Current flow in a wire conductor is defined by the number of electrons passing a point per unit time. The acceleration and deceleration of the electrons cause photons to be emitted. The more current and the longer the length of wire involved the larger is the rate of release of the photons. The faster the acceleration and deceleration i.e. the higher the frequency, the higher is the energy content per photon. The photons travel out at the speed of light. The current flowing in the wire also causes virtual particles to be briefly created which speed out from the wire and then return (Ref.4). These produce what we detect as a local magnetic and electric force field surrounding the wire which decreases as the square of the distance. The strength of this near field falls away so that at the distance of one wavelength and beyond the electromagnetic field is determined by the photons streaming out. Thus the larger the current involved, the longer the wire carrying that current, and the higher the repetition rate i.e. frequency, the more power is radiated. The radiating power can be represented by a notional radiation resistance referred to the input feed point of the antenna. The radiation resistance is therefore higher in physically longer structures, especially when they carry uniform current. Conversely the radiation resistance is reduced in shortened structures which can lead to reduced efficiency. Five topologies are examined in turn leading to the recommended choice of the doubly folded dipole for use in attics.
If you have a long attic then putting up the maximum length of wire fed centrally can be made to work with a high quality Antenna Tuning Unit. However the propagation diagram will contain a number of deep nulls for those frequencies for which it is longer than a wavelength, and there could be considerable losses in the ATU.
Resistor terminated folded dipole
This is a non resonant antenna which provides a low Standing Wave Ratio over a very wide range of frequencies so that an ATU may not be necessary. A typical design takes the form of a folded dipole with a 600-900 Ohm non inductive resistor closing the loop, and a 50/600 Ohm balun interfacing the coaxial cable to the antenna. There are sacrifices in the performance in achieving this flat response. The efficiency falls to typically 30% because of the losses in the damping resistor, and the antenna gain is typically 3-6dB below that of the half wave dipole for a particular frequency. It can also suffer from pronounced nulls in the propagation diagram when the antenna length corresponds to more than a wavelength at the desired frequency (Ref.5).
Parallel connected half wave dipoles
A half wave dipole antenna at resonance has a radiation resistance of 73 ohms referred to the input feed point when in free space. This falls to approximately 50 Ohms due to reflections from the ground when the height is less than a wavelength. There will be a significant amount of inductive or capacitive reactance also present when off resonance, this allows dipoles for the five amateur bands from 10 to 20 metres inclusive to be fed from the same coaxial cable. These can work very well but the ends of the antennas need to be spaced apart as far as possible to minimise interaction between them when adjusting their lengths (Ref.6). You soon run out of length in a small attic so that inductive loading has to be used. This reduces the radiation resistance causing a mismatch with the feeder, and the current has to be increased in the antenna to maintain the same radiated power reducing the efficiency.
Small loop antenna
These are single coil loops with a circumference of between 1/4 and 1/8 of the wavelength at the operating frequency and are sometimes called magnetic loop antennas. They are brought into resonance by an adjustable high voltage capacitor in series with the loop. A vertically mounted loop has the same type of propagation diagram as a horizontal half wave dipole with the energy radiating out along the plane of the loop. The compact size is achieved at the expense of a very low radiation resistance and a narrow bandwidth of a few kHz which makes it necessary to retune every time the frequency is altered. Commercially available loops are usually about 1m in diameter and made out of rigid 20mm diameter copper or aluminium tubing, which means they would not pass through the hatches of most attics. Two separate loops and tuning circuits would be required to cover the bands from 7 to 30MHz. Typical performance figures are 5 kHz bandwidth and 17% efficiency at 7MHz rising to 18kHz bandwidth and 70% efficiency at 14MHz. Design formulae are given in the ARRL Antenna Book (Ref.7), and a handy spread sheet ‘aa5tb_loop_V1.22a.xls’ is available from AA5TB (Ref.8).
Doubly folded dipole
A half wave dipole can be made to fit into a reduced length by bending it into an open rectangular loop, and hence is the recommended type of antenna for attics. However this bending reduces the radiation resistance from 50 to around 12 – 15 Ohms, it therefore requires twice the original current in the antenna to produce the same output. Fortunately it is possible to achieve a close match with a 50 Ohms feeder if the half wave dipole is changed to the folded dipole configuration before it is bent. This construction also provides two wires in parallel to share the increased current and thus maintains the antenna efficiency above 90%. It is easy to make the folded dipole from twin cored mains cable but a modification is required to the end terminations because the solid dielectric between the wires results in a transmission line Velocity Factor of between 0.5 & 0.7 depending on its construction instead of above 0.95 for bare conductors. The nett result is that the shorting positions have to be moved in from the remote ends to a distance from the feed point corresponding to the velocity factor x the 1/4 wavelength of the antenna. A good explanation of this phenomenon is given in section 2-32 of the ARRL Antenna Book (Ref.9), and further details are given in the section on the ‘nested loop design’.
The antenna loops can be set at an angle to the horizontal without much change to their propagation pattern. This makes it easy to nest the loops for each band by stapling them to the underside of the roof trusses on one side of the apex. The 5 bands from 14 to 29MHz are best nested together in a concentric arrangment to minimise the interaction between them. They are fed by a common co-axial cable. It is recommended that this co-ax is looped around 6 times near the antenna feed point to form a coil with a diameter of approximately 10cm to create a choke balun. This will discourage RF from flowing down the outside of the coaxial cable and make it easier to obtain consistent SWR readings.
The close proximity of the two ends of each bent loop causes partial cancellation of the electric field in that vicinity. This reduces the interaction between the nested loops making their adjustment easier. It also reduces the electric field strength in the living space below.
Antenna Simulation Programs
Most antenna modelling software employ the Numerical Electomagnetic Code (NEC) at their heart. There are at least four versions of NEC with NEC-2 being the highest that is free to use without a license.
The NEC software uses the ‘method of moments’ to approximate the antenna performance, where a ‘moment’ is numerically the size of the current times the ‘length and direction’ describing a small piece of the antenna. Each conductor in the antenna structure is therefore broken down into segments. The software represents the current per segment as the summation of a dc component, a sine wave, and a cosine wave, and solves the resulting set of equations to achieve continuity at the junctions between the segments (Ref.10).
Here is a list of some of the excellent free antenna modelling software available.
|Program MS Windows Linux Mac. OS X |
4nec2 Yes Yes (+wine) –
MMAMA-GAL Yes Yes (+wine) –
NECLAB Yes Yes (+wine) –
Xnec2c – Yes –
nec2++ – Yes –
CocoaNEC – – Yes
Antenna Simulation Files
The NEC input data file consists of a number of commands called cards in remembrance of the days of punch card entry. The structure can be separated into three different blocks, the full details are given in Ref.11 :-
CE End of comments
GW/SP/.. Geometry definition
GE End of geometry block
EX/GR/LD/FR/RP/… Program control
EN End of program
The following antenna file is in the NEC format and can be copied and pasted into a simple text editor program such as notepad or gedit and then saved as a .txt file. It can then be used directly by CocoaNET, nec++, Xnec2c, but 4nec2 needs the file type changing to .nec .
Unfortunately the MMAMA-GAL and NECLAB programs each have a slightly different input file format and in their cases it is better to run them and input the antenna geometry definitions using their inbuilt editors.
Guide to Modelling
The relevant lines of code in the NEC input files are easily deciphered using the manual in Ref.11 below. Here is a typical NEC input file for a 3.75 MHz dipole.
CM Dipole antenna for 80 metres.
CM Height = 20m above the ground.
CM Ground has typical conductivity and permittivity.
GW 1 19 -19.6 0.0 20 19.6 0.0 20 0.001
LD 5 0 0 0 58000000
GN 2 0 0 0 14 .006
EX 0 1 10 0 1 0
FR 0 0 0 0 3.75 0
NE 0 80 4 1 -20 -1 18 0.5 0.5 0
NH 0 80 4 1 -20 -1 18 0.5 0.5 0
In this example the dipole is represented by the GW line. The first number in the line is the reference or tag number for the line. The next value is the number of segments of uniform length that the wire is divided into by the program. The next three numbers are the x, y, z co-ordinates of one end of the wire, and the following three are the co-ordinates for the other end. The last number is the radius of the wire. All dimensions are in metres.
The size of the segments determines the resolution in solving the current in the model since the current is computed at the centre of each segment. Therefore there are a number of basic rules that need to be followed to ensure accuracy, a good introduction to getting started in modelling is provided by Ref.12:-
- λ = wavelength in free space ≅ 300 / frequency in MHz.
- Segments should be less than λ / 10 at the desired frequency.
- Extremely short segments less than λ / 1000 should be avoided.
- Wires which have the same co-ordinates for their ends are assumed to be connected.
- The radius of the wires should be less than λ / 100.
- When the model includes (segments lengths) / (wire radius) < 2 the extended thin-wire kernal option should be used by the by the inclusion of an EK card in the file.
- A segment is required at each point where a network connection or a voltage source is located. This may seem contrary to the idea of an excitation gap or break in the wire. However a continuous wire across the gap is needed so that the required voltage drop can be specified as a boundary condition.
Sample plots for the 80m dipole
Ref.4 – Richard Feynman – Science Videos; accessed at http://vega.org.uk/video/subseries/8.
Ref.5 – https://www.nonstopsystems.com/radio/pdf-ant/antenna-article-ttfd-1ayr.pdf
Ref.6 – http://www.qsl.net/hb9mtn/hb9mtn_40-10m_dipole.html
Ref.7 – ARRL Antenna Book (1991) section 5-13.
Ref.8 – http://www.aa5tb.com/loop.html
Ref.9 – ARRL Antenna Book (1991) section 2-32.
Ref.10 – http://eryptick.net/unisold/mmethod.html
Ref.11 – NEC-2 Manual, Part 111: User’s Guide; accessed at http://www.nec2.org/other/nec2prt3.pdf
Ref.12 – A Beginner’s Guide to Modelling with NEC; accessed at http://wireless.ictp.it/school_2005/download/nec2/nec_part1.pdf