Wednesday, July 25, 2018

Patch Antenna Design with NEC2

The older free Numerical Electromagnetic Code version 2 (NEC2) from Lawrence Livermore Lab only works with an air dielectric.  This makes it hard 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, but that is far too much money/trouble for most.

Air Dielectric Patch 

The obvious 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.

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 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 would 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.

Example Patch Antenna

Here is a set of NEC2 cards for a 33 cm Ham band or 900 MHz ISM band patch antenna:

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 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.

Circular Polarized Patch Array

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


A 24 dBi Quad Patch Array


An advantage of a quad array, is that the impedance is much reduced, so you can hook it up with garden variety co-ax.

A large patch array, could create a very high gain assembly - a pencil beam - the complete design of which would require an export license - so I'll just stop here with this article, before a black helicopter starts to follow me around.
;)

La Voila!

Herman

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