Antenna Modelling

Designing, building, testing and using antennas is a fun part of our Amateur Radio hobby. On the 40 metre Amateur Radio band, where we mainly operate, we use a loop antenna, comprising about 40 metres of insulated copper wire, suspended by 4 masts, each about 9 metres high. The antenna is connected to our transceiver, inside, via a length of coaxial cable attached to one corner of the loop. We use this antenna, every day, to talk to our radio friends in Victoria, New South Wales, South Australia and Tasmania.

There are many other types of antennas, too, and we have tried them all at home and when we operate with our portable equipment. Some antennas appear to work better than others. Whenever we talk about antennas on the air, we are always asked: "Which is the best antenna to use on 40 metres". Well, in our opinion, there is no best antenna for all situations, as it all depends on what you need. So we thought it would be interesting to evaluate all the different types of antennas under exactly the same conditions and comparing the results. However, to keep it simple, we won't be considering directional or multi-band antennas.

Table of Contents

Introduction

The problem with comparing antennas on-the-air is that you have to design, build, install and test each of them. That takes a lot of time, money and effort and the results will vary depending on many factors, such as their location and ionospheric propagation. The answer is to use antenna modelling: That is, using a computer program to simulate a real antenna and predict its performance. Then you can evaluate different types under absolutely identical conditions. But is computer modelling accurate? The answer is yes, it is accurate under certain conditions: Just like the mathematics of calculus, where the problem is broken down into small pieces, which are individually evaluated and then the results are summed to get the answer; antenna modelling programs divide the antenna into many segments and compute the individual segment currents to provide a complete picture of the electromagnetic fields produced. The condition for accuracy is that the computer program is given both the correct and the complete information. In other words, if you build an antenna exactly according to an antenna model and then place it next to a shed or trees, which were not in the model, or over ground which was different from the specification in the model, then it will not work as predicted.

Modelling Tools

We use EZNEC Pro/2+ v.7.0 and SimNEC 2.6. These are comprehensive tools with a lot of features. The examples shown here are fairly simple and only demonstrate a fraction of the tool's capabilities.

Building an Antenna Model

Opening and Saving EZNEC files

Note: The following examples use the 40 m Centre-Fed Dipole EZNEC file

Open an EZNEC file:

Press Open
Navigate to and select the EZNEC (.EZ) file
Press Open

Whenever closed, EZNEC will automatically save the current file as LAST.EZ. Whenever opened, EZNEC will automatically open the LAST.EZ file.

Very Important: The file must be saved by name at some point before opening another file.

Save the EZNEC file:

Press Save As
Select the EZNEC file (the current file by default)
Press Save
Confirm Save
Press Yes

Specify the Wire Geometry and Type

Click on Wires

For each wire enter the X, Y and Z coordinates of End1 and End2. Note: For symmetry, we like to centre the dipole along the X or Y axis.
Enter the wire diameter, number of segments, insulation and type

For a simple dipole antenna you only need to specify one wire, as the feed point can be positioned anywhere along the wire. The more segments you use to break up a wire the more accurate the model will be, but the longer it will take to run.

Specify the Feed Point

Note: We always connect a 1:1 transformer, instead of a source, directly to the antenna feed point so that we can easily change from viewing the unmatched and the matched antenna response. Set Port 1 to 50 Ω to see the unmatched response. Set Port 1 to the feed point impedance to see the matched response.

Click on Transformers

Connect Port 1 to the driven wire element at the required percentage from End1
Connect Port 2 to a "virtual wire" called V1
Set the Port 1 and Port 2 impedance to 50 Ω, creating a 1:1 transformer

Note: Since a transformer cannot be positioned at the junction of two wires (e.g. in the case of an inverted V antenna), position it as close as possible to the end of one of the wires instead. If you position it too close to the end (on the segment next to the junction) you will receive the error message: "Adjacent segment not in line".

Specify the source

Click on Sources

Connect the source to wire V1
Select a current source with an amplitude of 1

Viewing the Antenna

Press View Ant

The image shows the orientation of the antenna in relation to the X,Y and Z axes, the position of the transformer at the feed point and the antenna wire segments.

Setting the Operating Frequency and Range

Click on Frequency

Enter the operating frequency

Press SWR

Enter the start and stop frequency range. Note: In this example the operating frequency is in the centre of the range.
Enter the frequency step for no more than 20 steps in the frequency range

Press Run
Move the cursor to the operating frequency

Read the SWR, impedance, reflection coefficient and return loss

This is the unmatched response of the antenna at the antenna feed point.

Tuning the Antenna

Manually tune the antenna to resonance on the operating frequency

Adjust the wire length on the wires window to minimise the impedance angle (degrees) or reactance (+/- j)
Press SWR and Run each time the wire length is changed. This is an iterative process. Note that the resonant frequency may not necessarily occur at the point of lowest SWR.
In this example the impedance at the operating frequency is 66.51 Ω - j 0.0582 Ω

Observe the resistance value at resonance. In the example it is 66.51 Ω,
Copy this value to the transformer's Port 1 impedance, leaving the Port 2 impedance at 50 Ω

Press SWR and Run again
Move the cursor to the operating frequency

This is the expected response when the antenna is properly matched to the feed line and the feed line is matched to the rig. See the section below on impedance matching for that.

Antenna Gain and Radiation Pattern

Select Plot Type 3 Dimensional
Press FF Plot
Select Elev Slice
Select 90 Degrees Slice Azimuth - This is the on-axis direction, i.e. perpendicular to the antenna wire.
Select Show 2D Plot. Note the Gain at 90 degrees elevation (straight up) is 6.3 dBi
Select 45 Degrees cursor elevation. Note the Gain at 45 degrees elevation is 5.44 dBi
Select 0 Degrees Slice Azimuth - This is the off-axis direction, i.e. inline with the antenna wire. Note the Gain at 45 degrees elevation is 0.89 dBi

The following plots were obtained for the example antenna.

The values above for each antenna type were entered into the table in the Results section below.

Impedance Matching

This is a short note about some of the techniques we use to match the antenna to the rig (without the use of an antenna tuner). Since we build only mono-band, resonant antennas we can assume that the impedance at the feed point is purely resistive (although the following methods will also work for reactive impedances). To match the antenna we use either matching sections or capacitive stubs or inductive stubs. If the impedance is between 25 Ω and 100 Ω we can use a matching section comprising a length of 50 Ω coax at the feed-point followed by a length of 75 Ω coax, then any length of 50 Ω coax to the rig. Alternatively by adjusting the length of 50 Ω coax from the antenna feed-point to the rig we can use a capacitive (open circuit) or inductive (short circuit) stub of coax, connected at the rig end using a coaxial tee-piece. Sometimes an extra half-wavelength of coax is needed to be inserted if the feed line is physically too short to reach the rig. We use SimNEC to calculate the exact lengths of coax required. This saves on coax wastage. Here, we assume you have a basic understanding of Smith charts. If not, a good tutorial video can be found here.

The process of impedance matching using a Smith chart starts by plotting the antenna feed impedance on the chart. Then using components, such as coaxial matching sections or coaxial stubs, to bring the impedance into the centre of the chart, which is defined as a perfect 50 Ω, resistive impedance. Once upon a time this was done using a compass and pencil. These days, computer programs like SimNEC make it easy and fun. It is a bit like the "Snakes and Ladders" game, as adding a length of coax does not necessarily move the impedance in the intended direction, but it sometimes opens up new possibilities to be explored.

Opening and Saving SimNEC files

Open a SimNEC file:

Click file.
Click load circuit description.
Navigate to and select the SimNEC (.ss) file.
Click load.

Save a SimNEC file:

Click file.
Click save circuit description.
Navigate to the folder and enter the SimNEC (.ss) file name.
Click save.

Creating a SimNEC circuit

Click file | new circuit
Enter the Generator frequency (the operating frequency) and the resistance, e.g. 50 Ω. The later will become the centre of the chart. The impedance seen by the Generator will be plotted on the chart as a blue circle, initially in the centre.
Enter the Load impedance - This is the antenna feed-point impedance. The impedance seen by the Generator will now match the Load impedance
Drag and drop one or more components into the circuit between the Load (L) and the Generator (G). The impedance transformation along the length of each Component will be plotted on the chart as a line with the same colour as the Component.
Enter the Component parameters - specifically the cable model, e.g. RG-58C/U, and length. Note: The component's frequency is the frequency at which the models parameters apply and need not be changed. The lengths of transmission lines can be changed easily either by selecting them and using the mouse wheel or by right-clicking and dragging the coloured traces around on the chart.

The following Smith charts show how these methods work. The pink coax is connected to the antenna. The green coax is connected to the rig (or at the rig, using a coaxial tee-piece, in the case of stubs).

Matching Section for 50 Ω - 100 Ω using 50 Ω coax (pink) and 75 Ω coax (green):

Matching Section for 25 Ω - 50 Ω using 50 Ω coax (pink) and 75 Ω coax (green):

Inductive (short circuit) stub (green) at rig to match high impedances using 50 Ω coax:

Capacitive (open circuit) stub (green) at rig to match low impedances using 50 Ω coax:

Comparing 40 metre Antennas

We analysed the following 40 m antenna types (double-click on the links to download the EZNEC models that we used):

40 m Horizontal Loop (Square)
40 m Vertical Loop (Rectangular with 9 m high wire and 2.5 m low wire)
40 m Centre-Fed Dipole
40 m Offset Centre-Fed Dipole
40 m End-Fed Half-Wave (Optimised with 7% counterpoise and including a 40:1 transformer, comprising 3:19 turns = 50 Ω:2006 Ω)
40 m End-Fed Sloper (9 m down to 2.5 m. Optimised with 7% counterpoise and including a 22:1 transformer, comprising 3:14 turns = 50 Ω:1088 Ω. Note: Off axis gain is greater in the direction of the low end.)
40 m Centre-Fed Folded Dipole
40 m Inverted V Dipole (2.5 m end height)
40 m Inverted L (2.5 m end height, with 21% counterpoise and including a 52:1 transformer, comprising 3:22 turns = 50 Ω:2580 Ω))
40 m Vertical Dipole (22.5 m height, centre fed at 11.5 m via coax inside mast)
40 m Ground Plane with 4 Radials (Radials at 2.5 m)
40 m Ground Plane with 32 Radials (Radials at 2.5 m)
40 m Half Square (At 12 m height because vertical elements drop 10.4 m)
40 m Beverage (3 half-wavelengths at 2.5 m)
Terminated Three Element Folded Dipole (Fed with 600 Ω Open Wire line with a 1000 Ω termination resistor in at the centre of the centre wire)

Basic feed point transformer formulas:

r = z / 50;
s = p x sqrt(r)

where:
r = turns ratio : 1
z = impedance
s = secondary turns
p = primary turns (3)

For consistency we used the following frequency, height, wire and ground specifications, unless otherwise stated

Resonant Frequency: 7.1 MHz
Height: 9 m for horizontal antennas and above 2.5 m (EMR safety height) for vertical antennas
Wire: 1.5 mm copper wire with 0.75 mm PVC Insulation (εr = 4.0)
Ground Type: Real/MININEC (Conductivity = 0.005 S/m, Dielectric Constant = 13)

Results

Here are the comparative results for all antennas. All values are for the antenna perfectly matched to the feed line and the feed line perfectly matched to the rig. So, we are only comparing the antenna characteristics themselves. The results in bold indicate the best result for all antenna types (phased and travelling wave antennas excepted).

	Antenna View	Length	Feed Point Impedance	Elevation Pattern	Max Gain Angle	Max Gain	Gain @ 45° On Axis	Gain @ 45° Off Axis	SWR @ ±100kHz
Horizontal Loop		43.552 m	130.3 - j 0.7182 Ω		90°	6.84 dBi	4.84 dBi	1.91 dBi	1.39 : 1
Vertical Loop		41.296 m	163 - j 0.5018 Ω		90°	4.5 dBi	3.23 dBi	-0.99 dBi	1.30 : 1
Centre-Fed Dipole		19.490 m	66.51 - j 0.05821 Ω		90°	6.3 dBi	5.44 dBi	0.89 dBi	1.42 : 1
Offset Centre-Fed Dipole		19.498 m	86.23 - j 0.8624 Ω		90°	6.3 dBi	5.44 dBi	1.0 dBi	1.45 : 1
End-Fed Half Wave		20.015 m	2019 + j 282.1 Ω		90°	6.3 dBi	5.44 dBi	1.22 dBi	1.48 : 1
End-Fed Sloper		18.64 m	1092 + j 31.78 Ω		90°	5.88 dBi	4.46 dBi	2.55 dBi ¹ -0.98 dBi ²	1.68 : 1
Centre-Fed Folded Dipole		38.88 m	328 + j 0.5059 Ω		90°	6.00 dBi	5.09 dBi	0.53 dBi	1.25 : 1
Inverted V Dipole		22.807 m	30.2 - j 0.1768 Ω		90°	5.51 dBi	4.0 dBi	2.4 dBi	2.12 : 1
Inverted L		20.68 m	2580 + j 24.13 Ω		90°	5.38 dBi	4.69 dBi	1.89 dBi ¹ 0.48 dBi ²	1.51 : 1
Vertical Dipole		19.96 m	84.67 + j 0.3439 Ω		15°	-0.81 dBi	-8.87 dBi	-8.87 dBi	1.3 : 1
Ground Plane 4 - Radials		50.999 m	49.87 - j 0.3145		25°	-0.51 dBi	-3.34 dBi	-3.34 dBi	1.53 : 1
Ground Plane 32 - Radials		336.475 m	31.41 + j 0.244 Ω		25°	-0.46 dBi	-3.3 dBi	-3.3 dBi	1.45 : 1
Half Square		41.73 m	50.2 - j 0.3218 Ω		20°	3.47 dBi	-4.17 dBi	-5.43 dBi	2.38 : 1
Beverage		65.1 m	22110 + j 506.6 Ω		40°	9.7 dBi	9.59 dBi	5.52 dBi	36 : 1
Terminated Three Element Folded Dipole		61.8 m	648.9 + j 199.3 Ω		15°	3.82 dBi	- 3.98 dBi	-19.56 dBi	1.4 : 1

Notes:

Gain in the direction of the lowest end
Gain in the direction of the highest end

Conclusion

Here are some observations that we made when reviewing the results. It has really changed many of our long-held, often anecdotal, beliefs. For example: That a folded dipole has twice the SWR bandwidth of dipole and a lower angle of radiation than a horizontal loop; that vertical antennas have the same gain, but a lower angle of radiation than horizontal antennas; and that a large number of radials is required for a ground plane. Incredibly, the antenna modelling shows all of these assumptions to be wrong.

Horizontal Antennas

There really isn't very much difference between all the horizontal antenna types. The horizontal loop antenna appears to be the best all-rounder for gain and SWR bandwidth, by a very small margin. With higher vertical gains, the horizontal antennas are probably more suitable for Near Vertical Incidence Skywave (NVIS), or local, propagation. However, reduced gain at lower angles of radiation make them probably less suitable for DX, or long distance propagation. The flat-top dipoles might be a tiny bit better better for DX.

Vertical Antennas

For vertical antennas the radiation angle is lower. However, the vertical dipole has considerably less gain than the horizontal dipole. The reason for this is its proximity to the ground. In free space, both dipoles have 2 dBi gain, perpendicular to the wire. The radiation pattern is actually a "doughnut" shape around the wire (change Ground Type to Free Space to see this in EZNEC). The ground, however, is a partly reflecting and partly absorbing region, which has a dramatic effect on the antenna radiation pattern. When the horizontal dipole is brought close to the ground, its gain increases as the doughnut is "squashed" from the side. When the vertical dipole is brought close to the ground its gain decreases as the doughnut is squashed from the bottom. Vertical antennas have little vertical gain making them probably unsuitable for NVIS propagation.

Ground planes, are similar to the other vertical antennas, both in free space and near the ground. Contrary to common belief, a much larger number of radials appears to have very little effect on the antenna gain pattern.

Phased Antennas

Phased antennas have more than one radiating element.

The Half-Square antenna is a phased vertical antenna. It has better gain, on axis, than other verticals. It has a low angle of radiation of 20 degrees in its on-axis direction. Its gain at that angle is 2.5 dB greater than horizontal dipoles, probably making it better for DX in that direction. However, its vertical gain is 15.74 dB down on the horizontal loop antenna.

Travelling Wave Antennas

Travelling wave antennas have their main lobes on axis or at an acute angle to the wire direction, so we didn't include them in the same class as the simple horizontal antennas.

The three half-wavelength (65 m) Beverage antenna has an extremely narrow bandwidth (25 kHz) and, curiously, more low-angle gain the closer it is to the ground. So we used a 2.5 metre safety height.

The Terminated Three Element Folded Dipole has main lobes at +/- 55 degrees. It is a broadband antenna with under 1.6 : 1 SWR from 7 - 30 MHz! The radiation pattern varies dramatically with frequency.