Optimum use of a 4-element Yagi-Uda Antenna for the Reception of Several UHF TV Channels

Outdoor Yagi-Uda antennas are frequently used in Sri Lanka for the reception of UHF and VHF TV channels. An antenna designed for a particular channel can show poor reception characteristics to other TV channels due to their operating frequencies and physical locations. The first few TV stations, which were set up in nineteen eighties, had VHF transmissions. Those TV channels still operate on VHF, while some of them supplement with UHF transmissions. A large number of TV channels in Sri Lanka use UHF channels for the transmission of their TV programs. The paper studies the dependence of the maximum gain of the antenna, the input power to the dipole of the antenna , and the radiation pattern of the antenna on the operating frequency which are the key indicators of its receiving characteristics. Considering the physical distribution of TV stations in the lowlands of Sri Lanka, this paper searches ways of optimizing reception characteristics of a 4-element Yagi-Uda UHF antenna.


Introduction
The Yagi-Uda antenna was first proposed by Prof. Shintaro Uda and Prof. Hidetsugu Yagi in 1926. A considerable improvement in the gain and the directivity of the antenna could be achieved through this antenna. The antenna was frequently used in radar applications during Second World War.
With the introduction of TV broadcasting, the Yagi-Uda antenna became very popular among TV viewers, mainly due to its high gain. As the number of elements in it is increased, its gain and directivity also increase making it ideal to receive a distant TV station. A good study on the dependence of the directivity and the beamwidth of the antenna on its number of elements has been done in [6].
In the calculation of the gain, directivity and beamwidth of a Yagi-Uda array, the current distributions in the driving-and the driven elements play an important role. Although the sinusoidal current distribution is a good approximation for element lengths around 2  , it is not so for elements of higher lengths. This issue has been discussed in [1]. In this paper, the author discusses how gain optimization could be achieved for dipole lengths of  and 1.5  using a modified nonsinusoidal current distribution. When there are several TV channels, the viewers always prefer to use the same antenna for the reception of all the channels, even though it may not be practically possible. In order to design an antenna to cover several TV channels, not only the gain but also the beamwidth of the antenna has to be considered. To find out whether a given antenna can receive a remote TV station, one should know the 3 dB bandwidth (say  ) of the antenna.
With the help of two circular arcs with inscribed angles  and having the two stations as the two common end points, the antenna coverage can easily be predicted.

Coverage of more than one Station with a Single Antenna
The antenna located at Point P outside the two arcs AXB and AYB should receive both TV channels without any problem, provided that the receiving antenna has approximately the same for the operating frequencies of the two transmitting stations. Here, the transmissions of the antennas are assumed to be isotropic.

Antenna Equations
A very good analysis of the Yagi-Uda array with necessary fundamental equations is given in [3].
Using Maxwell's equations, the equations for scalar potential  and vector potential A can be derived with the help of Gauge Transformation and Lorentz conditions. In order to calculate electric-and magnetic field components, ) , shown in Figure 3, it is sufficient to know ) , can be written as: (1) ) , In a similar manner, he field components ) , can be used to calculate the mutual impedance 21 Z induced by the above dipole (say dipole 1) on another dipole (say dipole 2).
In an antenna array consisting of K elements, the mutual impedance pq Z on the th p element due to the th q element can be calculated from can be calculated using Equation (3).
extended to calculate the mutual impedance and the self-impedance of all elements in the array. Finally, the impedance matrix of the array   k k Z  given below consisting of selfimpedances and mutual impedances can be derived .

Experimental Setup
The antenna equations mentioned above can be used to calculate the maximum directive gain of the antenna and the power input to the dipole using tools developed in [3] along with standard Matlab tools. The variation of the antenna gain ) ( ,  g in the horizontal plane and the radiation pattern of the antenna can also be calculated for the array shown in Figure  5 .
If the antenna has been designed for a frequency 0 f , the corresponding maximum In grouping the transmitting stations, stations situated far away have been omitted.

Figure 4 -Grouping of transmitting stations
The possibility of receiving any other station without using the main lobe of the radiation pattern when the receiving antenna lies within the coverage area of all the stations (e.g. Point Q of Figure 2) was also investigated.
If the antenna is located among the transmitting stations (e.g. Point R of Figure 2), then the group has to be subdivided as shown in Figure  4 to suit the total radiation pattern.

Results and Observations
The azimuthal gain plots for

Conclusions
Since the Yagi-Uda antenna is highly sensitive to changes in its dimensions [2], its reception characteristics are usually optimized to receive a single transmission. This is done by maximizing the directive gain and the front to back ratio [1]. In practical situations like in the reception of TV channels, a single antenna installed on the rooftop is very often used for the reception of 1,2,3 .. 3,4 ... 1,2,3 . 4 In this study, the possibility of designing a suitable antenna to cover a maximum number of UHF channels was explored. Although high gains can be achieved by increasing the number of elements in an array, the reduction of the beamwidth can adversely affect the physical coverage of the antenna. Thus, a 4-element array had to be selected as a compromise. The methodology was developed on the assumption that the domestic antenna receives only the direct signal from the transmitter. The modification of the radiation pattern due to signal diffraction and other factors was neglected. The antenna coverage for the Colombo district and for the down south region covering Matara district was satisfactory. Hill country was not considered here.

.
The results show that an antenna designed for one particular station among a group of transmitting stations, might not be capable of receiving the rest of the stations successfully. The design parameters of the antenna should be selected considering the criteria discussed in this paper in order to maximize the number of stations it can receive.