Antenna Auto-tuner Design, Part 4: Relays and L-Network Schematic (Preliminary)

[Update, 21 June 2016:  I received a comment from Jukka Siitari, OH2AXE correcting some questions (and misconceptions I had regarding the relay specifications.  You can find the full text of his comment in the 'comments' section following this post.  I have also inserted his comments into the body of the blog post text.]

[Second Update, 20 November 2023:  Comments received via email from another reader, Nelson Sollenberger, KA2C, made some interesting points.  I'm including these in this blogpost, as they counter some of OX2AXE's points assumptions of mine.]

In this fourth post I thought I'd look into relays. (Part 3 of this series can be found here).

I noticed that Elecraft uses the Omron G2RL series in their KAT-500.  The "high capacity" version of this family (which they use) is spec'd at 16 amps.

Looking at the Digikey website for other high-current low-profile relays, I found one made by Panasonic (their ALZ family).  Coincidentally, it has the same specs as the Omron relay.

So that I could compare them, I ordered a few of the Omron and the Panasonic relays from Digikey.  Here are some photos...

Omron G2RL relays on the left, Panasonic ALZ relays on the right, all with covers removed.

Omron G2RL-14-E Relay, view of contact mechanism.  Note the width of the copper:

Omron  Relay, normally-open contacts forced closed (12VDC applied):

Looks pretty good!

Panasonic ALZ12B12 Relay, normally-open contacts forced closed:

Hmmmm.....It looks like the contacts aren't contacting center-to-center, but rather at their top. Personally, I prefer the Omron relay -- it looks like it the relay contacts connect at their centers.

Looking more closely at the Omron Relay specs...

The important Omron Relay Specs:

• Contact Material:  Ag-alloy (Cd Free).  (Note that an earlier datasheet states AgSnO2 for single-pole relays; AgNi for double-pole relays).

• Contact Resistance:  100 milliohms, max.

• Operating Current:  16A

• Max Switching Voltage:  440VAC, 300VDC. (I'm confused as to why the AC voltage is higher than the DC voltage -- I would think that the DC voltage would be Vpk of the AC, or about 600 volts.)  [Comment from OH2AXE (20 June 16):  they are like this because DC arcs easier than AC when contact opens with full load (ref. welding). These are power relays intended for DC or mains frequency. RF is even worse, because it ionizes air and causes an arc easier than 50/60 Hz DC. You have noted this later in the text. ALWAYS tune with a much lower RF power and arcing should not be a problem.]

• Dielectric Strength Between Contacts "of the same polarity":  1000 VAC, 50/60Hz, 1 Minute.  (I'm confused by what the meaning could be of "contacts of the same polarity", but I believe this spec is the same as Panasonic's "Breakdown voltage between open contacts.")  
• [Comment from OH2AXE (20 June 16):  This specification is valid only for relays with 2 or more "poles", in this case DPDT version. It is the breakdown voltage between two adjacent contact sets. Your assumption leads to significant errors later in your text. For HF frequencies use the DC switching voltage (300V in this case) + safety margin. You note this later ("Recommendations for Transmitter Site Preparation"). ALWAYS tune with a much lower RF power and contact breakdown (i.e. arcing over) should not be a problem.]   
• [Comment from KA2C (30 Nov. 23):  If the Omron specifications are compared to similar relays from other manufacturers (for example, Schrack, Zettler, or Panasonic), it becomes apparent that Omron's dielectric strength for contacts "of the same polarity" actually refers to the breakdown voltage between open contacts on the same pole.  Thus, it applies to any relay; SPST, SPDT, DPDT, etc.] 

Let's check that this breakdown voltage is OK for my tuner application...

At low frequencies (e.g. 50/60 Hz), the breakdown voltage is 440 VAC.  But for HF RF signals the breakdown voltage is lower.  [K6JCA update -- this is the wrong voltage to use.  I correct this just a bit further down this post.]

Per the image below (from Nautel's "Recommendations for Transmitter Site Preparation, Sept., 04", available here), for the frequencies that interest me, the breakdown voltage is about 0.8 times the low-frequency AC breakdown.

(click on image to enlarge)

Given this relationship, the RF breakdown voltage would be equal to 0.8 * 440 Vrms (about 350 Vrms, or about 500 Vpk).   K6JCA update -- this is not correct...

Note that OH2AXE (see comment section, below) recommends that the DC breakdown value of 300 VDC be used as the RF breakdown voltage.

An emailed comment from KA2C (30 Nov 23) recommends that relay switching be done at low power levels so that arcing is not an issue.  However, will the contacts arc over during actual transmissions, after tuning has been completed at a lower power?

To calculate if the breakdown voltage can be exceeded if transmitting at peak power, after the Tuner has been tuned, we first calculate the "Open Contact" breakdown voltage, which, if we compare the specifications of similar relays to the Omron relay and translate Omron's "contacts of the same polarity" to the less opaque "open contacts on the same pole," is 1000 VAC,

Next, derate (for operation at RF frequencies), the 1000VAC spec by 0.8.  The resulting breakdown voltage between open contacts, at RF, is therefore 800VAC [i.e. 1131 Vpeak -- K6JCA].

The table below shows simulated L-network voltages and currents (for an assumed a peak power level of 800 watts):

(click on image to enlarge)

K6JCA (30 Nov. 23):  Given the Vpk values in the above table for a peak transmit power of 800 watts and an SWR of 10:1, the maximum voltage across the capacitors of an L-Network is 880 Volts, peak, which is appreciably below an Omron relay's open-contact breakdown voltage at RF of 1131 Vpk.  (Inductor peak voltage would be 956 Vpk, also less than the contacts' rating of 1131 Vpk).

Therefore arcing during operation should not be an issue.

Relay Measurements:

I made a couple of measurements on a sample-of-one G2RL-14-E relay:

Contact Resistance: 0.005 ohms (measured between the N.O. contact and the pole, with the relay energized (contacts closed), using an HP3468A DVM in 4-wire resistance measurement mode).

Contact Capacitance: 1 pF (approx) (measured between the N.O. contact and the pole, relay off, using a GenRad 1657 Digibridge).

For relay inductance, I calculate that it should be around 12 nH (Assume internal path length of 1” and contact width of 0.34” (0.87cm)).

Omron G2RL-2 DPDT Relay:

I thought I'd also take a look at the construction of the DPDT member of Omron's G2RL family, the G2RL-2:

Unlike the G2RL-14-E SPDT relay, this relay is only rated for an 8 Amp load.

Other notes on the Omron Relay:

"Sealed" seems to refer to the sealing of a tiny hole on the top of the relay package.

I really didn't see any difference between UL Class B and Class F Insulation.  To me they looked the same, but I might have missed something.

With these relays and with the inductors and capacitors selected in the previous, two posts, I'll  draw a preliminary schematic of the L-Network components and connections:


L-Network Schematic:

This schematic only contains the inductors, capacitors, and relay contacts.  The relay magnets and other circuitry will appear in schematics later.

(click on image to enlarge)

In its Power-Off state, the tuner defaults to Bypass Mode.  That is, the capacitors are disconnected and the inductors are all shunted.  There will be some parasitic effects, though, due to the capacitance of the capacitor-relays' open contacts and the inductance of the inductor-relays and the wires (or traces) interconnecting them.  I'll have to see if these are an issue when I build the network.

>>>  Important Note!!!  <<<

Schematics will change as this design progresses.

Be sure to check later postings in this series 

(especially Part 7) for later versions.

OK -- that's it for this blog post!

The previous post in this series, Part 3, can be found here: http://k6jca.blogspot.com/2015/06/antenna-auto-tuner-design-part-3.html

And the final "release" schematics can be found in Part 10 of this series:  http://k6jca.blogspot.com/2016/01/antenna-auto-tuner-design-part-10-final.html


Links to my blog posts in this Auto-tuner series:

Part 1:  Preliminary Specification

Part 2:  Network Capacitor Selection

Part 3:  Network Inductor Selection

Part 4:  Relays and L-Network Schematic (Preliminary)

Part 5:  Directional Coupler Design

Part 6:  Notes on Match Detection

Part 7:  The Build, Phase 1

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

Part 9:  The Build, Phase 3 (Incorporating a Microcontroller)

Part 10:  The Final Schematics


Resources:

• Datasheet, Relay, GR2L series, Omron:  https://www.components.omron.com/components/web/pdflib.nsf/0/8F66C9A835A195FE85257201007DD572/$file/G2RL_0911.pdf
• Datasheet, Relay, ALZ series, Panasonic:  http://www3.panasonic.biz/ac/e_download/control/relay/power/catalog/mech_eng_lz.pdf

• Datasheets, GDT, 1000V, EPCOS: http://media.digikey.com/pdf/Data%20Sheets/Epcos%20PDFs/B88069X3880T502.pdf

• Data, RF Breakdown Voltage, Transmitter Site Preparation Recommendations Sep 2004, Nautel:  www.nautel.com/wp-content/uploads/2011/04/Transmitter-Site-Preparation-Recommendations-Sep-2004.pdf

• Calculator, High Voltage Gap, Cirris Systems:  https://www.cirris.com/learning-center/calculators/50-high-voltage-arc-gap-calculator

My Other Tuner posts:

A quick tutorial on Smith Chart basics:  http://k6jca.blogspot.com/2015/03/a-brief-tutorial-on-smith-charts.html

The L-network:  http://k6jca.blogspot.com/2015/03/notes-on-antenna-tuners-l-network-and.html

A correction to the usual L-network design constraints:  http://k6jca.blogspot.com/2015/04/revisiting-l-network-equations-and.html

A look at highpass T-Networks:  http://k6jca.blogspot.com/2015/04/notes-on-antenna-tuners-t-network-part-1.html

More on the W8ZR EZ-Tuner:  http://k6jca.blogspot.com/2015/05/notes-on-antenna-tuners-more-on-w8zr-ez.html  (Note that this tuner is also discussed in the highpass T-Network post).

The Elecraft KAT-500:  http://k6jca.blogspot.com/2015/05/notes-on-antenna-tuners-elecraft-kat500.html
 
 The Nye-Viking MB-V-A and the Rohde Coupler  :  http://k6jca.blogspot.com/2015/05/notes-on-antenna-tuners-nye-viking-mb-v.html


Standard Caveat:

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

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

Antenna Auto-tuner Design, Part 3: Network Inductor Selection

In this, my third blog post on my Automatic Antenna Tuner design, I'll select and do a preliminary design of the inductors that I'll use.  (My previous post on capacitor selection is here: http://k6jca.blogspot.com/2015/06/antenna-auto-tuner-design-part-2.html ).

I will:

• Select the values of inductors
• Calculate the maximum RMS voltage across each inductor
• Determine if an inductor should be air-wound or wound on a toroidal core
• Investigate which type of toroid core to use
• Calculate power dissipation due to iron powder toroidal core loss
• Estimate coil wire lengths for both air-wound and toroidal-wound inductors
• Calculate wire resistance and the resulting power dissipation of different gauge wires, per wire length for each coil.

OK, let's start!

Selecting the Inductor Values

Again, I'm going to assume that the worse-case SWR that I want to match is 10:1, and that the maximum power is 200 watts (average) and 800 watts, peak.

Here's the table I created of the maximum L and C values required to match any load with an SWR of 10:1:

(click on image to enlarge)

As you can see, at 3.5 MHz I should have at least 6820 nH of inductance to guarantee a match anywhere on the Smith Chart's 10:1 Constant SWR Circle.

And I'd like to have the smallest inductor be less than the 50 nH used by Elecraft in their KAT500 -- at 30 and 54 MHz it is this inductance, and not their smallest capacitance, that is the limiting factor in fine-tuning SWR (see http://k6jca.blogspot.com/search/label/Elecraft%20KAT500

So let's say that I simply halve this value to 25 nH and call it my smallest inductor.

If I do this, then, stepping inductor values in powers of 2, the resulting inductors would be

25 nH

50 nH

100 nH

200 nH

400 nH

800 nH

1600 nH

3200 nH

These sum to 6375 nH -- not quite my coal of 6820 nH, but close.  Is it close enough?

I ran a quick simulation with a Matlab routine I wrote -- I'd still be able to tune any 10:1 SWR down to 1.2:1 or better (usually better) with 6375 nH as the max inductance.  So, as a first cut, these values are close enough.

If I were very very picky, I could make the smallest inductor, say, 27.5 nH.  This would result in values of 27.5, 55, 110, 220, 440, 880, 1760, and 3520 nH, for a total inductance of 7012 nH.  More than enough.

But, to be honest, I like the simplicity of the first set of values (25 nH - 3200 nH) and for the moment I'm going to go with them.  But -- I might decide to change my mind later.

To summarize:  My initial selections of inductor values are these:

25 nH

50 nH

100 nH

200 nH

400 nH

800 nH

1600 nH

3200 nH

With these values of inductance and the values of capacitance selected in my previous post (see the values listed in the summary at the end of that post, here), what would this tuner's "Match Space" look like?

Here's the "Match Space" at 3.5 MHz:

(click on image to enlarge)

Not too bad!  Just slightly inside the 10:1 SWR circle for reflection coefficients with angles between about -45 and 45 degrees.

And here it is at the other end of the spectrum, 30 MHz:

(click on image to enlarge)

 Looks good.  I believe this will work.

And although I don't plan to operate on 160 or 6 meters, here's how the match space looks on those two bands:

(click on image to enlarge)

Yes, not too great on 160 meters.  Really needs more L and C.

(click on image to enlarge)

6 meters is probably tunable.  But if I were serious about using the tuner on this band I would probably make both the minimum capacitance and the minimum inductance values smaller.

OK, so the match-space looks about what I'd expect it to be.  Let's continue on...

One question I need to answer:

Which coils will be Air-Wound and which will be on an Iron-Powder Core?

To minimize coil loss, I'd like to "air wind" (air core) as many inductors as possible, but there will be size constraints and coupling constraints (inductor-to-inductor, inductor-to-other-stuff) that will limit which inductors should be air-wound solenoid coils and which should be wound on iron powder toroid cores.

As a starting point (which will probably change), I'm going to say that:

1. The 25, 50, 100, 200, and 400 nH inductors will be air wound.
2. The 1600 and 3200 nH inductors will be wound on iron powder toroid cores.
3. And the 800 nH inductor might be air wound (preferable), or it might be on a toroid core.

I'll use a nice program, "Mini Ring Core Calculator" (available here) to calculate these coils parameters and, where appropriate, the optimum toroidal core material and core size, but to use this program I first need to know the maximum RMS voltage across each inductor.  So let's calculate these voltages.

Calculating Maximum Coil Vrms

I'm using maximum Vrms (based on a 200 watt average) instead of Vpeak (based on 800 watts, peak) because the end result of the following calculations will be coil power dissipation.  And thus, because this heating of an inductor does not occur immediately, but rather over time, the RMS voltage value is more appropriate to use.

The inductors are connected in series, and I've calculated (using Excel) the max Vrms across the total inductance as the load reflection-coefficient is stepped around a Smith Chart's 10:1 SWR Circle.  I can then easily sort this data for the maximum voltage value.

And for a power in of 200 watts and at an SWR of 10:1, the max Vrms voltage across the entire inductance is 338 V.

The table below summarizes these calculations.  Note that they are independent of frequency.
 

(click on image to enlarge)

But to use the "Mini Ring Core Calculator", I need to know the voltage across each inductor, rather than the voltage across the entire inductance.  Luckily, this isn't too hard to calculate (especially with Excel and Matlab available).   Using the previous data generated via Excel, I wrote a simple Matlab routine that calculates voltage across each inductor as the load's reflection coefficient is moved around a Smith Chart's 10:1 SWR Circle (with Power In  = 200 Watts).

Here's a graph showing how these voltages change at 3.5 MHz.

(click on image to enlarge)

And here's a similar graph showing the voltage changes at 30 MHz.

(click on image to enlarge)

The maximums of the inductor voltages shown in these charts (and those for the other bands of interest) are collected in the table below:

(click on image to enlarge)

So let's plug these values into "Mini Ring Core Calculator" and start figuring out what these inductors should be!

I'll start with the 3200 nH inductor.  It's only used on 3.5 and 7 MHz, per the above table.  And let's look at the programs results for this coil at  3.5 MHz (max Vrms = 300 V).  I've assumed that the toroidal core is a T157-6 core.

(click on image to enlarge)

Note the two numbers in red at the lower right.  One is "Flux" (actually, Flux Density), and the other is "Temperature Rise".  Of these two numbers, it is the Temperature Rise value that is the important number (Flux Density really just feeds into the Temperature Rise Calculation).

Why is Temperature Rise important, and what should it be limited to?

At the end of the post I've linked to a number of Amidon and Micrometals data sheets and app notes.  Here's a summary of the data regarding flux density and temperature:

• Iron Powder materials can tolerate up to 5000 Gauss without significant saturation effects (Amidon).
• Overheating of a core will take place long before saturation (in most applications) (Amidon).
• Flux Density Limits (i.e. the "max. Flux" box in the screen capture above) is used as a guideline to avoid excessive heating (Amidon).
• All iron powder cores are susceptible to permanent increases in core loss when exposed to elevated temperatures for extended periods of time.  This thermal aging is irreversible. (Micrometals). 
• If a core is used intermittently, keep its operating temperature below 100° C (Amidon).
• If a core is used continuously, keep its operating temperature below 75° C (Amidon).
• Long term operation of iron powder cores above 80° C can cause a permanent reduction in both Q and inductance.  (With constant power dissipation, it typically takes a core about 2 hours to reach its final temperature) (Micrometals).

So, to repeat:  the important number from the Mini Ring Core Calculator is "Temperature Rise", not "Flux".

The Mini Ring Core Calculator's "Temperature Rise" value turns red for delta-T's of 50° C or more.  So a good design target is to design an inductor so that its temperature rise is less than 50° C.

(Note -- a delta-T of  50° C over an ambient of 25° C results in a core temperature of 75° C, which isn't bad.  But if the circuit is inside a box that has little or no internal airflow, the box's internal ambient temperature will be higher.  If, say, the box's internal ambient is 50° C, then core temperature could be 100° C, and this would concern me.)

Below are tables with the Calculator's results for 3200, 1600, and 800 nH inductors (using the max voltages when power-in is 200 watts and SWR is 10:1), with different core sizes and materials.

Here's the table for the 3200 nH inductor.  The values in red reflect the red values returned by the Calculator:

(click on image to enlarge)

Although the T157-6 core is probably acceptable, I prefer to be conservative in this design and so I lean towards the last three (T184-6, T157-17, or T184-17).  The T157-17 and T184-17 cores both have very good core-loss numbers.  Of these two, I'm going to choose the last one: 19 turns on a T184-17 core.

Here's the comparison table for the 1600 nH inductor:

(click on image to enlarge)

Of these four, I only really like the last two (again, core loss looks pretty good).  Both use type-17 material.  Of these two, I'm going to choose the last one: 14 turns on a T184-17 core.

And finally, here's the comparison table for the 800 nH inductor:

(click on image to enlarge)

None of these look great.  Even the type-17 material in the T184 core becomes excessively lossy, in my opinion.  So I'll try to make this coil air-wound.

So to summarize, the inductors wound on toroid cores, thus far, are:

• 3200 nH:  T184-17, 19 turns.  Wire diameter to-be-determined.
• 1600 nH:  T184-17, 14 turns.  Wire diameter to-be determined.

(Core size or material might change, though, after I try to wind these).

A couple of quick note on '6' versus '17' material.  As you can see from the tables above, the '17' material has better loss characteristics.  It's only drawback (as far as I can tell) is a slightly worse temperature coefficient, but I don't think this difference is too significant.  Below are Amidon's TC charts.  The first contains the curve for -6 material, the second contains the curve for -17 material.

Also, per Amidon pricing, the 17 material is more expensive than the 6 material.  Not a big deal for a "one off" design like this, but something to be aware of if one were designing a product.

(click on image to enlarge)

(click on image to enlarge)

So if the core of an inductor built using type-17 material rises to 100° C, inductance will change by about 0.5%.  That's acceptable, in my opinion.

Toroid Core Wire Diameter

What should the wire diameter be?  As frequency increases skin-effect will become more pronounced and thus losses will increase, so the "thicker" the wire is, the better.

Using an on-line "AC Resistance" (i.e. skin-effect) calculator (here: http://chemandy.com/calculators/round-wire-ac-resistance-calculator.htm), I've calculated the AC resistance of different wire gauges at different frequencies:

(click on image to enlarge)

If I use these resistance numbers (in ohms-per-inch) and multiply them by the wire length determined by the Mini Ring Core Calculator program, I can determine power loss due to resistance.

So...for each toroid coil, I've taken its highest frequency of operation (where we should see the highest loss due to skin effect) and assumed the worst current (6.2Arms).  The different wire lengths for a particular coil in the tables below represent the different amounts of wire required for the various core options (size and number of turns -- see the inductor tables, above).

The resulting power loss, versus wire gauge, is:

(click on image to enlarge)

(Note that, although the table above shows the 800 nH coil as being wound on a toroid core, I'm going to try to make it an air-wound solenoid coil, instead).

To minimize wire loss, I'd like to use 12 AWG, if possible (and I have a roll of it).  (And I'll give 10 AWG a try, too, but if these gauges are too unwieldy to use, I might need to fall back to 14 AWG).

Total toroid coil loss will be the sum of two losses:  core-loss plus wire-loss.

OK, let's move on to the air-wound inductors...

Air-wound Inductors:

I would like these inductors to be air-wound solenoid coils:

• 25 nH
• 50 nH
• 100 nH
• 200 nH
• 400 nH
• 800 nH

Fortunately, the Mini Ring Core Calculator also lets me calculate air-wound coils.

So, to use this calculator, I will first roughly estimate coil diameter and length.  From these dimensions and the target inductance, the calculator returns:

• Number of Turns
• Wire Length
• Max AWG

Using the calculator, I can then tweak the dimensions to give me an "integer" number of turns.

When I'm satisfied with the results, I can take the calculated wire lengths and estimate total coil resistance (due to skin effect) for frequencies of interest.

Because I know the maximum RMS voltage across a coil (see earlier table), I can calculate the current passing through a coil (I = V/(2πfL)).  With this current and the ESR I can then calculate the coil's loss (ESR*I^2).

I've run these calculations and I've put the results into the table below.  Note that, in addition to power loss at 30 MHz, I've also calculated power loss at 54 MHz.

Note, too, that the 800 nH coil is calculated at 24.9 MHz (the highest frequency it's used for matching a 10:1 SWR), but I used the skin-effect resistance (ohms per foot) for 30 MHz.

(click on image to enlarge)

And finally, please note that these coil dimensions are really just place-holders to get an approximation of the wire lengths.  These dimensions will probably change when I actually build the coils.

OK, that completes this preliminary inductor selection and design.  Let's summarize...

Summary of Inductors:

(click on image to enlarge)

And a quick comment on these inductor values...they will change.

The relays and the interconnecting wires (or PCB traces) each have their own inductances (parasitic).  To maintain my goal of a 25 nH step between successive inductance steps, I need to account for these parasitic inductances, otherwise I will have varying inductance deltas as I successively step through the values.

Conceptually, compensating for these parasitic inductances isn't hard to do, as I've described in the drawing below (showing the smallest three inductors, but the principle is applicable to all):

(click on image to enlarge)

If you go through the arithmetic you'll see that, with these new inductor values, the inductance delta is always 25 nH.  As I said...conceptually easy.  The "interesting" task will be determining what these actual parasitic inductance values are!

That's the end of this post!  The next post will discuss relays and other components in the RF path.

The previous post, Part 2 -- Capacitor Selection, is here:  http://k6jca.blogspot.com/2015/06/antenna-auto-tuner-design-part-2.html


Links to my blog posts in this Auto-tuner series:

Part 1:  Preliminary Specification

Part 2:  Network Capacitor Selection

Part 3:  Network Inductor Selection

Part 4:  Relays and L-Network Schematic (Preliminary)

Part 5:  Directional Coupler Design

Part 6:  Notes on Match Detection

Part 7:  The Build, Phase 1

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

Part 9:  The Build, Phase 3 (Incorporating a Microcontroller)

Part 10:  The Final Schematics


Resources:

Website, Amidon:  http://www.amidoncorp.com/
Website, Micrometals:http://www.micrometals.com/

Data, Iron Powder Cores, Amidon:  http://www.amidoncorp.com/product_images/specifications/1-02.pdf
Data, Iron Powder Materials, Amidon:  http://www.amidoncorp.com/product_images/specifications/1-03.pdf
Data, Property Chart, Iron Powder, Amidon:  http://www.amidoncorp.com/product_images/specifications/1-41.pdf
Data, Toroid Cores, Material 6, Amidon:  http://www.amidoncorp.com/product_images/specifications/1-06.pdf
Data, Toroid Cores, Material 17, Amidon:  http://www.amidoncorp.com/product_images/specifications/1-07.pdf
Data, Temperature Coefficients, Iron Powder Toroidal Cores, Amidon: http://www.amidoncorp.com/product_images/specifications/1-08.pdf
Data, Iron Powder Details, Micrometals:  http://www.micrometals.com/materials_index.html
Data, Iron Powder Cores, General Properties, Micrometals:  http://www.micrometals.com/materials_index.html 
Data, Magnetic Tolerance versus Iron Powder Material, Micrometals:  http://www.micrometals.com/materials_index.html
Data, Wire Diameters, AWG:  https://en.wikipedia.org/wiki/American_wire_gauge


App Notes, Index, Iron Powder Cores (see "RF Applications" section), Micrometals:  http://www.micrometals.com/appnotes_index.html
App Note, Design, "Power Considerations (Iron Powder and Ferrite)," Amidon: http://www.amidoncorp.com/product_images/specifications/1-35.pdf
App Note, "Power Considerations (cont')", Amidon:  http://www.amidoncorp.com/product_images/specifications/1-36.pdf 
App Note, Thermal Aging (Important note!), Micrometals: http://www.micrometals.com/thermalaging_index.html

Software, Toroid Inductor Calculator (including loss), Mini Ring Core Calculator: http://www.electronicecircuits.com/electronic-software/mini-ring-core-calculator-program

Calculator, Web, AC Skin Resistance (round wires):  http://chemandy.com/calculators/round-wire-ac-resistance-calculator.htm


My Other Tuner posts:

A quick tutorial on Smith Chart basics:  http://k6jca.blogspot.com/2015/03/a-brief-tutorial-on-smith-charts.html

The L-network:  http://k6jca.blogspot.com/2015/03/notes-on-antenna-tuners-l-network-and.html

A correction to the usual L-network design constraints:  http://k6jca.blogspot.com/2015/04/revisiting-l-network-equations-and.html

A look at highpass T-Networks:  http://k6jca.blogspot.com/2015/04/notes-on-antenna-tuners-t-network-part-1.html

More on the W8ZR EZ-Tuner:  http://k6jca.blogspot.com/2015/05/notes-on-antenna-tuners-more-on-w8zr-ez.html  (Note that this tuner is also discussed in the highpass T-Network post).

The Elecraft KAT-500:  http://k6jca.blogspot.com/2015/05/notes-on-antenna-tuners-elecraft-kat500.html
 
 The Nye-Viking MB-V-A and the Rohde Coupler  :  http://k6jca.blogspot.com/2015/05/notes-on-antenna-tuners-nye-viking-mb-v.html


Standard Caveat:

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

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

Antenna Auto-tuner Design, Part 2: Network Capacitor Selection

In this second blog post, I'll select the capacitors for my auto-tuning L-Network antenna tuner.  (The first blog post for my Automatic Antenna Tuner is here:  http://k6jca.blogspot.com/2015/06/antenna-auto-tuner-design-part-1.html).

In this post I will:

• Determine the capacitor voltage rating
• Calculate the maximum RMS current through each capacitor
• Select the type of capacitors to use
• Estimate capacitor ESR
• Estimate capacitor power dissipation (using the max RMS current through each capacitor and its estimated ESR).

Let's get started...

To recap the specification from the first post, I'm limiting low-frequency operation to 3.5 MHz.  Also, I am assuming that the worse-case load will have an SWR of 10:1 and that it could lie anywhere on a Smith Chart's "Circle of Constant SWR" for an SWR of 10.

Given these constraints, I calculated the following maximum L and C requirements for a lowpass L-Network, per band:

(click on image to enlarge)

So I'll need 2730 pF (and max inductance is 6.82 uH) to match the anywhere along the circumference of the 10:1 Smith Chart SWR-circle at 3.5 MHz

Also, I want to know the current and voltage specifications that the capacitance and inductance must meet.

To accomplish this, I created an EXCEL spreadsheet to step around a Smith Chart's "circle of constant SWR" (which determines the range of possible load impedances) and, given each load impedance, the value of the matching components to match that load impedance, and a given transmit power, I calculated peak and average voltages and currents for the matching network's components.

From the range of calculated values, the maximum peak and maximum average currents and voltages are tabulated in the table, below.  Note that they assume an average power of 200 watts (e.g. AM Carrier), a peak power of 800 watts (e.g. SSB peak), and a maximum SWR of 10:1, and thus the peak voltage across the L-network capacitance is 880 volts.

(click on image to enlarge)

Let's round the Vpeak requirement of 880 up to 1000 volts (to give us a bit of headroom).  Therefore...

Capacitor Voltage Specification:  Vpeak of 1000 VDC (min).

And from the table:

Capacitor Current Specification:  Irms of 6.9 A

But this last spec is a bit tricky --  the total capacitance is made up of capacitors connected in parallel, so this current might be divided through a number of parallel caps.

I'll calculate the maximum current in each cap in just a bit, but before I do, I first want to select the values of caps that I'll use, because these values will determine the amount of current that flows through each.

Although I have a box of miscellaneous-valued high-voltage doorknob caps, their ESR is unknown.  So rather than spending time sorting them and measuring their Q's, why not use high-Q SMD ceramic capacitors?  I used these in my class E/F amplifier (http://k6jca.blogspot.com/2011/01/80-meter-class-ef-rf-amplifier.html), why not use them again?  And I noticed that Elecraft also uses SMD caps in their KAT500 auto-tuner, which is very good internal tuner-loss (see:  http://www.ad5x.com/images/Presentations/KAT500Review.pdf).

Well, that was an easy decision!

There are a number of manufacturers who make high-Q ceramic chip caps for RF applications,  They include:

• AT Ceramics (ATC)
• AVX
• Johanson
• Vishay

Which ones should I use?

As of 25 June 2015, Digikey only carries AVX, Johanson, and Vishay  SMD high-Q capacitors for RF applications.  And of these three, there is no stock on hand for the Johanson caps.

So Johanson is out.

AVX prices are listed at around $17 per cap, while Vishay is much less expensive at about $2 per cap.

Given the significant cost difference, I think Vishay might be the way to go.  But I need to check their specs.

Vishay's "Quad Hifreq" Series datasheet is available here:  http://www.vishay.com/docs/45221/quadhifreq.pdf) 

Digikey carries this series in 0505 and 1111 case sizes.  Only the 1111 case size has the voltage rating that's at least 1000 VDC (ratings are 1500 VDC for values below 100 pF and 1000 VDC for 100, 120, and 180 pF).

So I'll focus on the caps in the 1111 package size.  Here are their specs, from the Vishay data sheet:

ESR:

(click on image to enlarge)

Well, this looks pretty good (but I'll do some more checking a bit later in this post -- I'd like to get an estimate of power loss in my application).  At 30 MHz, the ESR approximately is:

10 pF ESR @ 30 MHz = 0.25 ohms

180 pF ESR @ 30 MHz = 0.04 ohms

Here's the chart for Self-Resonant Frequency (SRF):

(click on image to enlarge)

No issue here.  SRF is well above 30 MHz (and the SRF for the capacitor values that I'll be using (see further below) is well above 400 MHz)!

Now, Current Rating:

(click on image to enlarge)

This looks pretty good -- max current is above 10 Amps.  I'm going to assume that the 10 Amp limit is good down to 3 MHz.  (By the way -- the "diagonal" limit in the template above will be automatically met if I keep the cap voltages below their Vpk (i.e. Vdc) specification).

From my table earlier in this post, I know that the max current through the L-Network capacitance will 6.9 amps (for an SWR of 10 at 200 watts)  so there should be plenty of margin.  But we'll delve further into this a bit later in this post.

And finally, Temperature Coefficient:

(click on image to enlarge)

Very good!

For completeness, here's Q versus Frequency from the datasheet.  I don't know how I'd use this, though, because it just seems to duplicate the ESR spec (Q = Xc/ESR).

(click on image to enlarge)

Everything looks good so far.  But what capacitor values should I use?

To ensure that I can match any load with a 10:1 SWR, I need a maximum capacitance of around 2700 pF with a voltage rating of at least 1000 VDC.  But at this voltage rating, the three largest values in this series that Digikey stocks are:  100, 120, and 180 pF.

But I can create larger cap values by connecting 180 pF caps in parallel.  So, if I use 180 pF as the basis for the larger caps (and if I also divide 180 pF down by powers of two), I get the following 8 values of capacitance:

1440 (8 x 180)

720 (4 x 180)

360 (2 x 180)

180 (1 x 180)

90

45

22.5

11.25

These values sum to 2869 pF.  Great!

And the minimum step size of 11 pF should give me adequate coverage on 30 MHz (but I'll need to verify this later, after I've selected my inductors).

Note that none of the four smaller values are standard capacitance values.  But they are close to standard values (and of course the fractional parts of these values are unimportant).  If standard values aren't close enough (i.e. off by more than a few pF), I can parallel two smaller values to make a value sufficiently close to what is required.

And as I mentioned, I'll create the 360, 720, and 1440 pF caps by paralleling 180 pF caps.  There's an advantage to doing this -- paralleling these caps will effectively lower the ESR (and thus power dissipation).


Delving deeper into capacitor current...

Let's get back to checking capacitor current (because I'd like to estimate the power dissipation).

For each of the 8 capacitor values that I've selected, its current must fit within the Current template shown in the Vishay "Current Chart":

(click on image to enlarge)

For each capacitor I've calculated (using Excel and Matlab) its maximum RMS current (Irms) on each of the ham bands, for an SWR of 10:1 and an input power of 200 watts.

Here's a plot showing these currents at 3.5 MHz as we move the load around a Smith Chart's "Circle of Constant 10:1 SWR" :

(click on image to enlarge)

Note that the max current for, say, the 1440 pF cap does not occur at the same load as the max current for, say, the 720 pF cap.

And here are the capacitor currents at 28 MHz for the same 10:1 SWR and the same power:

(click on image to enlarge)

I've listed these maximums in the table below.

(click on image to enlarge)

If you compare the currents in the table with the currents shown in the graph, the maximum capacitor currents are easily within the capacitors' current ratings.

Let's continue on to my goal of estimating power dissipation...

Estimating capacitor ESR and Power Dissipation

First, I need to determine the ESR for each capacitor.  Let's use the ESR graph from earlier in this post.

(click on image to enlarge)

 

10 MHz is the graph's lowest frequency.  But I'll assume that the ESR lines remain linear down to 1 MHz (the next decade down) on the log-log scale, so I will extend the graph down to 1 MHz (by hand), which allows me to estimate ESR for any of the frequencies that interest me.

Here are my estimates:

(click on image to enlarge)

To create this table I've assumed:

• The ESR of the 11 pF cap is about the same as the 10 pF cap, which is available via the graph.
• The 22 pF cap will be two 11 pF caps in parallel.  Thus, the combined ESR is half the 10 pF ESR.
• Ditto for the 45 pF cap, but with four 11 pF caps in parallel.
• The ESRs of the 90 pF cap are a guess, which is why they are red.
• The 180 pF cap ESR is from the graph.
• The ESRs of the 360, 720, and 1440 nF caps, being composed of paralleled 180 pF caps, are just the 180 pF ESR divided by either 2, 4, or 8, depending upon the number of paralleled caps.

With these ESR estimates and the earlier "Maximum Capacitor Current" table, I can get an idea of worse-case capacitor power dissipation for each cap (this is simply ESR* I^2):

(click on image to enlarge)

It should be obvious, but please note:  you cannot simply sum these losses to get the total power loss due to capacitor ESR at a given frequency.  Each capacitor's max current occurs at a different load (see the earlier graphs of  capacitor current versus angle of reflection coefficient).  This table simply identifies the worse-case loss we should expect for any given cap on any given band.

So, from the table above, my estimated worse-case power dissipation is about 1.6 watts in the 180 pF cap (at 30 MHz).  This is not too bad, but it might be worthwhile to try to reduce its ESR even further by paralleling smaller-valued caps of the same 1111 package size.  I'll have to do some experimentation after my caps arrive...

Summary:

• The capacitor SRF, Max Current, Peak Voltage, and Temperature Coefficient specs all meet my requirements. 
• I've tweaked the values to correspond those available from Digikey

Here's a summary of my capacitor selection:

(click on image to enlarge)

I want to stress -- these caps might change (and probably will) as I get further into the design process.  This is my first cut at their selection.  I'd like to try either the ATC caps (their 700C or 800C series) or the AVX caps (their HQCC series).  The ATC 700C and AVX HQCC series are in larger cases sizes (0.23 x 0.25 inches) and  they have similar characteristics.  For example, at 30 MHz their ESRs are:

(These numbers are from eyeballing the graphs in the datasheets, so I could be slightly off).



OK, this ends Part 2 of this series.  Part 3 will deal with the L-Network inductors.  It can be found here:  http://k6jca.blogspot.com/2015/06/antenna-auto-tuner-design-part-3.html

The previous post, Part 1 -- Preliminary Specifications, is here: http://k6jca.blogspot.com/2015/06/antenna-auto-tuner-design-part-1.html


Links to my blog posts in this Auto-tuner series:

Part 1:  Preliminary Specification

Part 2:  Network Capacitor Selection

Part 3:  Network Inductor Selection

Part 4:  Relays and L-Network Schematic (Preliminary)

Part 5:  Directional Coupler Design

Part 6:  Notes on Match Detection

Part 7:  The Build, Phase 1

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

Part 9:  The Build, Phase 3 (Incorporating a Microcontroller)

Part 10:  The Final Schematics


Resources:

Datasheet, Capacitor, Vishay, Quad Hifreq:  http://www.vishay.com/docs/45221/quadhifreq.pdf
Datasheet, Capacitor, AT Ceramics, 700C series:  http://www.atceramics.com/UserFiles/700c.pdf
Datasheet, Capacitor, AVX, HQCC series:  http://www.avx.com/docs/Catalogs/hi-q.pdf



My Other Tuner posts:

A quick tutorial on Smith Chart basics:  http://k6jca.blogspot.com/2015/03/a-brief-tutorial-on-smith-charts.html

The L-network:  http://k6jca.blogspot.com/2015/03/notes-on-antenna-tuners-l-network-and.html

A correction to the usual L-network design constraints:  http://k6jca.blogspot.com/2015/04/revisiting-l-network-equations-and.html

A look at highpass T-Networks:  http://k6jca.blogspot.com/2015/04/notes-on-antenna-tuners-t-network-part-1.html

More on the W8ZR EZ-Tuner:  http://k6jca.blogspot.com/2015/05/notes-on-antenna-tuners-more-on-w8zr-ez.html  (Note that this tuner is also discussed in the highpass T-Network post).

The Elecraft KAT-500:  http://k6jca.blogspot.com/2015/05/notes-on-antenna-tuners-elecraft-kat500.html
 
 The Nye-Viking MB-V-A and the Rohde Coupler  :  http://k6jca.blogspot.com/2015/05/notes-on-antenna-tuners-nye-viking-mb-v.html


Standard Caveat:

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

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

Antenna Auto-tuner Design, Part 1: Preliminary Specification

(The final destination of this series of blog posts)

For the past months I've been looking at various tuner topologies and their tradeoffs, my ultimate goal being to actually build a tuner.  Specifically, I would like to build an Automatic Antenna Tuner.

I've now started the design!  This blog post is the first of a series of posts I have planned in which I will log the progress of the design as well as my design process.

In this first post I will set out the initial Tuner specifications and why I chose them.

But you should expect the design to change from post to post.  After all, this design is a work in progress, and from my experience, rarely does the finished design match its initial specifications -- there are tradeoffs that will come up during the design process, and the design will change to accommodate those tradeoffs.

So let's get to started!  First step -- nail down the initial tuner specifications...

1.  I don't operate on 160 meters (nor on 6 meters), so I'll focus on 80 through 10 meters (and if 6 meters happens to become included, great).  This will save me from adding a large inductor that would be required for 160 meters.

2.  If you've read my previous Antenna Tuner posts, you'll see that I much prefer the Lowpass L-Network topology to, say, T-Networks.  The T-Network can have smaller-valued components, but there's a tradeoff associated with this -- more power can be wasted within the T-Network tuner for a given load (assuming L and T networks have equivalent component Q's).

One of my goals is to minimize power loss inside the tuner.  So, the L-Network is the way to go, in my opinion.

3.  What component values will I need?  Here's a table I generated showing the max L and C values required to match an impedance anywhere on a specific "Smith Chart SWR Circle" to an SWR of 1:1. 

(click on image to enlarge)

4.  Because I want to minimize power loss, I don't want to use a roller inductor.  These can have low Q's (see:  http://www.w8ji.com/antenna_tuners.htm), and I never know if I should short the unused portion of the coil or leave it open (leaving it open can result in very high induced voltages at the open end, and shorting it might reduce Q, although this seems to be open to debate).

So instead I'm going to follow the same route Elecraft uses with their KAT500:  individual fixed inductors whose values increase by powers of 2 and are selected via relays.  (Their power-loss numbers are very nice.  See this review:  http://www.ad5x.com/images/Presentations/KAT500Review.pdf).

To maximize Q, I'll like to have as many of these inductors as possible be air wound.  But where necessary (e.g. for large values of inductance) I'll use coils wound on iron powder toroids.

5.  For the variable capacitor there are a number of options:  vacuum-variable, air-variable, or switched fixed-capacitor.  Because of its inherent high Q, the vacuum-variable is tempting, but -- as you can see in the table above, a 10:1 SWR on 80 meters can require a maximum capacitance of about 2700 nF to match it (depending where on the Smith Chart's "Circle of Constant SWR" the load lies).  2700 nF is much larger than any of the vacuum variables I have in my junk box.  So I plan, again, to follow the Elecraft (and SGC, and LDG) route -- fixed capacitors selected via relays.  Just like the inductors.

6.  As for power ratings -- I don't operate really high power, so to keep inductor and capacitor specifications reasonable I'd like them to meet the max voltage and current requirements for an operating power of 200 watts continuous (e.g. AM carrier), 800 watts peak (e.g. SSB) at an SWR of 10:1, which should easily meet my operating requirements.

Here's a table showing those voltage and current requirements:

(click on image to enlarge)

For the inductors, I will assume that heating of the iron powder toroid cores is the main issue, so max Vrms is the important value (if using a program such as Mini Ring Core Calculator to determine power loss and flux density).

Capacitor Voltage Rating is usually in terms of Vpeak across the cap, so I need max Vpeak and also max RMS current (Irms) -- the latter affects capacitor heating (i.e. power loss).

7.  And finally, this tuner will be an Automatic Antenna Tuner (Auto-tuner).  I'll probably use a PIC processor to control tuning, which will give me a chance to learn to program one and play around with tuning algorithms!

So, to summarize:

K6JCA Auto-tuner, Preliminary Specifications:

• Frequency Range:  3.5 - 30 MHz, continuous (and perhaps to 54 MHz, if it's free)
• Matching Network Topology:  Lowpass L-Network
• Load Matching Range:  Match to 1.2:1 (or better) for any load with a 10:1 SWR.
• Input Power:  200 watts average, 800 watts peak.  ICAS operation.
• Internal Tuner Power Loss:  (Unspec'd.  Design to minimize).

Now to select the tuning network inductors and capacitors.  I'll go through this process in the next post.  It can be found here:  http://k6jca.blogspot.com/2015/06/antenna-auto-tuner-design-part-2.html


Links to my blog posts in this Auto-tuner series:

Part 1:  Preliminary Specification

Part 2:  Network Capacitor Selection

Part 3:  Network Inductor Selection

Part 4:  Relays and L-Network Schematic (Preliminary)

Part 5:  Directional Coupler Design

Part 6:  Notes on Match Detection

Part 7:  The Build, Phase 1

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

Part 9:  The Build, Phase 3 (Incorporating a Microcontroller)

Part 10:  The Final Schematics


Resources:

Inductors, W8JI discussion:  http://www.w8ji.com/loading_inductors.htm
Inductors, Roller, W8JI (part way down this post):  http://www.w8ji.com/antenna_tuners.htm

Antenna Tuners, W8JI:  http://www.w8ji.com/antenna_tuners.htm
Antenna Tuners, G3YNH:  http://www.g3ynh.info/comps/Vari_L.html

Review, Elecraft KAT500:  http://www.ad5x.com/images/Presentations/KAT500Review.pdf

Software, Toroid Inductor Calculator (including loss), Mini Ring Core Calculator: http://www.electronicecircuits.com/electronic-software/mini-ring-core-calculator-program


My Other Tuner posts:

A quick tutorial on Smith Chart basics:  http://k6jca.blogspot.com/2015/03/a-brief-tutorial-on-smith-charts.html

The L-network:  http://k6jca.blogspot.com/2015/03/notes-on-antenna-tuners-l-network-and.html

A correction to the usual L-network design constraints:  http://k6jca.blogspot.com/2015/04/revisiting-l-network-equations-and.html

A look at highpass T-Networks:  http://k6jca.blogspot.com/2015/04/notes-on-antenna-tuners-t-network-part-1.html

More on the W8ZR EZ-Tuner:  http://k6jca.blogspot.com/2015/05/notes-on-antenna-tuners-more-on-w8zr-ez.html  (Note that this tuner is also discussed in the highpass T-Network post).

The Elecraft KAT-500:  http://k6jca.blogspot.com/2015/05/notes-on-antenna-tuners-elecraft-kat500.html
 
 The Nye-Viking MB-V-A and the Rohde Coupler  :  http://k6jca.blogspot.com/2015/05/notes-on-antenna-tuners-nye-viking-mb-v.html


Standard Caveat:

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

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