Chapter 3: Antenna Theory
Prior to the design phase of the project, extensive research into the theory behind the operation of all three antennas was completed. This was done to ensure a full understanding of the functionality of each antenna so the design process could be more efficient and effective. Within the research phase it was important to clearly identify the variables that would affect the radiation pattern and impedance matching of the antenna.
3.1. Yagi-Uda Antenna
The Yagi-Uda Antenna is a widely used antenna design due to its high gain capability, low cost and ease of construction. It consists of a dipole arranged with various parasitic elements. There are two types of parasitic elements that can be used to change the radiation pattern, they are:
a. A Reflector called thus due to the fact that it appears to reflect radiation from the driver.
b. One or more Directors whose function is to direct radiation from the driver in the direction of the directors.
Generally the reflector will be 5% longer than the driven element (ie dipole) and the directors will be 5% shorter. The dipole will be directly driven from the feed network, whereas the parasitic elements achieve excitation by near field coupling from the driven element. A diagrammatic representation of a Yagi-Uda Antenna is shown in Figure 3.1.1.
The design of an antenna will be specified by the application of it. The Yagi-Uda Antenna produces an Endfire radiation pattern. This pattern can be tailored to the requirements of the project by varying specific design variables.
Figure 3.1.1: Yagi-Uda Antenna.
Theoretical parameter limits have been summarised as follows :
a. Reflector: LR = 0.47 - 0.52 l
b. Driven Element: L = 0.45-0.49l .
c. Directors: LD = 0.4-0.45l .
d. Separation between Directors: SD = 0.2-0.35l .
e. Radii of directors: 0.15-0.25l .
f. Separation between driven element and reflector: SR = 0.2-0.35l .
All of the above variables will effect the output of the antenna. Optimization can be achieved by simulating the radiation patterns for varying values of the above variables. Factors to be considered in the design process that affects the antenna output are :
a. For an antenna with a length of 6 wavelengths or more, the overall gain is independent of the director spacing.
b. The reflector size and spacing have negligible affect on the forward gain and large affects on the backward gain and input impedance.
c. The size and spacing of the directors has a large affect on the forward gain, backward gain and input impedance.
d. More than one reflector provides little improvement on the directivity of the antenna.
e. The addition of more directors will increase the gain of the antenna, although after the addition of approximately 5 directors the advantages of adding more directors decreases significantly.
f. The use of a folded dipole will increase the input impedance of the driven element. This is an advantage as the Yagi design generally has a low input impedance and the antenna impedance needs to match the transmission line impedance.
g. Circular polarisation of the Yagi-Uda Antenna is achieved by using crossed dipoles and crossed parasitic elements.
The outputs of the antenna that are of interest in the simulations and tests are:
a. forward and backward gains,
b. input impedance,
e. front-to-back ratio, and
f. magnitude of the minor lobes.
These variables will determine if the Yagi-Uda antenna will meet the specifications of the project.
3.2. Helical Antenna
The Helical Antenna is consists of a conducting wire wound in the form of a screw thread. There are two main modes of operation of the Helical Antenna. They are:
a. Normal Mode: where the maximum field that is radiated by the antenna is in the plane that is normal to the helix axis. The minimum is along the axis.
b. Axial Mode: This mode of the antenna is equivalent to the endfire mode, that is, there is only one major lobe of the pattern and it is in the direction of the axis of the helix.
To achieve the endfire pattern, the diameter and the spacing of the coil must be large fractions of the operating wavelength. Circular polarisation is achieved by restricting the range of the circumference of the antenna to :
3/4 < C/l < 4/3
where: C = circumference of helix.
l = operating wavelength of antenna.
To achieve optimum circular polarisation:
C/l = 1.
and the spacing of the turns to:
S = l /4.
The geometrical configuration of the helix consists of :
a. N turns,
b. a diameter D,
c. spacing S between turns,
d. a total antenna length, L = N*S, EQN 3.2.1
f. a circumference, C = p D, EQN 3.2.2
g. length of wire between each turn, L0 = Ö (S2 + C2), EQN 3.2.3
i. a total wire length of Ln = N* L0 , and EQN 3.2.4
j. a pitch angle of, a = tan-1 (S/p D) = tan-1 (S/C). EQN 3.2.5
Varying the dimensions listed above can control the output of the antenna. The input impedance is generally dependent upon the pitch angle and the size of the conducting wire near the feed point into the transmission line. The terminal impedance of an axial mode antenna is approximately 140W . Most antennas need to be matched to a 50W transmission line that can be achieved in one of the following ways:
a. by using a quarter wave matching transformer between the feed line and the feed point of the helix, or
b. increase the conductor size between the end of the helix and the feed point.
The second method is the cheaper option and the most commonly used method in ammeter radio telescopes. If the helix is fed at the periphery, the first half turn of the helix conductor acts like in a similar manner to a transmission line, that is a single conductor over a perfectly conducting ground plane. The impedance of a transmission line like this is given by :
Z0 = 138log(4h/d) EQN 3.2.6
where: Z0 = the impedance of the line.
h = the height of the centre of the conductor above the ground plane.
d = the conductor diameter.
Other output parameters of the antenna will be :
a. Impedance at the terminal point of the helix,
R = 140(C/l ), EQN 3.2.7
b. The Half Power Beamwidth,
HPBW = (52l 3/2)/(C*Ö NS), EQN 3.2.8
c. The First Beamwidth between Nulls,
FNBW = (115l 3/2)/(C*Ö NS), EQN 3.2.9
d. the directivity,
D0 = 15*N*((C2*S))/(l 3)), and EQN 3.2.10
e. the axial ratio,
AR = (2N + 1)/(2N). EQN 3.2.11
A number of the above variables will have a pronounced effect on the radiation pattern. The following relationships have been observed by a number of scientists and engineers and are generally accepted :
a. The beamwidth can be reduced and thus the directivity increased by increasing the number of turns.
b. For Helices that have a total length greater than a half wavelength, the effect of the ground plane can be ignored.
c. The diameter of the conductor has negligible effect on the axial mode of a helical antenna. Although it will have an effect on the input impedance of the antenna.
e. A coaxial cable will feed the helix, and the centre of the conductor should be attached to the helix and the outer conductor has to be attached to the ground plane.
The two main parameters that can be used to optimize the radiation pattern are the number of turns and the circumference of the helix.
3.3. Cavity Antenna
This antenna consists of a dipole surrounded by an open ended circular cavity. The radiation pattern is produced by the formation of fields within the cavity, which are radiated through the sidewalls. The antenna is tuned to resonate at a particular frequency that is dependent on the application. There are two types of resonant antennas. They are :
a. Exoresonant: resonance occurs without the use of a cavity.
b. Endoresonant: that is the excitation occurs within the cavity and comprises of a resonating or resonant cavity.
Within the second type of resonant antennas there are two basic groups of antennas:
a. Dual reflector antennas: consist of 2 reflectors and a plane with one dimensional field resonance between them.
b. Cavity Backed Antennas: Three dimensional cavity resonators.
The second type of resonant antenna was researched for this project. To achieve circular polarisation crossed dipoles would have to be mounted within the cavity and then generate two orthogonal signals by a single input. The arrangement of the dipoles would have to be similar to the configuration shown in figure 3.3.1.
Figure 3.3.1: Cavity Antenna Dipole Arrangement. 
Consider figure 3.3.2 below in which the dipole arrangement is shown. A voltage induced across the slot energises the radiating system. If there was no short circuiting post then the TEM and higher modes would be generated in the open ended termination. These modes would be symmetrical with respect to the plane containing the slot axes that would mean that there would be no field created across the slot and the dipole would not be excited. With the post there the modes are generated that are symmetrical to the plane which are determined by the axis of the post and the inner conductor.
Figure 3.3.2: Crossed Dipole Arrangement in the cavity.
The previous two modes superimpose to give a field in which the tangential electric field is zero over the surface of the post and propagate through the slotted region. The resultant field is zero along the post and increases with angle to a maximum value directly opposite the post, which means that the dipoles are excited. Left of right hand polarisation will depend upon the orientation of the dipoles to the shorting post.
The dimensions of the cavity have also to be specified according to the frequency that is to be used. As with the Yagi-Uda antenna, parasitic elements can also be present to increase the directionality of the antenna. The cavity dimensions are shown in figure 3.3.3.
Figure 3.3.3: Cavity Dimensions.
where: A = 1.0l
2h = 0.5l
l1 = 0.25l
L = 1.2l
l = required operating frequency.
This type of configuration produces sidelobes in the H-plane. To eliminate these sidelobes a director can be placed in front of the dipole at a distance of approximately 0.25l and a length of 0.44l.