Patch Antenna Design with NEC2

The older free Numerical Electromagnetic Code version 2 (NEC2) from Lawrence Livermore Lab assumes an air dielectric.  This makes it hard (but not impossible) for a radio amateur to experiment with Printed Circuit Board Patch antennas and micro strip lines.

Air Spaced Patch Antenna Radiation Pattern

You could use the free ASAP simulation program, which handles thin dielectrics, you could shell out a few hundred Dollars for a copy of NEC4, You could buy GEMACS if you live in the USA, or you could add distributed capacitors to a NEC2 model with LD cards (hook up one capacitor in the middle of each element.), but that is far too much money/trouble for most.

More information on driving an array antenna can be found here: https://www.aeronetworks.ca/2019/03/driving-quad-patch-array-antenna.html

Air Dielectric Patch 

The obvious lazy solution is to accept the limitation and make an air dielectric patch antenna.

An advantage of using air dielectric, is that the antenna will be more efficient, since it will be physically bigger and it will have less loss, since the air isn't heated up by RF, so there is no dielectric loss.

An air spaced patch can be made of tin plate from a coffee can with a pair of tin snips.  A coffee can doesn't cost much and it comes with free contents which can be taken orally or intravenously...

Once you are done experimenting, you can get high quality copper platelets from an EMI/RFI can manufacturer such as Tech Etch, ACE UK and others.

Wire Grid With Feed Point

This grid is not square.  The length is slightly shorter than the width, to avoid getting weird standing waves which will disturb the pattern.   Making these things is part design and part art.  You need to run lots of experiments to get a feel for it.  It may take a few days.  You need lots of patience.  If the pattern looks like a weird undersea creature, then it means that the design is unstable and it will not work in practice.

Find the range where the radiation pattern looks pleasing with a well defined rounded main lobe and the gain is reasonable and go for the middle, so that you get a design that is not ridiculously sensitive and can be built successfully.  It doesn't help to design an antenna with super high gain and then when you build it, you only get a small fraction thereof, due to parasitic and tolerance effects - rather design something that is repeatable and not easily disturbed.

If you cannot find suitable tin plate, then you could try 1/32nd inch FR4 (0.8 mm) and then keep the gap to the ground plane relatively big, so that the effect of the little bit of dielectric is minimized, but if you don't build exactly what you modeled, then making a numerical model is not very useful...

Ground Plane

To model a patch antenna, you need to design two elements, the patch and the ground plane.  The ground plane needs to be a bit bigger than the patch.  The distance between the two is extremely critical and it is important that you can easily vary the gap to find the sweet spot where you get the desired antenna pattern.  With a patch antenna, varying the height by only one millimeter, has a large effect on the pattern.

The NEC ground plane GN card is always at the origin Z = 0.  If you model the patch as a grid of wires, then changing the height above this ground is a very laborious job.  A grid with 21 x 21 wires has 84 values of Z.  You need a programmer's editor with a macro feature to change all that, without going nuts in the process.  It would be much easier if the antenna grid could be kept still and the ground plane shifted up or down instead.

It turns out that the Surface Patch feature of NEC can be successfully misused as a ground plane.  Make a ground plane with GN 1 and make a surface patch and compare the radiation patterns - you'll see they are the same.

Normally, something modeled with SP cards must be a fully enclosed volume, but it works perfectly as a two dimensional ground plane if the antenna is always above it, with nothing below.  The height of a multi patch surface 'ground plane' can be altered by changing only three values of Z, which is rather easier than the 84 Z heights in the wire grid.

Wire Grid

You could model the patch using SP cards, but then you need to define all 6 sides of the 3D plate, which is just as much hassle as making a wire grid with GW cards.  You could also make a wire grid by starting with one little two segment wire and careful use of GM cards, to rotate it into a little cross and replicate it to the side and down, but then it becomes hard to figure out where to put the feed point, since the tag numbers of the wires become unknown after using GM cards.

In the end, I modelled the example patch grid using GW cards, since it is rather mindless to do and then defined the feed point on wire #16.  If you used the replication method, then define a tiny 1 segment, 1 mm long vertical wire, with the (x,y) co-ordinates calculated to be exactly on a grid wire, without having to know what the tag number of that wire is.  For this method, I assign a high number (1000) to the tiny feed wire tag, so I can tie a transmission line TL card to it.

You will see the logic in this approach once you try to make a multi patch array by rotating and translating the first patch with multiple GM cards and then sit and stare at the screen and wonder where the heck to put the feeds.

Parallel Plate Capacitor

A patch antenna is a parallel plate capacitor.

 Smith Chart - Capacitive Load

Whereas a Helical Antenna is inductive, a Patch is capacitive and you got to live with it.  The impedance on the edge is very high and can be made more reasonable by offsetting the feed point about 30% from the edge, but whatever you do, it will be capacitive, on the edge of the Smith chart.  For best results, you may need to add an antenna matching circuit to a patch array antenna.

Design Formulas

Designing an air dielectric patch antenna turned out to be very simple.  Whereas a PCB patch requires a complex formula to describe it, due to the edge effects that are through the air, vs the main field that is through the dielectric - with an air spaced patch, everything is through air and all complications disappear in a puff of magic.

Where c is the speed of light and f is the design frequency:

• The wavelength WL = c / f
• The width of the patch W = WL / 2
• The length of the patch L = 0.49 x W
• The feed point F = 0.3 x L

The height above ground is best determined experimentally and will be a few millimeters.

If you start with say a 10 mm gap and gradually reduce the height, then after a while you will find a spot where the calculations explode and the radiation plot becomes a big round ball (cocoanec), or just a black screen (xnec2c).  This is the point where the antenna resonates.  For this patch, it happens at 5 mm height.  The optimal pattern is achieved when the gap is one or two mm wider than that, at 6 or 7 mm - simple.

The design frequency should be 3% higher than the desired frequency.  

When you build an antenna, there are always other things in close proximity that loads it: Metal parts, glue, spacers, cables, etc.  All these things will make the antenna operate at a slightly lower frequency than what it was designed for.  Therefore design for a slightly higher frequency and then it will be spot on.  The Ham Radio rule of thumb is to design for the top end of a radio band, but that may not be high enough for a narrow band like this.

In this case, the ISM band is 900 to 930 MHz, so the mid point is 915 MHz and 1.03 x 915 = 942 MHz, so that is what I would design to. 

PCB Dielectrics Modeled With NEC2

If you really want to make a Printed Circuit Board (PCB) antenna, then you need to use a special type of Teflon (PTFE) PCB that has a controlled dielectric value.  Ordinary fibre glass and epoxy resin FR4 has a relative permittivity that varies wildly from 4.2 to 4.7, this is too much for consistent reproducible results.  Read this for details: https://www.arrowpcb.com/laminate-material-types.php

You need to find a PCB house, look at the available materials and then design the antenna accordingly.  For microwave RF applications, pure PTFE on a fiberglass substrate, with a relative permittivity ε0 of 2.1 and Loss of 0.0009, is the best available in wide commercial use.  Calculate the capacitance of a little elemental square with the simple thin parallel plate formula:
C = ε0A/d

You can simulate the dielectric in NEC2 by attaching a load (LD) card with a small capacitor as calculated above to the middle of each element - calculating all the co-ordinates will keep you busy for a while!   The NEC2 simulation result should be quite accurate when you add all these little parasitic capacitors.  The easier way to handle it is to create one little element and then use GM cards to rotate and replicate the elements in two dimensions to make a patch, without having to calculate hundreds of x,y co-ordinates, which would drive any sane person up a wall.

Signal speed is inversely proportional to the square root of the dielectric constant. A low dielectric constant will result in a high signal propagation speed and a high dielectric constant will result in a much slower signal propagation speed.  This has a very large effect on the dimensions of the antenna.

The problem is that you can only vary the patch to ground spacing in a few discrete steps, since it is determined by the thickness of the chosen PCB, which is typically 0.2, 0.8, 1.6 or 3.2 mm.  You can vary the length and width in the simulation using a geometry scale GS card, but scaling will also change the spacing, so then you have to modify the position of the ground plane to get the model back to the fixed thickness of the PCB.  Nothing is ever easy with this clunky old program, but it is free, so that is fair enough.

Example Patch Antenna

Here is a set of NEC2 cards for an air dielectric 33 cm Ham band or 900 MHz ISM band patch antenna made from a tin or copper rectangle, a few mm above a somewhat larger ground plane:

CM Surface Patch Antenna
CM Copyright reserved, GPL v2, Herman Oosthuysen, July 2018
CM
CM 940 MHz (915 + 3%)
CM H=7 mm, W=160 (80), L=156 (78)
CE
#
# Active Element: 21x21 Wires in a Rectangle
# X axis
# GW Tag NS X1 Y1 Z1 X2 Y2 Z2 Radius
GW 1  21 -8.00E-02 -7.80E-02 0.00E+00 +8.00E-02 -7.80E-02 0.00E+00 1.00E-03
GW 2  21 -8.00E-02 -7.02E-02 0.00E+00 +8.00E-02 -7.02E-02 0.00E+00 1.00E-03
GW 3  21 -8.00E-02 -6.24E-02 0.00E+00 +8.00E-02 -6.24E-02 0.00E+00 1.00E-03
GW 4  21 -8.00E-02 -5.46E-02 0.00E+00 +8.00E-02 -5.46E-02 0.00E+00 1.00E-03
GW 5  21 -8.00E-02 -4.68E-02 0.00E+00 +8.00E-02 -4.68E-02 0.00E+00 1.00E-03
GW 6  21 -8.00E-02 -3.90E-02 0.00E+00 +8.00E-02 -3.90E-02 0.00E+00 1.00E-03
GW 7  21 -8.00E-02 -3.12E-02 0.00E+00 +8.00E-02 -3.12E-02 0.00E+00 1.00E-03
GW 8  21 -8.00E-02 -2.34E-02 0.00E+00 +8.00E-02 -2.34E-02 0.00E+00 1.00E-03
GW 9  21 -8.00E-02 -1.56E-02 0.00E+00 +8.00E-02 -1.56E-02 0.00E+00 1.00E-03
GW 10 21 -8.00E-02 -7.80E-03 0.00E+00 +8.00E-02 -7.80E-03 0.00E+00 1.00E-03
GW 11 21 -8.00E-02 +0.00E+00 0.00E+00 +8.00E-02 +0.00E+00 0.00E+00 1.00E-03
GW 12 21 -8.00E-02 +7.80E-03 0.00E+00 +8.00E-02 +7.80E-03 0.00E+00 1.00E-03
GW 13 21 -8.00E-02 +1.56E-02 0.00E+00 +8.00E-02 +1.56E-02 0.00E+00 1.00E-03
GW 14 21 -8.00E-02 +2.34E-02 0.00E+00 +8.00E-02 +2.34E-02 0.00E+00 1.00E-03
GW 15 21 -8.00E-02 +3.12E-02 0.00E+00 +8.00E-02 +3.12E-02 0.00E+00 1.00E-03
GW 16 21 -8.00E-02 +3.90E-02 0.00E+00 +8.00E-02 +3.90E-02 0.00E+00 1.00E-03
GW 17 21 -8.00E-02 +4.68E-02 0.00E+00 +8.00E-02 +4.68E-02 0.00E+00 1.00E-03
GW 18 21 -8.00E-02 +5.46E-02 0.00E+00 +8.00E-02 +5.46E-02 0.00E+00 1.00E-03
GW 19 21 -8.00E-02 +6.24E-02 0.00E+00 +8.00E-02 +6.24E-02 0.00E+00 1.00E-03
GW 20 21 -8.00E-02 +7.02E-02 0.00E+00 +8.00E-02 +7.02E-02 0.00E+00 1.00E-03
GW 21 21 -8.00E-02 +7.80E-02 0.00E+00 +8.00E-02 +7.80E-02 0.00E+00 1.00E-03
#
# Y axis
# GW Tag NS X1 Y1 Z1 X2 Y2 Z2 Radius
GW 22 21 -8.00E-02 -7.80E-02 0.00E+00 -8.00E-02 +7.80E-02 0.00E+00 1.00E-03
GW 23 21 -7.20E-02 -7.80E-02 0.00E+00 -7.20E-02 +7.80E-02 0.00E+00 1.00E-03
GW 24 21 -6.40E-02 -7.80E-02 0.00E+00 -6.40E-02 +7.80E-02 0.00E+00 1.00E-03
GW 25 21 -5.60E-02 -7.80E-02 0.00E+00 -5.60E-02 +7.80E-02 0.00E+00 1.00E-03
GW 26 21 -4.80E-02 -7.80E-02 0.00E+00 -4.80E-02 +7.80E-02 0.00E+00 1.00E-03
GW 27 21 -4.00E-02 -7.80E-02 0.00E+00 -4.00E-02 +7.80E-02 0.00E+00 1.00E-03
GW 28 21 -3.20E-02 -7.80E-02 0.00E+00 -3.20E-02 +7.80E-02 0.00E+00 1.00E-03
GW 29 21 -2.40E-02 -7.80E-02 0.00E+00 -2.40E-02 +7.80E-02 0.00E+00 1.00E-03
GW 30 21 -1.60E-02 -7.80E-02 0.00E+00 -1.60E-02 +7.80E-02 0.00E+00 1.00E-03
GW 31 21 -8.00E-03 -7.80E-02 0.00E+00 -8.00E-03 +7.80E-02 0.00E+00 1.00E-03
GW 32 21 +0.00E-00 -7.80E-02 0.00E+00 +0.00E+00 +7.80E-02 0.00E+00 1.00E-03
GW 33 21 +8.00E-03 -7.80E-02 0.00E+00 +8.00E-03 +7.80E-02 0.00E+00 1.00E-03
GW 34 21 +1.60E-02 -7.80E-02 0.00E+00 +1.60E-02 +7.80E-02 0.00E+00 1.00E-03
GW 35 21 +2.40E-02 -7.80E-02 0.00E+00 +2.40E-02 +7.80E-02 0.00E+00 1.00E-03
GW 36 21 +3.20E-02 -7.80E-02 0.00E+00 +3.20E-02 +7.80E-02 0.00E+00 1.00E-03
GW 37 21 +4.00E-02 -7.80E-02 0.00E+00 +4.00E-02 +7.80E-02 0.00E+00 1.00E-03
GW 38 21 +4.80E-02 -7.80E-02 0.00E+00 +4.80E-02 +7.80E-02 0.00E+00 1.00E-03
GW 39 21 +5.60E-02 -7.80E-02 0.00E+00 +5.60E-02 +7.80E-02 0.00E+00 1.00E-03
GW 40 21 +6.40E-02 -7.80E-02 0.00E+00 +6.40E-02 +7.80E-02 0.00E+00 1.00E-03
GW 41 21 +7.20E-02 -7.80E-02 0.00E+00 +7.20E-02 +7.80E-02 0.00E+00 1.00E-03
GW 42 21 +8.00E-02 -7.80E-02 0.00E+00 +8.00E-02 +7.80E-02 0.00E+00 1.00E-03
#
# Ground plane
# H = 5 mm, Feed = 16
# Frequency 940.000 MHz
# Resonance; the calculation explodes
#
# H = 7 mm, Feed = 16
# Frequency 940.000 MHz
# Feedpoint(1) - Z: (0.116 + i 133.600)    I: (0.0000 - i 0.0075)     VSWR(Zo=50 Ω): 99.0:1
# Antenna is in free space.
# Directivity:  7.68 dB
# Max gain: 12.54 dBi (azimuth 270 deg., elevation 60 deg.)
#
# SM NX NY X1 Y1 Z1 X2 Y2 Z2
# SC  0  0 X3 Y3 Z3
SM 25 25 -1.00E-01 -1.00E-01 -7.00E-03  +1.00E-01 -1.00E-01 -7.00E-03
SC  0  0 +1.00E-01 +1.00E-01 -7.00E-03
#
# Frequency 850.000 MHz - 3 dB down
# Feedpoint(1) - Z: (0.176 + i 129.320)    I: (0.0000 - i 0.0077)     VSWR(Zo=50 Ω): 99.0:1
# Antenna is in free space.
# Directivity:  7.42 dB
# Max gain: 9.54 dBi (azimuth 270 deg., elevation 60 deg.)
#
GE
#
# Frequency 940 MHz
FR     0     1     0      0   9.40E+02
#
# Excitation with voltage source
# EX 0 Tag Segment 0 1Volt
EX     0     16     11      0         1
#
# Plot 360 degrees
RP     0    90    90   1000         0         0         4         4      0
EN

Now you can go and get a coffee can and tin snips and have fun.  The trick is to space the tin plate with paper or plastic washers and glue it to the ground plane with two or four hot glue blobs on the corners, then after hardening, remove the spacers.

For more information on what exactly to do with the contents of the coffee can, you can read this https://2b-alert-web.bhsai.org/2b-alert-web/login.xhtml

Once you have the first rectangular patch working in simulation, you can explore cutting the corners, or making slots in it, to get circular polarization for Satcom or mobile use.  You could also try drilling holes in two opposing corners and using those for little nylon bolts.  That could provide robust mounting and circular polarization, in one swell foop.

Once you built the widget, you need to measure it to see how close you got to your model and how you should tweak things.  It is very seldom that the first try is good enough. The aliexpress web site lists many different VNA models from $300 to $3000, which is orders of magnitude less than a couple decades ago.  I got a Measall KC901V, and I am very happy with it.

Patch Antenna Calculators

There are various patch antenna calculators on the wild wild web, for example:
http://www.emtalk.com/mpacalc.php

A calculator can quickly create a starting point for experiments.

To hook the antennas together, you can use microstriplines, which can be calculated with this one: https://www.pasternack.com/t-calculator-microstrip.aspx

However, at a height of 7 mm, the stripline tracks would need to be impractically wide.

If you put four patches in parallel, then the impedance becomes 90/4 = 22.5 Ohm, which is not a good match to a 50 Ohm co-ax.  For a good match, you can instead uptransform each patch with a taper (height 7 mm) from 90 Ohm (14 mm) to 200 Ohm (2 mm), so that when you combine them, you get 50 Ohm.

Where to put the taper?  A wide 14 mm track is a bit impractical, while a thin 2 mm track is a bit lossy, so how now brown cow?

One solution is to use two impedance tapers:
The impedance of the start and end of the transmission line is important, but what exactly it is in the middle, doesn't matter.  Therefore, at the patch, taper from 14 mm to 5 mm, run the track to the connector in the middle and then taper from 5 mm to 2 mm.  It is always a give and take - trade off one thing for another and try again!

Note that it is important that you run the tracks in a kind of swastika with the 50 Ohm connector in the middle of the panel, such that each branch is progressively 1/4 wavelength longer, to provide the required 90, 180, 270 degree phasing.  However, don't make 90 degree corners - make them rounded, or 45 degree sections - else the corners will radiate and cause reflections.

Note that 93 Ohm coaxial cable is available from Pasternack, so you could use it instead of strip lines: https://www.pasternack.com/93-ohm-coax-rf-cables-category.aspx

However, if you decide to use coax, then you can just as well probe the patch with a network analyzer till you find the exact spot where it is 50 Ohm and run garden variety RG316U coax - choices, choices...

Eventually, just to prove it, I got busy with tin snips on thin 0.8 mm FR4 since it is easy to work with and made a bunch of patches and measured them all - too big, too small, too big, too small - aaargh!

The little bit of FR4 epoxy has a significant effect on the resonant frequency and I had to make the patch about 20 mm smaller than the original design.  This exercise showed that to make a properly tuned patch you must have a reasonably decent VNA and a lot of patience.

On the right is an example that is almost the right size - about 1 mm too small - with a usable bandwidth from 908 to 938 MHz, which is 8MHz too high.  The 50 Ohm co-ax feed is soldered in from the bottom.   I made a 6 mm hole in the reflector, soldered the braid there and a 2 mm hole in the patch for the centre wire.  For these tests, the patch is held down with wads of 'chewing gum' (Faber-Castell Tack-It).
  

Circular Polarized Patch Array

With careful use of GM cards, one can replicate and rotate the patch and create an array of 4, 9 or 16 patches and then tie them together in series with 1/4 wave transmission line TL cards (the skew faint lines between the feed points on the below picture).  One can make the EM field rotate right or left depending on whether one feeds it at patch 1 or at patch 4.

One can daisy chain patches like this in a model, but for the real thing, I would hook them in parallel with a star of striplines or coax to ensure that the transmit power level is the same on each patch.

Coax delay lines are good for a one off test, while microstriplines are good for replication.  In the end, the whole assembly will be only as accurate as your test tools and your patience allow.

A 24 dBi Quad Patch Array Simulation

Obtaining 24 dBi from only four patches is very good - very well optimized.  Typical commercial quad patch antennas will yield 17 to 21 dBi, which is probably what you will get when you actually build it.

A simulation helps very much to figure out what should work and what won't, but to measure is to know!

A problem with using 9 (3 x 3) or 16 (4 x 4) patches, is the law of diminishing returns: Losses and radiation from the transmission lines will become significant and will distort the patterns from the patches.  Therefore, the NEC model may look great, but the practical results may disappoint. 

 

More information on patch design here: https://www.aeronetworks.ca/2019/03/driving-quad-patch-array-antenna.html

 

A large patch array with nine or sixteen patches, could create a very high gain assembly - a pencil beam - the complete design of which would require an export license, due to the Wassenaar agreement on dual use items.  Therefore I'll rather just stop here with this article and not provide the complete design, before a black helicopter starts to follow me around.
;)

La Voila!

Herman