The design process for the Yagi-Uda and Helical Antenna were very similar, whilst the design process for the cavity antenna was quite difficult. All three antennas were simulated on a program called ELNEC that is a derivation from the MININEC software package. ELNEC [16] simulates the combined radiation pattern of a number of small straight wires that model an antenna. A disadvantage of the package is that it only has the facility to input small straight wires and there is a limitation on the number of wires that can be used.

The design procedure for the antennas was as follows:

a. Design parameters were identified through the analysis that was presented in Chapter 3,

b. The variables that would effect optimisation of the antenna were identified,

c. A particular geometry for the design was chosen,

d. Co-ordinates for all wires were calculated,

e. This design was entered in ELNEC and simulated,

f. The optimisation variables were changed to achieve the design that best met the specifications, and

g. A sensitivity analysis of the design parameters was completed to determine how robust each antenna was.

The Cavity antenna had to be designed in a different manner. The known theory behind the cavity antenna as summarised in Chapter 3 gives an antenna that is one wavelength in diameter. This would produce a very large shadow area on the dish and reduce the effective area of illumination. The Physics Department already had a functional cavity antenna that operated at a frequency of 1.684GHz. This antenna had a diameter of approximately half a wavelength as opposed to the theoretical antennas described in Chapter 3. To achieve the design aim of having a minimal shadow area the cavity antenna for the project would have to have a similar design. As the theory behind the production of the radiation pattern was uncertain, the antenna at 1.638GHz was reverse engineered. The simulated design was input into ELNEC in such a way that the results were as close as possible to the telescope specifications. In this way it was assured that the simulation was correct and that the 1.42GHz simulation would be reliable. The dimensions were then changed to the project requirement of 1.42GHz and the antenna simulation in ELNEC repeated.

The results produced by the cavity antenna were then compared to those produced by the Yagi-Uda and Helical Antenna and the design that best fit the project specifications was chosen to be constructed and tested.

Theoretical limits for a Yagi-Uda antenna are generally specified in most antenna theory books. However to get the desired radiation pattern for the specific purpose of a radio telescope is somewhat more of a trial and error process through the use of a simulation package. This is due to the fact that antennas have various applications and an extensive difference in the radiation pattern that needs to be produced.

The design parameters that effect the results of the simulation are:

a. the length of the driven element,

b. the length of the reflector and directors,

c. the spacing between all elements,

d. the diameter of all elements, and

e. the number of extra parasitic elements.

A table of design variations was developed to cover the spectrum of limits for each of the variables. This table is shown in Table 4.1.1. The third design type is the optimised design. The parameters for this antenna were finalised through many variations of the design limits. A summary of the effects to the output of changing different parameters is summarised in the next section. See figure 3.1.1 for a diagrammatic representation of the Yagi-Uda Antenna.

Table 4.1.1: Yagi-Uda Antenna Design Variations.

1. This design incorporates all of the minimum lengths of each of the variable parameters.

2. These are the maximum lengths or sizes of all of the variable parameters.

3. This is a compromise between the variable limits.

GP. Ground Plane used.

These three basic designs were used to investigate the effect of each of the parameters and for the ultimate goal of obtaining an optimum design. To fully analyse the effect of each variable all other variables had to remain constant. The other variable that would effect the radiation pattern was the number of directors, so each of the designs had directors added to them and the radiation pattern was analysed.

Once the full range of variable limits had been analysed the optimised design was chosen. This was based upon the output variables such as the radiation pattern, the input impedance, -3dB, -10dB and -15dB point.

The first design to be input into ELNEC was the minimum design limits as defined in table 4.1.1 above. The number of directors that this design required meeting the dish specifications was 3. The output results of this antenna are shown in table 4.1.2.

Table 4.1.2: Yagi-Uda Antenna - Minimum Design Parameter Simulation.

The radiation pattern for this antenna design is shown in graph 4.1.2.

For the radiation pattern to effectively illuminate the dish the -15dB point should be as close to the 25 degree and 155 degree points, which as can be seen from Graph 4.1.1. The gain of this antenna is also very good. The drawback with this design is that the impedance of the input is 17.73 +J4.8W. This gives a VSWR of 2.85 that is totally unacceptable for the matching requirements of the antenna.

Graph 4.1.1: Yagi-Uda Antenna - Minimum Design Parameter Radiation Pattern

The next design that was simulated using ELNEC was the one that incorporated the maximum design parameters. The output results of this antenna are shown in table 4.1.3.

Table 4.1.3: Yagi-Uda Antenna - Maximum Design Parameter Simulation.

The radiation pattern for this antenna is shown in Graph 4.1.2.

Graph 4.1.2: Yagi-Uda Antenna - Maximum Dimensions.

The radiation pattern clearly shows large sidelobes produced by the antenna. There is also a large amount of spillover on the edge of the dish. The simulations from this point on involved a compromise of the minimum and maximum designs. The effects of each of the parameters were carefully analysed and the optimum design was finalised based upon how those designs’ outputs met the specifications.

A number of hours were spent in optimising the design for 1.42GHz. A number of relationships were observed about the Yagi-Uda Antenna and the effect of the design on the radiation pattern. They were:

a. As the spacing between the director and the reflector was increased, the gain also increases until a certain limit. After this point the gain of the antenna drops.

b. The spacing increase produces a drop in the Front-to-Back Ratio and the beamwidth is continually reduced. The optimum spacing value, whilst keeping all other values constant was 2.46cm = 0.41 wavelengths.

c. The addition of another director increases the gain of the antenna in the forward direction, but decreases the Front-to-Back Ratio initially until another director is added.

d. The optimum number of directors for this frequency was three, spaced at the optimum spacing of 0.41 wavelengths.

Once the design parameters had been optimised to produce the correct radiation pattern, this design was then used to investigate the effects of the impedance matching and alter the parameters so that the antenna matched correctly with the transmission line. The following effects were observed:

a. An increase in the diameter of the elements increases the impedance, both resistance and reactance, which means that the VSWR is also increased.

b. Conversely, a decrease in the element diameters decreases the impedance.

Table 4.1.4: Yagi-Uda Antenna - Optimum Design Parameter Simulation.

Once the impedance of the antenna reached the best point of matching the dimensions were changed again to improve the VSWR. By increasing the spacing between the last two directors the VSWR was reduced to 1.153, which is an excellent match for any antenna system. The results of this antenna design are shown in Table 4.1.4.

The radiation output of this antenna is shown in Graph 4.1.3.

Graph 4.1.3: Yagi-Uda Antenna - Optimum Parameter Simulation.

There are some sidelobes present in the optimised design however their power is well below the -15dB level so their effect on the antenna temperature will be negligible.

The temperature of the antenna can be determined by using the definition of the antenna temperature given in Chapter 2. That is:

T_ant = (M-N)T_sky + NT_gnd + (1 - M)T_gnd ´ FS

where: M = Fraction of energy entering the main lobe,

N = Fraction of energy in main lobe that sees the ground,

FS = Fraction of the side lobes that see the ground.

From graph 4.2.3 the values of the above variables are:

M = 0.8

N = 0

FS = 1

Therefore the antenna temperature for the Yagi-Uda simulation will be:

T_ant = 68K

which is 18K over the specified value.

There are a few design parameters that will effect the total geometrical design of the Helical antenna. In particular they are the circumference of the antenna and the number of turns. Each time one of these parameters is changed the whole geometry of the antenna changes, as can be deducted from the equations of the antenna given in Chapter 3.

A program for the geometrical antenna calculations was done in Pascal and is listed in Annex A. This program also calculates the x, y and z co-ordinates for the small straight wires that approximate the antenna. As ELNEC is limited to simulations of small straight wires only, the helical antenna has to be approximated into straight segments, in three dimensional space.

Once this program had been completed it was relatively simple to calculate a number of geometry’s to simulate. These geometries are listed in Table 4.2.1.

Table 4.2.1: Helical Antenna Geometry’s for simulation.

where: C = Circumference of the antenna.

D = the diameter of the antenna.

S = Spacing between each turn.

L = Total length of the antenna.

L0 = Length of wire in one turn.

a = Pitch Angle.

N = Number of turns.

The results expected from these geometries are listed in Table 4.2.2.

Table 4.2.2: Expected Results of Helical Antenna Geometry’s.

where: C = Circumference of the antenna.

N = Number of turns of the antenna.

R = Resistance of the antenna at the terminus of the helix.

HPBW = Half Power Beamwidth.

FNBW = Beamwidth between first Nulls.

D₀ = Directivity.

AR = Aspect Ratio.

To optimise circular polarisation a circumference of 21.113cm was required, thus this was the first simulation to be done. The beamwidth output from this antenna was too narrow; thus the number of turns of the antenna was decreased to three. All other dimensions of the antenna were calculated using the Pascal program and the results are tabulated in table 4.2.3.

Table 4.2.3: Calculated Geometry of Optimised Helical Antenna Simulation.

This antenna had a ground plane of 11cm diameter. The actual antenna was raised half a centimeter above the ground plane in the simulation. This gave the best impedance match between the antenna and the transmission line.

The parameters of the antenna all followed the theoretical effects stated in chapter 3. The interesting parameter to observe was the input impedance and the effect that various parameters had on its value. The optimised simulation of the helical had the antenna raised half a centimeter above the ground plane. The wire connecting the antenna to the transmission line was of a different radius to the antenna wire. The input angle of the connecting wire also had a great effect on the impedance. The following effects were seen through various simulations:

a. An increase in the diameter of the input wire decreased the impedance greatly.

b. Increasing the input angle from 0 degrees to 90 degrees improves the impedance match of the antenna.

c. Changing the diameter of the helical has a negligible effect on the impedance.

d. Increasing the elevation of the antenna above the ground plane increase the VSWR undesirable.

A sensitivity analysis of these factors is given in Chapter 5.

The final design was elevated half a centimeter above the ground plane and the input wire diameter was 5.4mm. The radiation pattern for this antenna is shown in Graph 4.2.1,

Graph 4.2.1: Radiation Pattern for Optimised Helical Antenna.

There is a small sidelobe present in the simulation. This is probably due to the presence of the input wire that enters at a sharp angle into the transmission line. This can be seen in Figure 4.2.1.

Figure 4.2.1: Input wire for the Helical Antenna.

The results of the simulation are given in table 4.2.4.

Table 4.2.4: Helical Antenna - Optimum Design Parameter Simulation.

Once again the antenna temperature can be determined using graph 4.2.1 as:

M = 0.99

N = 0.05

FS = 1

T_ant = (M-N)T_sky + NT_gnd + (1 - M)T_gnd ´ FS

This gives an antenna temperature for the Helical Simulation of:

T_ant = 28K

This is well below the specified value of 50K.

The initial design step for the cavity antenna was to successfully simulate the radiation pattern for the 1.684GHz. The difficult part about this simulation is getting straight wires to correctly model a cavity. This will never be ideal and has to be taken into account when the radiation patterns are analysed. To achieve circular polarisation cross dipoles had to be used in the cavity. This is also another variation that could not be proved that it had been modeled correctly. The modeled antenna is shown in figure 4.2.1. The wires that make up the cavity can be increased in diameter so that they are at the point where they touch. This was done and greatly improved the output radiation pattern.

Figure 4.2.1: Cavity antenna modeled with straight wires.

All dimensions of the cavity were carefully measured and converted to fractions of wavelength. These parameters are shown diagrammatically in figure 4.3.2.

Figure 4.3.1: Cavity Antenna Dimensions - 1.684GHz.

The dimensions for each of the components for the 1.684GHz and 1.42GHz antennas are tabulated in table 4.3.2. The dimension number refers to the numbers allocated to each parameter in Figure 4.3.2.

The cavity antenna that was reverse engineered was from the Denki Kogyo Company, a Japanese firm. The Instruction Manual outlines the specifications that the antenna should meet. These are shown in table 4.3.1.

Table 4.3.1: Specifications for the 1.684GHz Cavity Antenna.

Table 4.3.2: Cavity Antenna - Dimensions for 1.684GHz and 1.42GHz.

The radiation pattern for the 1.684GHz antenna was simulated first. This is shown in Graph 4.3.1.

Graph 4.3.1: Cavity Antenna Radiation Pattern - 1.684GHz.

The output results of this antenna are:

Table 4.3.3. Output results of 1.684GHz Cavity Antenna.

This design was the best optimisation that could be achieved from ELNEC. As can be seen by the results above there are a few undesirable effects. They were:

a. The huge sidelobes on the radiation pattern. These were not present in the specifications of the 1.684GHz antenna however they could not be reduced from the ELNEC simulations. This could be due to the fact that lip of the cavity could not be simulated as the limit of the number of wires to be used for the simulation had been reached. These sidelobes could not be ignored as their magnitude was too large and would greatly increase the antenna temperature.

b. The VSWR for the simulation was greater than 100 that means that this antenna would be useless. This high ratio could be due to the fact that crossed dipoles were used instead of the single dipole, however this generally did not increase the impedance significantly in the Yagi-Uda antenna. The cavity should not have that much effect on the actual impedance.

The fact that a satisfactory simulation of the 1.684GHz antenna could not be done meant that a reliable simulation of the 1.42GHz antenna could not be completed either. The antenna as specified in table 4.3.1 was input into ELNEC to investigate the outputs. The radiation pattern for this antenna is shown in Graph 4.3.2.

Graph 4.3.2: Cavity Antenna - Radiation Pattern for 1.684GHz Antenna.

As was thought with the simulation of the 1.684GHz antenna, a reliable result for the project frequency cannot be simulated. This immediately eliminates this antenna from the project, as a satisfactory simulation has to be achieved prior to construction of an antenna.

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