Tuesday, August 6, 2019

Differential Backups Made Simple

To backup or not to backup.  That is the question.

Who likes to make backups? Anyone, Aynone?

Hmm, I thought so...

Versioned Backups
I prefer to make backups with very simple tools, since when things go south, I don't want to have to install a complicated system just to get my data back.

Most UNIX backup systems are based on rsync and by using a careful system of  hard links (multiple new names for the same old file), differential backups can save you oodles of disk space in the long run, while making it very easy to step through an archive and retrieve specific versions of old files:

Three for the Price of One
The original article by Mike Rubel describes how to keep three backups for the price of one, using a combination of hard links and rsync. That idea then spawned the rsnapshot (pull) and rdiff-backup (push) scripts.

Since the PSU of my Raspberry Pi server blew up, I now have a little NUC with a 2TB solid state disk that has all my music, movies and backups as a WiFi enabled file server, using this idea to good effect.   (The RPi is fine, it just needs a new USB widget.)

Differential Backup Script
On my MacBook, my backup script is directly based on Mike's and looks like this:
#! /bin/bash
# Rsync to Muzak and keep 3 old hard linked copies.
# Assumes the public key is installed in /home/herman/.ssh
ssh herman@muzak "mv ~/Backups/Herman.3 ~/Backups/Herman.tmp"
ssh herman@muzak "mv ~/Backups/Herman.2 ~/Backups/Herman.3"
ssh herman@muzak "mv ~/Backups/Herman.1 ~/Backups/Herman.2"
ssh herman@muzak "mv ~/Backups/Herman.0 ~/Backups/Herman.1"
ssh herman@muzak "mv ~/Backups/Herman.tmp ~/Backups/Herman.0"
ssh herman@muzak "cp -al ~/Backups/Herman.1/. ~/Backups/Herman.0"
rsync -avze ssh --progress --delete --max-size=20M --exclude "*Trash*" --exclude "*bak" \
--exclude "*old" --exclude "*cache*" --exclude "*Cache*" --exclude "*iso" ~/ herman@muzak:~/Backups/Herman.0/

The script follows the principle of: Include everything and Exclude the cruft. This makes the script maintenance free.

I simply run this little script whenever I feel like it.

La voila!


Friday, August 2, 2019

Micro Wind Genny

Who didn't play with whirlygigs as a child?  I sure had hours of fun with paper and wood twirly whirlies, but I frequently wondered about making something bigger, that can produce useful power.

Fifty odd years later...

Little Alternator with 6 LEDs

A small three phase alternator that can be had for the princely sum of about $5 from aliexpress.com, can produce a few Watts of power.  Twirl it by hand to light up 6 LEDs.

I took it to our production manager Siegfried Losch, who is always willing to play with a new toy and we stuck it into a drill press.  With no load, it generated 14V AC rms when running at 3000 rpm.  So it can charge a 12V SLA motor cycle battery when hooked to a high speed engine, but it will not do much with a wind rotor that will only turn at about 200 rpm or less.

If you are content with 6 or maybe 12 LEDs to light up a little tree in your backyard, then you can skip all the electronics below, get some balsa or spruce wood and go carve a propellor.

If you are like me, then you can invest/waste (depending on your point of view!) some more money and time and build a boost power supply to charge a battery in your radio shack, or power a SatNOGS ground station with it https://satnogs.org/

Boost PSU
Assuming that the alternator can be spun up to generate at least 5V DC, you can build a little boost PSU using a triple five timer and a coil.  One can buy a fancy switcher from Linear Technology, but next time you want to do the same, the IC you used before, is guaranteed to be obsolete.  I like learning new things, but I don't like having to reinvent the wheel all the time.  The venerable 555 timer however, has developed a life of its own - similar to the 741 op amp - somebody will always make them.

NE555 Boost PSU Circuit

With this simple circuit, one can get almost any output voltage to power a toy, from 14V to charge a battery, to 160V for a Nixie tube.  Just change the 18k resistor and use higher voltage output capacitors.  If you play with high voltages and thermionic valves https://www.aeronetworks.ca/2015/02/cool-amplifier.html, then I can assume that you know what you are doing and don't need to look at this circuit - but those who don't know what they are doing yet, may find it a shocking experience...

Before you start building this, please put a rubber carpet on your workshop floor.  You won't regret it.

The components are not critical, but you need to take care to make the design efficient, otherwise you will not get much power from it - if any.  The most important parts are the MOSFET and the Diode.  Both of those are typical parts of switch mode PSUs - ultrafast, high voltage devices.  The electrolytic capacitors should be at least 25V rated, high ripple current types.

Boost Switch Mode Battery Charger

The parts in the schematic are seriously overspecced at 5A.  This should ensure long life, but if you short the output, the transistor will immediately blow up and adding a fuse won't help.  So do try not to do that and when you buy parts, get extras - you may need them.

To say again: Before you start building this, please put a rubber carpet on your workshop floor.

How it works
The 555 timer runs as an astable oscillator which turns the MOSFET on/off.  When the MOSFET turns off, the coil generates a high voltage which pumps through the high speed diode and charges the output capacitor.

The ideal switching speed should be fast enough to avoid saturating the coil, but not so fast that the diode/FET become inefficient.  All depends on the input/output voltage and current.  I expect having a 5V input and 14V output with a current of maybe 100 mA.  What I'll actually get is anyone's guess.  The 555 timer is tuned for 10 kHz to begin with - a nice round number - and round numbers are always wrong...  Well, it turned out to be good enough.

NE555 Oscillator - 10 kHz

The feedback circuit is optional.  I added it to limit the output voltage when there is no load, to avoid blowing up the output capacitor - set it to something between 15 and 20 Volt.  You could do the same with a 15V 5W zener diode crowbar.

The NPN transistor will turn on hard, once its base to emitter voltage reaches about 0.65V and pull the Control input down, the timing capacitor will Discharge and the Output will drop, turning the MOSFET off.  Tweak the little 1k trimmer to limit the maximum output voltage to something above 14.4V that won't blow the 25V output capacitor.  When you hook up a small 12V Sealed Lead Acid battery, the voltage will drop and will eventually stabilize at about 14.4V when fully charged.

Since this is a micro power system with a very small wind genny, it will at best only trickle charge a SLA. One could therefore hook it permanently to a SLA, in which case the output capacitor and feedback circuit are both not required.  The chemistry of the SLA will limit the voltage to about 14.4V and it can stay connected forever.  However, if one would disconnect it, then a high voltage will result, so it is best to develop the PSU as a standalone module that can operate without sparks and smoke, on its own.

Boost Switcher Test
Testing the circuit is tricky, since without a load, it doesn't run (only runs for a few cycles, then stop) and putting a big load on it right off the bat is not a good idea either.  So keep the 555 timer output open circuit, till you are sure it runs, then keep a scope on the 555 output, connect it to the MOSFET and observe that it stops oscillating almost immediately.  Try different loads and tweak the trimmer, till it stabilizes at about 15V.

With strip board, take care that you don't make a short circuit somewhere. A thorough cleaning with alcohol and an inspection with a magnifier is recommended before you turn it on.

Hooked to a bench PSU set to 5V and current limit set to 200 mA initially, with a SLA as a load, I pushed the Vero Board circuit to 2A (24 Watt) and the MOSFET hardly got warm, so this circuit is very efficient.  The input voltage stabilizes at the minimum voltage that the 555 can operate at, which is about 4.5V, below that, nothing will happen.

Once it is working properly, clean it with alcohol and then lightly spray it with conformal coating (e.g V66) to keep it working.

This circuit seems to be efficient enough that you could use it with a better motor cycle alternator, but don't hook it to a 1 kW generator, unless you are a masochist...

The output of the alternator needs a full wave rectifier, which can be made from 6 diodes.  Again, in the interest of efficiency, don't use garden variety rectifier diodes.  You need 6 Schottky diodes, which have a much lower forward voltage drop than the ubiquitous 1N4001.

Schottky Diode Rectifier

I have an amazing collection of parts in my workshop, but I am fresh out of Shottkys,  which is why I started with the PSU, while I wait for mouser.com to deliver my diodes.  The SB5100T https://eu.mouser.com/ProductDetail/Diodes-Incorporated/SB5100-T, will do.  I don't expect to get much current out of this little genny, so a 5A diode should not be stressed and last for a long time.

One thing I learned over the years with hobby electronics, is to always seriously overrate the parts.  For a a little toy, I don't want to spend much time designing and usually just use a first order thumb suck.  Therefore it is easy to overlook something and end up with disappointing smoke signals.  However, if one overrates the parts by 5 or 10 times, then it either works or not, but usually doesn't go pop.

This circuit will work fine in normal weather, but if there is a storm, the alternator could generate more than 18V and blow up the 555 timer.  If you are worried about losing 40 cents, then for another 30 cents, you could add a big fat 15V, 5W zener diode or two as a crowbar, to clamp the output and prevent sparks and smoke in the PSU: https://eu.mouser.com/ProductDetail/ON-Semiconductor/1N5352BRLG

Slip Rings
A wind genny doesn't need slip rings.  The wind normally doesn't go round and round and if you ever get caught up in a tornado, then you will have more to worry about than a few twisted wires on your toy wind genny.  Just run the wires loosely down the post and let it be.  It will not wind up.

If you put the rectifier diodes at the genny, then you only need two wires - a saving of 33%.

Carving a Prop
Most of the fun is carving the prop.  If you have never done it before, it is very easy.  You get a piece of soft wood and carve it, till it looks sort of like a prop - that's it.  For good measure, balance it with a small piece of solder.

Just bear in mind that a wind prop is opposite from a model aircraft prop.  You want the leading edge to lead, the trailing edge to trail and the wind to blow onto the flat side of the wing.  The curved side should be leeward.

If you want to go seriously scientific, then you can design a fancy aerodynamic wind prop, thanks to the Berlin Institute of Technology http://www.q-blade.org/

Q-Blade Wind Prop Designer

If you are like me, then you can wing it, but it will help if you keep a few things in mind:
  • Any blade shape will work, since the wind is free, but a proper aerodynamic shape will not make noise.
  • The faster the blade moves, the more efficient it is, so the tip of the blade should have a lower angle of attack than the centre.  
  • The centre should be at about 42 degrees or less and the tip at about 3 to 5 degrees angle of attack. 
  • The efficiency of a blade depends very much on the trailing edge, which must be thin and sharp.
  • As for the profile, if it more or less looks like a wing, then it will work.  I use the NACA-TS (thumb suck) profile.
How big should the blade be?  Well, that is why you have two thumbs, one for the profile and one for the size...

I decided to make this blade 300mm by 50mm and slightly S-shaped, cut from a Japanese Daiso store bread board.  After about an hour of carving, it looked like this:

Poplar Soft Wood Rotor

A power tool will make quick work of it, but with a lot of dust.  Living in the desert is bad enough, I don't want to breathe wood dust also, so I use a carving knife.

There are many prop carving tutorials on the wild wild web, but all you need to do is glue a couple sheets of Japanese soft wood bread boards together with white glue, drill a hole for the shaft - glue two washers over the hole, draw some guide lines, get your jig saw and sharpen your knife:

So, get some balsa or poplar wood and go for it!


Wednesday, March 6, 2019

Driving A 900 MHz Quad Patch Array Antenna

A Circular Polarized Quad Patch Array for the 900 MHz ISM Band

Driving a patch array antenna is a tricky and multidisciplinary affair - a combination of electrics, magnetics and mechanics - where theory meets reality.  Patch antennas are useful between about 1 and 5 GHz.  Below that, they are too big and above that, too small to be practical for the manufacturing tolerances of a hobbyist.  For L, S and C-band, a radio amateur can use patches with good effect, using not much more than tin snips and a nibble tool.

902-928 MHz ISM Band LCP Quad Patch Antenna

The patch antenna theory can be explored with a simulation program such as NEC2: https://www.aeronetworks.ca/2018/07/patch-antenna-design-with-nec2.html

You could make an array with any number of patches, but more than four would be a whole lot of hassle.  A SAR radar antenna may have 300 tiny little patches.  However, a two by two is about the limit of my patience.

Any piece of metal within half a wavelength of an antenna, becomes part of the antenna and an array antenna is the sum of its parts.  If you want to construct a phased array with circular polarization, then it is even more true.

To work with microwave antennas, you must have a fairly decent two port vector network analyzer (A KC901V costs only about $2500 on Aliexpress).  The Q of a microwave antenna is very high and reality will always differ from the design by a few percent.  Therefore, your design will have to be tuned and tweaked to get it right, since the overall bandwidth is only a few percent.

A patch antenna is a ridiculously sensitive thing.  You have to mount it very securely with nylon standoffs and use good quality connectors and cables, otherwise your results will not be repeatable. 

Let me say that again:

A patch antenna is a ridiculously sensitive thing.  You have to mount it very securely with nylon standoffs and use good quality connectors and cables, otherwise your results will not be repeatable. 

It may be good to say that a third time...

If you assemble a rough test patch and measure it, then quickly take it apart and put it back together without changing anything and measure it again, the centre frequency can be several MHz different - it can shift by more than the bandwidth of the patch antenna for no apparent reason.  Therefore, tuning a patch antenna requires a lot of patience and you got to assemble it with care: Nuts, bolts, connectors - the whole nine yards.  Otherwise you will waste your own time.

I have looked at many different patch array antennas and came to the conclusion that all of them are too complex to my liking and that there is room to simplify the design of the patch layout and the drive circuitry, to make one that is more easily tunable and manufacturable.

Impedance matching of a single patch is relatively easy.  At the edge it is 100 to 200 Ohm and at the centre zero Ohm.   In between those, you can get 50 or 75 Ohm for a coaxial cable drive, or you can work directly with the measured impedance on the edge, if fed with a microstripline.

I probe it for a 50 Ohm spot by drilling a few little holes 25 to 35% from the edge and pick the best one for a coaxial cable to a VNA and then, once tuned up, measure the edge impedance for a microstripline feed.  With a little experience and luck, the very first hole can be spot on.

A probe (pin) feed is fine if the patch is not ridiculously thick, with h < 3% of the wavelength.

 FR4 Patch Test Antenna

Microstriplines and patches can be designed with the Pasternack or Microwaves 101 calculators, which will provide a good starting point for your new tin snipping hobby: https://www.microwaves101.com/calculators/1201-microstrip-calculator

In a single patch antenna, one can achieve circular polaration either by phasing the drive signal (by driving two sides with a 90 degree phase shift), or by perturbing the dimensions (to cause a current and field shift).  In this case, the phasing approach tends to yield better circular polarization - the mechanical trimming result is more elliptical.

Similarly, an array can achieve circular polarization by using multiple circular polarized elements, or by rotating and phasing the drive of the elements.  Again, the rotating and phasing approach is more circular and the other more elliptical.

Another problem with a patch antenna is that it is a very narrow band device.  If you tune a patch to 915 MHz (The centre of the ISM band), it may have a VSWR at that frequency of 1.2, but at the edges of the band, it may be 2 or 3, which is not so good.   The bandwidth of the patch can be increased by increasing the height above the ground plane (decreasing the capacitance), but that will reduce the centre frequency also, so you need to trim it slightly smaller.   The maximum usable height is about 3 to 5% of the wavelength.

Return Loss Plot of a Test Antenna

To get the phasing of the patches right, you need to use different length transmission lines.  With 4 patches, a successive shift of 90 degrees is required, which, if done with a single piece of line, will act like a quarter wave transformer, which may be an unwanted side effect.  Also, the length of the line is dependent on the frequency, so the phasing circuit will make the antenna even more frequency sensitive.

One way to increase the bandwidth of the array, is to tune each patch to a slightly different frequency (by changing the spacing with little nylon washers).   Intuitively, you can think of a Yagi or Log Periodic array, where each piece of wire is tuned differently, yet all the elements work together as one.  The same thing happens in a patch array with slightly differently tuned elements - the overall bandwidth of the array then opens up.

Therefore, instead of designing all four patches for exactly 915 MHz, one could tune them to 912, 914, 916 and 918 MHz, or 910, 913, 916 and 919 MHz and achieve better performance over the whole 902 to 928 MHz ISM band.

Alternatively, one could cut a notch in the left and right sides of a patch, which could increase the bandwidth from 3 % to about 10 % while still keeping it linear polarized, but cutting the notches will reduce the centre frequency a little bit and you may have to adjust the height by 1 mm to compensate.  Choices, choices...

Power Divider/Combiner
The patch feeds need to be divided/combined into one drive signal.  It can be done with a succession of Wilkenson dividers, but when you also need to create a phase shift and an impedance match for each patch, it becomes a rather complex and narrow band affair.

Unified Phasing, Power and Impedance Matching
When you need to do power dividing/combining, you also need to match to different impedances.  Two impedances can be matched with a quarter wave transformer, but that is a narrow band device.  A more broadband match can be achieved with three transformers in series.

If you squint at a series of quarter wave transformers, they resemble a tapered line and it was found that a tapered line of one or more quarter wavelengths, does indeed provide impedance matching with a significantly broader bandwidth than discrete 1/4 wave transformers.

The ultimate is the Klopfenstein Taper: https://www.microwaves101.com/encyclopedias/klopfenstein-taper  However, a longer linear taper works just as well in practice.

This leads to the following conclusion for a circular polarized array:
  • Place the 4 patches 1 effective wavelength apart (centre to centre).
  • To combine 4 transmission lines and get a 50 Ohm drive impedance, each line should be 200 Ohm (like 4 resistors in parallel) at the coaxial connector, OR
  • Make an H circuit and convert 50 Ohm to 100 Ohm to 50 Ohm using 6 striplines.
  • On the patch side, the transmission line should match to the patch impedance.
  • The first line is however long it needs to be and an odd multiple of 1/8th wavelength overall - to avoid making a 1/4 wave transformer.
  • To get a succession of phase shifts, each transmission line should be 1/4 wave longer than the previous. 
  • Each patch should be rotated by 90 degrees, compared to the previous. 
  • To improve the bandwidth, use long tapered lines and avoid the inadvertent creation of 1/4 wave transformers.
  • To reduce spurious transmissions from the microstriplines, do not make sharp corners.  Rather make 45 degree corners, or smooth S lines.

Simple Array Drive Solution
As O'l Albert Einstein said:

A thing should be as simple as possible, but no simpler.

The final drive result is a simple four legged cross of microstriplines, each leg of the spider longer than the previous by a quarter wavelength (At the specific de-tuned patch frequency).
Quad Patch Layout

Each microstripline leg should be tapered from 200 Ohm at the connector and pass underneath the patch with a feed probe to the 50 Ohm (~3 mm wide) point.  However, since a 200 Ohm microstripline is too thin to be practical, it would need thicker 3.2 mm board.  Therefore, rather create an H shaped circuit and convert 50 to 100 Ohm, combine them and convert to 100 Ohm again and then join these in the middle - I'll make a better sketch later.

Tweaking and Tinkering
A low cost patch array antenna can be built from FR4 PCB. At 1 GHz, the permittivity of this board is about 4.3.  To tweak your design, make a 50 Ohm strip, 3 mm wide and  5/8th wavelength long.  Solder two 1/8th Watt 100 Ohm resistors in parallel over the far end to terminate it and measure it with a VNA.  (Putting two resistors in parallel, reduces their inductance by half).  This way you can get a fudge factor for the permittivity, track width and wave length to tweak your designs with.

You can experiment with microstriplines and patch antennas using copper tape on single sided PCB and a (new!) pair of sharp scissors: https://www.digikey.com/en/product-highlight/3/3m/copper-foil-tape-1181 or from my favourite high tech electronics store: https://www.sparkfun.com/products/13828

You will also need a large variety of nylon bolts, nuts and spacers for tuning purposes.  Digikey has a good selection: https://www.digikey.com/en/product-highlight/r/raf/nylon-spacers-and-standoffs.

This assumes that your VNA is tuned!

To tune a VNA, buy a decent quality ready made short coaxial cable from Pasternack - say 12 inches long, using the coaxial cable type that you usually use (SR402AL, RG58U or RG316U), with a N connector at one end and a (cheaper) BNC or TNC at the other end.  I used two BNC male connectors and short circuited the one, and soldered two 1/8th Watt 100 Ohm resistors in parallel over the other as a 50 Ohm load.

DIY VNA Tuning Plugs: Short and 50 Ohm Load

Then get your VNA manual and calibrate it with an Open, Short and Load.  I prefer BNC connectors for use in a lab, since they are easy to connect.  In the field, a TNC may be more secure.

For added Brownie points, you can mount the two connectors in a metal box and label it to make it easier to find your tuning kit again...

Slots and Cutouts
A smooth, regular sided patch - square or otherwise - tends to oscillate in a single mode and has a very narrow bandwidth of 2 to 3%.  By cutting little slots on the side or middle of a patch, multiple oscillation modes can be excited and then the bandwidth can become very wide indeed.  For example the famous U-slot of K.F. Tong can achieve 20 to 30% BW.  Mr Tong must have been a very patient guy, since he sat down and made 27 different shaped U-slots and measured them all!

Cutting a slot with a Dremel cutting wheel tool is a whole lot of fun - you get glass and metal powder in your clothes, hair, eyes and will itch for days after...  I came to prefer tin snips and a nibbling tool as a result: https://www.digikey.com/product-detail/en/gc-electronics/12-1806/GC395-ND/258502

Slot perturbations can cause cross polarization, which is fine if you actually want to have cross polarization - it is sort of midway between linear and circular.  For my application, I wanted pure circular polarization, so I tried to avoid slots and funny feeds and rather widened the BW with 4 patches of slightly different sizes, but it turned out to be too difficult to replicate.  I think I now have almost as many discarded PCB squares as Mr Tong.  Note that discarded 900 MHz pieces can be reused for 2.4 GHz patches, so there is an advantage to starting at the lower end of the spectrum...

Two small 20 mm slots, the width of the nibbling tool, made the patch design much less sensitive and widened the bandwidth about 10 times to 40 MHz, so that is what I eventually used:
  • W = 143 mm, L = 133 mm, h = 9 mm, Slots = 20 mm (by 5 mm)
  • Material = FR4, 1/32 inch single sided, copper side up
  • Spacers: 9 mm nylon, one near each corner
  • Connector feed: BNC, mounted on bottom ground plane
FR4 fibreglass PCB is easier to work than copper or tin sheet, since it flexes and doesn't bend permanently - so when you are done drilling, cutting and trimming, it is still flat and doesn't look like a corrugated roof sheet after a hurricane.  The only drawback is the itching from getting glass dust in your skin - a lab coat and a Dustbuster help a lot.  The patch is made from thin 0.8 mm board to reduce the effect of the dielectric and the ground plane from regular 1.6 mm board - for mechanical stiffness.

920 MHz Test Patch with 20 mm Slots

As you can see from the nibbling tool debris field under my chair, I tried several different configurations and found that bigger slots are certainly not better.   The small 20 mm edge notches successfully reduced the Q and made the antenna design repeatable.  If you follow the above instructions and copy this design within ~0.5 mm, it should work fine over the 902 till 928 MHz ISM band.

Slot Debris Field

Cleaning this kind of cruft up again, is quite a chore.

The test patch feed is a BNC wall mount socket directly under it in the ground plane board.  For an array antenna, use a double sided ground plane board and run a microstripline with a pin  feed up to the patch, or for a one-off home/lab use antenna, use RG316U coax.

Test Antenna BNC Feed

Since I am not a complete masochist, I avoid circular patches, since it is difficult to cut a circle with tin snips!

It is interesting to note that square, rectangular, triangular and circular patches are equivalent.  It is possible to make an antenna with exactly the same electrical specifications using any one of these shapes.

Once you made your spiffy new antenna, you may need to enclose it in a waterproof jacket.  The best way to do it, is to include the radome material in your experiments and fine tuning the whole sandwich right from the beginning.  By doing this, you can make the assembly very thin, with the radome in contact with the patch.

However, if you later make a radome add-on, then you may be relieved to know that provided that you keep the radome material at least 10 mm or so away from the patch, it will be reasonably transparent and won't affect the antenna significantly.

For airborne use, Polycarbonate or Glass Fibre reinforced Epoxy are good materials to consider for a radome.  For a ground antenna, ABS or Nylon may be good enough.

A decent radome needs a hydrophobic coating, to cause water to bead and run off: http://www.hirecpaint.com/product_hirec100.html

It is quite easy to make a test microstripline, using a piece of single sided PCB and copper tape.

The Pasternack Microstripline Calculator is handy:  https://www.pasternack.com/t-calculator-microstrip.aspx
  • FR4 Fibreglass/Epoxy PCB Dielectric Constant = 4.3
  • Width = 3 mm
  • Height = 1.6 mm
  • Width/Height = 1.875
  • Effective Dielectric Constant = 3.257
  • Impedance = 51.36 Ohm
The effective Dielectric Constant gives the Velocity factor:
  • VF = 1/sqrt(3.257) = 0.555
At the speed of light, the wavelength of 915 MHz is 328 mmMultiply that with VF for the effective wavelength in the microstripline Le = 182 mm.  This is the value to use for length calculations of 1/4 wave transformers and tapers.

Microstripline Test Piece

With a sharp pencil and even sharper scissors, cut a 5/8th wavelength, 113 mm long, 3 mm wide strip and stick it to the PCB.  Mount two 100 Ohm resistors in parallel on one end and a BNC connector on the other end.  Glue the BNC on with epoxy first before you solder it, else it will lift the tape.

Why 5/8th wavelenth?  Avoid an exact 1/4 wave transformer for this test.

 Microstripline Impedance

With your VNA, you can now measure the impedance, or make a Smith Chart.

Microstripline Smith Chart

If your hands were steady, it will measure ~50 Ohm, proving that the Pasternack calculator works well enough (OR, that my low cost Chinese VNA works well enough!).

Air Dielectric Power Divider/Combiner
Note that one cannot reach 200 Ohm with 1.6 mm FR4 PCB.  A 3.2 mm board can work, but 3.2 mm board is heavy and hard to work with and if you saw it, then you end up with itch powder all over the place again.

An air dielectric taper would be good for 200 Ohm, at 6 mm high, 2 mm wide, but the 50 Ohm side would be 'too wide' - 100 Ohm would be more practical, so one may need to do the impedance conversion in multiple stages (or use a sloped transmission line, as explained later on).

Tapered Power Divider

A suspended air gap power splitter is a hassle to make, but it can solder directly to the pin of a panel mounted BNC connector, so making a little 4 bladed fan does have merit.  When a strip line gets too wide, it starts to radiate, like a patch antenna, so one has to be reasonable with the maximum width of the taper.

 Tapered Power Divider Test Set

To make a 200 Ohm to 100 Ohm taper line with copper tape on FR4 board requires great care and dexterity.  With 6 mm spacing, 200 Ohm is 2 mm and 100 Ohm is 10 mm wide. A quarter wave at 915 MHz with 0.555 Velocity Factor is 46 mm and with a VF of 0.666, it is 55 mm.  So I erred on the long side for wider bandwidth and cut a piece of blank board 110 mm long and 30 mm wide for the divider with a somewhat larger single sided board as earth plane and put the connector in the middle.

 Power Divider Smith Chart

Four 100 Ohm resistors were soldered on the ends of the tapers to test the circuit.  The result works quite well.  The impedance varies between 38 and 55 Ohm and is 48 Ohm in the middle of the band.  The VSWR varies between 1.1 and 1.4 over the whole band.

The taper lines create a good wide band device which is not critical and which can be replicated without undue trouble.  A wide band four way power divider/combiner like this, can cost hundreds of dollars when you buy it off the shelf.

Using strips of PCB and copper tape, with a whole lot of patience and a big mug of hot chocolate, one can make a tinker toy kit, to hook up four patches to form an array antenna.

More Accurate Dielectric Constant
In order to make reasonably accurate delay lines, it is useful to have a more accurate value for the dielectric constant and velocity factor.  One could use impedance controlled PTFE/Ceramic board, but a typical Radio Amateur will not have the pocket money for that.

One way to measure and calculate the dielectric constant is with a microstripline resonator circuit.  The VNA can then scan and measure the resonant frequency and then one can recalculate the dielectric constant:

First, a handful of formulas that you need to figure out:
L = c/f
VF = 1/sqrt(E)
Le = L x VF
Le = L/sqrt(E)
E = (L/Le)^^2

Once you made peace with the above, assume for FR4 1.6 mm board E = 4.3 at f = 915 MHz and c = 299792458 m/s

L = 299792458 / 915000000 = 0.328 m
Le = 0.328 / sqrt(4.3) = 0.158 m

Radius of the test resonator:
2 x Pi x r = 0.158 m
r = 0.158 / (2 x Pi) = 0.0251 m

From Pasternack's microstripline calculator and the test way above:
50 Ohm stripline on 1.6 mm FR4 = 3 mm wide

Make the above resonator and measure the real resonance frequency fr.
For example fr = 920 MHz

Finally, calculate the more accurate dielectric constant Er and Velocity Factor VF:
L = 299792458 / 920000000 = 0.326 m
Er = (0.326 / 0.158) ^^2 = 4.26
VF = 1/sqrt(4.26) = 0.485

Another way, is to go back to the microstripline test piece way above, remove the 50 Ohm load, put a second connector on it and measure S21 with the VNA and look at the 'Unwrapped Phase Trace': https://www.rfglobalnet.com/doc/methods-for-unambiguous-electrical-delay-measurements-using-a-vector-network-analyzer-0001

Making a circular resonator may be more fun though!

Either way, once you have a better idea of the actual dielectric constant and velocity factor of the striplines on your batch of printed circuit boards, the next step is to make a set of delay lines that will transform the impedance from 100 Ohm to 50 Ohm and delay the signal by 0, 90, 180 and 270 Degrees respectively, for each of the four patches.

To transform the impedance from 100 Ohm to 50 Ohm, I made four microstriplines on 1.6 mm board of length 55 mm, 1.5 mm at one end and 3 mm at the other end.  This worked, but was a whole lotta hassle...

Coax Phasing
Eventually, I made the delay lines from RG316U (a.k.a. RG316D) coaxial cable, fed through from the back of the ground plane.  The velocity factor of RG316U is 0.795, so the effective wavelength Le = 228 mm.  This is good for a one off lab/home antenna.  Microstriplines are better for mass production.

The first cable is 80 mm and each next one is a 1/4 wave longer:
1) 80 mm
2) 137 mm
3) 194 mm
4) 251 mm

You could cut each cable 15 mm longer than that and strip 5 mm at one end and 10 mm at the other end.  The important thing is the exact difference in length between them, not the overall length.

Sloped and Tapered Power Divider
I finally made an even simpler power divider, consisting of four sloped transmission lines.  If one would glue or tie the end of a RG316U coax to the reflector board, then the centre is 1.2 mm above the board.  I then placed four pieces of 65 mm SWG20 copper wire, sloped from the coax to the end of the BNC connector, 6 mm above the board.

A thing should be as simple as possible,
but no simpler.
-- Albert Einstein

SWG20 wire is 0.9 mm diameter and at 6 mm height, is 230 Ohm.  Addition of a thin triangle of copper foil, 5 mm wide at the bottom coax end at 1.2 mm height above ground, transforms 50 Ohm to 200 Ohm.  Four 200 Ohm lines in parallel, is 50 Ohm at the connector.

Sloped Wires With Copper Triangles

Fold copper tape around the 20 SWG wire, mark the triangle with a pencil and trim it with scissors - super easy for a one off home/lab experimental build.  The PCB methods are easier for a factory build.

Sloped Tapered Power Divider

Clearly, there is more than one way to do it, but I particularly like the sloped and tapered design, since it is the simplest and it keeps the transmission lines further away from the patches.  I think this one will do O'l Einstein proud.

After putting the whole kit and kaboodle together for the umpteenth time, the centre frequency was 902 MHz, which is a few MHz too low to my liking.  All four patches therefore need to be trimmed a couple mm smaller all around again.  I'll do it another day!

 900MHz Quad Array VSWR

The VSWR plot shows that the slots opened up the bandwidth quite a bit.

 900 MHz Quad Array Impedance

The impedance match and return loss is actually quite good.  It shows that the tapered transmission lines do their job very well.

 900 MHz Quad Array Return Loss

A Smith chart is always a good summary of the whole ball of wax.

900 MHz Quad Array Smith Chart

Parasitic Patches
I have read numerous articles that alledge that stacking a parasitic patch on top of a radiating patch, will increase the bandwidth.  However, when I tried it, it halved the bandwidth!

So who does one believe now?  I believe my VNA:  To measure, is to know.

I guess that to really open the BW, the top patch will have to be a little smaller than the driven patch, not the exact same size as on my first try.  I'll give this another spin some day.

To Explore Further
  • Trim the patches 1 mm smaller on each side (it is difficult to cut off only a little bit), to move the frequency up by a few MHz.
  • Try a patch with two slots on each side - that should open up the bandwidth a little more.
  • Make the power divider from two pieces of PCB, instead of wire and tape, to make it stronger.
Now it just needs to get cooler, so I can measure the antenna pattern outdoors.  At the moment it is 11 pm and still 37 Celsius here in the desert.

OK - copying and improving this design will sure keep you busy and out of trouble with your significant other for a while!

La voila!