with x > 0 and points below the horizontal axis have a capacitive component with x < 0.  Also, the angle of the reflection coefficient vector (hence phase of the reflection coefficient) is positive and varies between 0 and 180 degrees on the upper half of the Smith Chart and is negative and varies between 0 and -180 degrees on the lower half of the Smith Chart.  

I should also talk through the properties of the AD8302 phase comparator.  When the phase difference is positive, as the phase difference increases from zero to 180 degrees, the output voltage decreases from 1.8 volts to zero volts.  When the phase difference is negative, as the difference decreases from zero to -180 degrees, the output voltage also decreases from 1.8 volts to zero.  So, when the reactance in the upper half decreases (phase of the reflection coefficient moves towards zero), the output voltage increases.  When the reactance in the lower half decreases (phase of the reflection coefficient moves towards -180 degrees), the output voltage also decreases.

By increasing the frequency, reactance on the upper half of the Smith Chart increases and that results in lowering the phase angle (the output voltage goes up).  If this condition is encountered, the positive phase angle value is the right answer.  Increasing the frequency, decreases the reactance on the lower half of the Smith Chart and hence it decreases the phase angle (output voltage goes down).  If this condition is encountered, the negative phase angle value is the right answer.

For points close to the real (horizontal) axis and above it, rotating clockwise could cause the point to cross the x axis and potentially make the phase angle smaller.  Similarly, for points close to the x axis and below it, rotating counter clockwise could do the same.  So, the I will also test the location of the point by decreasing the frequency.  The only time this will become a problem is close to the edge of the band and close to the real axis.  In this case, I will test both solutions and select the smaller SWR.

Which brings up the question how much to move the frequency to get a measurable result.  Looking at the graph below (TPC26), the measurement accuracy is within a few tenths of a degree in the 30 to 150 degree range (or -30 to -150 range), within about one degree in the 15 to 165 range and to within and to within 2 degrees in the 10 to 170 degree range.  It is important to note that from 0 to 180 degrees, the graph is (locally) monotonic.  This is also true from 0 to -180 degrees (though not true from -180 to +180 degrees).  This might come in handy in practice.

The lowest frequency range that the phase transfer function of the AD8302 device is specified is at 100 MHz (see figure below).  This function is specified up to 2,200 MHz and as the frequency goes up, the accuracy deteriorates.   So, I can safely assume that the device performance in the HF band will be as it is at 100 MHz or better.

So, I am going to assume that I need to move the frequency enough to see a 5-6 degree change in the phase angle.

To see how much frequency change I need to see 5-6 degrees of phase change, I started by testing my antennas.  I have four: 10m, 15m, 20m, and 40m ground mounted verticals fed in parallel with lots of ground radials.  The 40m antenna is made of a load coil and a stub on top of the 20m antenna.  So, I ran the tests, saved the NanoVNA data as csv files and used Excel to analyze them.  By inspection, in the 40m band, at the bottom of the band a 36 KHz and at the top of the band a 93 KHz shift gives a 6 degree phase shift.  In the 20m band, the required changes in frequency at the two end of the band are 84 and 49 KHz (interesting to note that at the top of the 20m band, my antenna goes from being inductive to being capacitive, so I will at least have one good test case).  The required frequency changes in the 15m band are 58 KHz and 54 KHz and for the 10 meter band are 340 KHz and 68 KHz.  They all look manageable.

I will have to test some of the antennas at the DVRA shack to see if the results hold.

In doing this analysis, my other observation is that these large errors occur near the Smith Chart x axis where the phase angel is small.  So, I will only need these larger frequency changes at low phase angles.

With the phase measurement algorithm somewhat settled, I will move to the interface between the directional coupler and the AD8302.  

• The input range of AD8302 is 60 dB from 0 dBm to -60 dBm referenced to 50 ohms
• The highest power level in my various simulations without triggering the hardware trip circuit is about 550 watts.
• I will add an extra 100 watts of safety margin and map 650 watts (58 dBm) output power to 0 dBm at the input of the AD8302.  That eats about 1.1 dB into the dynamic range relative to 500 watts.  
• Hence there needs to be 58 dB of attenuation between the output and AD8302.
• This puts the voltage at the input of the AD8302 at -14 dBV for 500 watts against a max input specification of -13 dBV.  650 watts at the output maps to -12.9 dBV (800 watts would put the voltage at -12 dBV which is not great but still much less than -3 dBV absolute maximum).
• I will implement 30 dB of attenuation (32:1 turns ratio) in the transformers and 28 dB in a three stage cascade of attenuators.
• Forward power is split into two branches, one for measuring reflection coefficient and the other for measuring power output.
• The attenuation in the leg for measuring the reflection coefficient is composed of Pi (-8 dB), splitter (-6 dB), T (-10 dB), and Pi (-4 dB) for a total of 28 dB.
• The attenuation in the power measurement leg is composed of Pi (-8 dB), splitter (-6 dB), T (-8 dB), and Pi (-2 dB) for a total of 24 dB.
• Reflected power is also split into two branches.  The branch for measuring the reflection coefficient is exactly the same as the forward power leg.  The other branch is simply terminated in 50 ohms.
• Since the minimum input to the AD8302 is -60 dBm, the lowest power level in the output that maps into the AD8302 range is -2 dBm or 0.6 mW which is more than enough dynamic range.

For the design of the attenuator, I used the tools at the RF Cafe (There is a copy of the schematic and simulation results below): https://www.rfcafe.com/references/electrical/attenuators.htm

The values used are from the 1% resistor value table, not the absolute values from the RF Cafe tool.

Now I need to work on the voltage sense inductor.  I have the number of the primary turns (32).  I am looking for an inductance value for the primary that does not put too much of a load on the output line (3% would be around 100 mA rms), maybe around 2-3K which at 3.5 MHz would be in the 90-130 micro Henries.  

\begin{equation}A _{L}=\frac{L}{N ^{2}}\end{equation}

Plugging 90-130 micro Henries and 32 turns gives us:

\begin{equation}A _{L}=\frac{90,000-130,000}{32 ^{2}}=90-130\  nH/turns ^{2}\end{equation}

Let's leave this here as it is and come back to it in a bit.  These Al values and the required frequency range in combination might be hard to come by.

For the purpose of thermal design, Jeff, K6JCA used a 3:1 SWR at 200 watts and I will do the same.  At this SWR, the reflection coefficient is 0.5 which yields a load resistance of 3 times 50 ohms or 150 (or 16.67) ohms.  200 watts into 150 ohms requires 173 volts rms which is what I will use for thermal design.

For the purpose of avoiding saturation, he used the 800 watts peak into the same load which yields 490 volts peak by the same math (he also recommends using peak instead of rms value for calculating the maximum flux density which I will follow).

I will start with the heating requirement by going back to the RF Circuit Design book:

\begin{equation}B _{op} = \frac {E \times 10 ^{8}}{4.44fNA _{e}}\end{equation}

Where E is the maximum rms voltage, f, the frequency, N, number of turns and Ae is the effective cross section area in centimeters squared.  Since f is in the denominator, we will use the smallest f, 3.5 MHz for the largest flux.

I will start with Fair Rite ferrite toroid cores.  I have had good luck with them in past projects, they are available from Mouser where I usually shop and I have been driving by their plant on my way to Troy, NY for the past 50 years which should be reason enough.

Looking through the Fair Rite catalog, there are only 3 inductive (vs. suppression and power) materials that are recommended for HF and higher operations: 61 (<40 MHz), 67 (<150 MHz) and 68 (<500 MHz).  There is nothing in the 68 material that even comes close to the Al that I need.  So, I will start by looking at 68 material since it can get me into 6 meters.  The highest Al in this family is 55, so the highest inductance will be 56 micro Henries and at 3.5 MHz, it will yield an impedance of 1.2K Ohms, not quite what I was targeting, but still ok, we are in the 100-200 mA range (61 material has much higher Al values, but I will only look at it if I have to because of the recommended frequency range).

I will work this backwards.  There are ten 67 material toroids available from Mouser.  There are two that are a bit pricy, so I will drop those for now.  There are also a bunch where Al is 25 or less which would too high of a load on the output.  That leaves three with Al values of 39, 47, and 48.  We want to keep the temperature rise below 35 degrees:

\begin{equation}\Delta T (^{\circ} C) = \left [ \frac {P (mW)}{A (cm ^{2})} \right ] ^{0.833} \end{equation}

This table shows the three cores with acceptable Al values and uses the above equation to calculate total acceptable power dissipation for a 35 degree C temperature rise.  Then it divides it by the effective core volume to determine power density.  The heat dissipating surface area is assumed to be the surface area of the core.

Core	Area (sq. cm)	P (mW)	Ve(cc)	Pl (mW/cc)
1901	9.77	697.62	0.93	750.13
1701	25.30	1,805.78	4.5	401.29
1201	28.43	2,029.20	5	405.84

The graph below is from the Fair Rite 67 material data sheet.  I have used the higher temperature data since it is a bit more conservative.  To keep the temperature rise to 35 degrees, the flux density has to keep the power density to the limits in the above table.  

Now, looking at the flux densities across the band:

Band	3.5 MHz	7 MHz	14 MHz	18 MHz	21 MHz	24.9 MHz	28 MHz	50 MHz
1901	330	165	82	64	55	46	41	23
1701	167	84	42	32	28	23	21	12
1201	143	71	36	28	24	20	18	10

Clearly a 330 Gauss flux density exceed the required power density to keep the temperature rise under 35 degrees C.  So, the 1901 core is out.  The 1701 and 1201 cores both meet the requirements since they both have flux densities between 100 and 200 Gauss at 3.5 MHz and that puts the power density at 300 mW/cc, below the 400 mW/cc limit.  This makes sense since these two cores are about the same size made from the same material.  Clearly from the above table, at higher frequencies the flux densities are lower and from the graph, the power density requirement is easily met.

Now we need to test the saturation flux density:

\begin{equation}B _{op} = \frac {490 \times 10 ^{8}}{4.44 \times 3.5 \times 10 ^{6} \times 32 \times 0.69}=142 \ Gauss\end{equation}

Well short of the saturation flux density as you see in this figure from the 67 material data sheet:

Given that the 5967001201 core is a bit less expensive, I will go with that for the voltage sense transformer and for no other reason than to match it, I will use the same for the current sense transformer (calculations for that next).

The drive for the current sense transformer is the power amp feed line.  So by the application of Ampere's law:

\begin{equation}B=\frac {\mu _{r} \mu _{0}NI}{2\pi r}\end{equation}

All units are in the MKS system, so the result will be in Teslas.  Under worst case scenario of 800 watts and 3:1 SWR, the current through the primary will be 7 amps.

\begin{equation}B= \frac {40\times 4\pi 10 ^{-7}\times 1\times 7}{2\pi \times .024}=2.33\times 10 ^{-3}\  Tesla = 23 \ Gauss\end{equation}

The voltage across the secondary is 7 amps divided by 32 (turns ratio) and times 50 ohms (the terminating resistance).  That is 11 volts.  So, if the core can support the voltage sense transformer stress, it can surely support 11 volts.   Hence any 67 material toroid that supports 32 turns of 22 AWG wire will do.   Speaking of 22 AWG wire, I am planning to use it for all current sense transformer secondary and voltage transformer primary.  Resistance per meter is 0.05315 ohms which is more than adequate.

Finally, here is the LT Spice schematic of the directional coupler transformers and attenuators:

The voltage sense primary inductance is the calculated inductance of the winding (32 turns through the 5967001201 core).  The secondary inductance is calculated to feed Spice since it maps turns ratios by the square of the inductance values.  The current sense primary inductance is the calculated inductance of one turn through the same core.  The secondary inductances are similarly calculated to satisfy Spice.  

The load resistor is 150 ohms to simulate a 3:1 SWR.   Also note that the splitter in the reflected path with one of its legs terminated in 50 ohms is there to equalize the two paths and not introduce extra phase shift in the reflected signal.

Both transformers are providing a 30 dB attenuation.  Vfor1 and Vref have equal (58dB) attenuation for measuring the gain and phase of the reflected voltage.   Vfor2 feeds the AD8361 true RMS power meter device.  The internal resistance of the device is the 225 ohm resistor in the HF band which in parallel with the external 63.4 ohm resistor forms the 50 ohm load to the attenuator network.

Input to the AD8361 with a 54 dB attenuation and 50 ohm load is as follows:

Power (Watts)	500	200	100	50	25
Output voltage (Vrms)	158	100	70	50	35
AD8361 input (mVrms)	315	199	141	100	71

Reasonably low error range of the AD8361 from the data sheet is in the 30 to 40 mVrms.  So, for the values of interest, the design is in range.  The maximum input to the device is 1 Vrms which translates to 500 Vrms or 5 KW into a 50 ohm load or 1.7 KW into a 150 ohm load.  For loads lower than 50 ohms, the voltages will be lower.

Next, the translation of measured AD8361 output by the microprocessor to output power.  I will be using a 3 volt precision reference and the Raspberry Pi Pico has a 12 bit A/D converter, so the conversion factor between the A/D reading and voltage output will be:

\begin{equation} V _{out} = \frac {3.0} {2 ^{13} -1} V _{in} \end{equation} And the voltage at the output when referenced to a 50 ohm load for a given power level P is: \begin{equation}V _{rms} = \sqrt{50 \times P}\end{equation} Atenuation of 54 dB as a voltage ratio between the load voltage and input to the AD8361 translates to: \begin{equation}\frac {V _{in}} {V _{load}} = 1.995 \times 10 ^{-3}\end{equation} Or: \begin{equation} V _{out} = 7.5 \times 1.995 \times 10 ^{-3} \times \sqrt {50} \sqrt{P}\end{equation} 

 \begin{equation} P = 89.335 V _{out} ^{2}\end{equation}

500 Watt Antenna Tuner Part 1 - Introduction

500 Watt Antenna Tuner Part 2 - Analytical Model

500 Watt Antenna Tuner Part 3 - Simulator

500 Watt Antenna Tuner Part 4 - Capacitors and Inductors

500 Watt Antenna Tuner Part 4A Capacitors

500 Watt Antenna Tuner Part 4B Inductors

500 Watt Antenna Tuner Part 5 - Directional Coupler

500 Watt Antenna Tuner Part 6 - Matching Algorithm

500 Watt Antenna Tuner Part 7 - User Interface

500 Watt Antenna Tuner Part 8 - Software and Microcontroller

500 Watt Antenna Tuner Part 9 - Pre Build Schematics and Board Layout