Optimize antennas using NEC and a genetic algorithm

## Project description

This project can optimize anntennas using genetic algorithms. It uses my pgapy Python wrapper for PGApack, the parallel genetic algorithm library, originally by David Levine at Argonne National Laboratory and currently maintained by me. It also uses PyNEC, the Python wrapper for NEC2++, the C++ version of the Numerical Electromagnetics Code.

Originally this started out with a low-gain two-element antenna where the driven element is a folded dipole. One of the requirements for that antenna was that it should have 50 Ω impedance and at least some forward gain. Optimizing this antenna by hand soon turned out to be tedious and I started experimenting with optimization by a genetic algorithm.

You can find the original experiments in folded.nec and folded2.nec. These are input files to the command-line NEC programs. You can either use the nec2c command-line program which produces an output file that can be viewed with xnecview or you can use graphical xnec2c program. All run under Linux and are included in the Debian Linux distribution. The .nec files may also be usable with other NEC versions on other operating systems but I have not tried.

For optimizing the two-element Yagi-Uda you can use the command-line tool folded_antenna where the optimizer is implemented in folded.py. Later a 3-element antenna with the same principles was added in folded_3ele.py callable with the command-line tool folded_3ele_antenna.

The antenna_model.py factors out the common parts of the various antennas.

The hb9cv.py with the command-line tool hb9cv_antenna models the well-know HB9CV antenna but only very crudely. NEC2 isn’t really suited for modelling the phasing stubs of that antenna because it doesn’t like parallel wires that are too close. I mainly did this for comparing some of the antennas resulting from optimization with the well-known performance of the HB9CV.

In the file logper.py with the command-line tool logper_antenna you can find a 9-element log-periodic antenna. It can currently not be optimized, the performance of the real antenna is better than the results obtained with NEC, so I didn’t implement an optimizer for it yet.

All the antenna programs take an action as mandatory argument. The action is typically either optimize for running the optimizer or necout for creating a .nec file which can then be fed to one of the nec programs mentioned above. When running the optimizer it makes sense to experiment with different random seeds, each random seed will usually produce a different antenna. In addition there are some experimental actions, frgain prints the forward and backward gains (in dBi) for the lowest, the middle, and the highest frequencies and the VSWR for those. The gain action visualizes the 3D antenna gain pattern and the swr action visualizes the VSWR over the given frequency range. Note that both, the gain and the swr action compute the antenna data over the whole frequency range using NEC and that may take some time.

The output of the optimizer is text (usually redirected to a file) that prints the evaluation, the VSWR, maximum gain, and forward/backward ratio of the best antenna for every 10th generation of the genetic algorithm. In addition the command-line options to create that antenna are printed. When the genetic algorithm doesn’t make any more progress, the search terminates and the data of the best evaluation are given. An example of the last lines of such a text is as follows. The data is from one of the best 2-element antennas was obtained with the random seed 26 of an earlier version of the program:

The Best Evaluation: 2.886437e+02.
The Best String:
-r 0.0364 -d 0.0444 -l 0.1704 -4 0.1075
VSWR: [1.7901433511443068, 1.1495780609982815, 1.7995760521232753]
GMAX: 6.69913175227, RMAX: -3.03663376703
Cache hits: 5670/9243 61.34%
Eval: 288.64
[ 101011001100101001111000000010011 ]


This tells us the evaluation (which is meaningful only to the genetic algorithm), the genetic algorithm maximizes this value. The command-line options after the line The Best String: can be used to create a .nec file for that antenna. The antenna in the example has a voltage standing wave ratio of < 1.8 at the band ends and around 1.15 in the middle of the band (the 70cm band from 430 to 440 MHz in that case). The forward gain (in the middle of the band) is 6.7 dBi. The RMAX value is the (maximum) backward gain (in a 30 degree area in the back). So the F/B ratio of that antenna is:

6.7 dB - -3.0 dB = 9.7 dB


The last line of the text output contains the genetic representation of that antenna. The .nec file for the antenna above which was optimized with an early version of this package can be created with the command:

folded_antenna -r 0.0364 -d 0.0444 -l 0.1704 -4 0.1075 necout > folded-opt.nec


The command-line options specify the radius of the folded dipole, the distance of the reflector from the folded dipole, the (half) length of the reflector, and the (half) length of the straight part of the folded dipole, respectively.

According to NEC it has a standing wave ratio (VSWR) of < 1.8 from 430-440 MHz, a forward gain of > 6.5 dBi over the whole frequency range and a Forward/Back Ratio of 8-11 dB.

If you want to implement an optimizer for your own antenna, look at the file folded.py: You need to implement a class that defines the geometry of the new antenna and an optimizer class that initializes the gene ranges and implements a compute_antenna method that returns an instance of your antenna class with the parameters obtained from the given gene. All lengths in the models are metric (in meters) as is the default in NEC.

A recent addition to this package involves modelling of coax cables. This uses information from an old article by Frank Witt [1] to derive everything necessary to model a transmission line with loss from the manufacturer cable data. The command-line tool for using these coax models is named coaxmodel. Again this command has several sub-commands:

• loss: This displays the fitted loss-curves from the manufacturer data against the curve-fit algorithm used, you can see how much difference in dB the fitted curve has to the loss at certain frequencies given by the manufacturer data.
• match computes the impedance at the load and input (depending on which was given as an input the other is computed), the matched and total loss (the matched loss is the loss in the cable if the load is prefectly matched, the total loss is the sum of the matched loss and the additional loss due to reflections), the SWR and data for various stub-matches to get to the cable impedance Z0.
• resonator computes the resistance and Q-factor of a coax resonator at the given frequency. A resonator is a piece of cable that either has a short-circuit or an open-circuit at the far end. The sub-command computes resonators for quarter and half wave at the given frequency.
• stub computes the length, Q-factor, and resulting impedance as well as the inductance or capacitance of a stub for a given impedance and frequency. The impedance by default is -100j Ohm and can be changed with the -x option. The stub with the shortest resulting length is chosen, so for a negative reactance an open stub is chosen while for a positive reactance a closed stub is chosen.

For all these sub-commands you can specify the frequency, length of cable and impedance (either at the load or at the end of the cable) to be used in computing the results. You can specify complex impedances as a python complex number in the format a+bj, e.g. 50-500j.

Finally the transmission_line program can optimize the stub-matching for a transmission line using NEC. By default a lossless line is asumed. Also by default a closed stub at the closest possible position is searched.

Transmission lines can be modelled by NEC with the TL (transmission line) card. But NEC can also model arbitrary (symmetric, passive) networks with the NT (network) card. We use this (and the code in coaxmodel.py) to model a real cable with loss for stub matching. It is instructive to compare the values for stub-matching obtained analytically from coaxmodel with the values obtained from an optimization with the genetic algorithm by transmission_line. Note that the coaxmodel takes frequecies in Hz while transmission_line (which uses NEC) accepts frequencies in MHz. So we match a complex impedance of 75+15j Ω for example:

coaxmodel -c sytronic_RG_58_CU -f 435e6 -z 75+15j match


This yields a stub of length 8.007 cm attached 7.888 cm from the load when matching with a closed stub. When optimizing with transmission_line:

transmission_line -c sytronic_RG_58_CU -f 435 -z 75+15j optimize


we get 8.016cm for the stub length and 7.6cm for the distance of the stub from the load. We can visualize this over a given frequency range by either producing NEC output:

transmission_line -c sytronic_RG_58_CU -f 435 -z 75+15j -i 50 \
-l 0.0816 -d 0.076 --frqstart=430 --frqend=440 necout > x1.nec
transmission_line -c sytronic_RG_58_CU -f 435 -z 75+15j -i 50 \
-l 0.08007 -d 0.07888 --frqstart=430 --frqend=440 necout > x2.nec


And the compute the nec model and display with:

nec2c -i x1.nec > x1.out
nec2c -i x2.nec > x2.out
xnecview x1.out
xnecview x2.out


Or directly display the VSWR curves with:

transmission_line -c sytronic_RG_58_CU -f 435 -z 75+15j -i 50 \
-l 0.0816 -d 0.076 --frqstart=430 --frqend=440 swr
transmission_line -c sytronic_RG_58_CU -f 435 -z 75+15j -i 50 \
-l 0.08007 -d 0.07888 --frqstart=430 --frqend=440 swr


Both are close enough, the SWR is below 1.1 over the whole frequency range given. Note that this can change drastically if load impedances with a higher VSWR are matched.

Also note that the NEC files produced in the example above have a different NEC network for each frequency. This is because NEC models networks using an admittance matrix which is frequency dependent.

This means the sequence of two NT cards, a TL card, a FR card and a RP card are repeated for each frequency. Here the two NT cards define the network of the cable from the load to the stub and the stub itself while the TL card defines the length of a lossless transmission line from the stub to the source. The FR card specifies a single frequency and the RP card defines a radiation pattern and triggers computation. This format is perfectly valid NEC code, but certain programs (like the popular xnec2c) cannot deal with this format and display only a single frequency.

 [1] Frank Witt. Transmission line properties from manufacturer’s data. In R. Dean Straw, editor, The ARRL Antenna Compendium, volume 6, pages 179–183. American Radio Relay League (ARRL), 1999.

## Changes

Version 0.2: More cable data

• Fix setup to correctly specify dependencies

• Add more cable data the following command will list supported cable types:

coaxmodel --help


Version 0.1: Initial Release

## Project details

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