Yagi-Uda Antenna Design AbstractJeremy Goldberg, Andrew Blalock, Kim Lewis

College of Engineering Florida Atlantic University

Boca Raton, FL, USA

Abstract— The task of this report is to analyze and document the design and construction of a Yagi-Uda Antenna. The target audience should already have a basic understanding of antenna theory and the underlying parameters that are taken into consideration subsequently listed in this document.

I. INTRODUCTION

The basic architecture of the antenna consists of conducting thin rod dipoles referred to as elements. They are aligned in parallel with specfic lengths and spacing which are calculated relative to the gain and operating frequency. Not all elements have the same role. The first rod, which is the longest, is used as a reflector to ensure the directivity resonates in the correct direction. The next element in the array is the drive element. This is where the current is fed through and is usually 5% less than .5 . The rest of the elements are directors. The amount of elements used in the design is related to how much gain is required for the design.

A. Design Parameters • Operating Frequency • Directivity Relative to Half-Wave Dipole (dB) • Number of Elements • Length of Elements • Spacing of Elements • Diameter of Elements • Length of Boom • Boom Margin Error Relative to Material

Composition • Gamma Matching • Connector Type

B. Calculations All the calculations that were performed are directly

related to λ. The antenna is designed to operate at 1.2Ghz, which was chosen arbitrarily. The calculation for λ is shown below:

λ= C/f

λ= 3E8/1.2E9= .25 meters The directivity relative to the half wave dipole was chosen to be 10.2dB. In relation to an isotropic source the gain is specified to be 12.36dB. In order to determine the number, length and spacing of the elements, a table containing these

parameters is used [1]. As seen in the table the space between the reflector and the drive element is generally fixed at .2 . The table specifies for a 10.2dB gain, 6 elements are required at a spacing of .25 for the director elements. Full spacing calculations are seen below: Reflector ! Exciter ! D1 ! D2 ! D3 ! D4 ! Looking further, it is seen that not all lengths are similar. Rather than list all calculations, they are tabulated in the table below for convenience.

Element Calculation Length (cm) Reflector .482  λ 12.05 Exciter .46  λ 11.5

D1 .428  λ 10.7 D2 .42  λ 10.5 D3 .42  λ 10.5 D4 .428  λ 10.7

Please see the next page for predetermined element parameters table.

TABLE 1 OPTIMIZED UNCOMPENSATED LENGTHS OF PARASITIC

ELEMENTS FOR YAGI-UDA ANTENNA OF SIX DIFFERENT LENGTHS

The diameter of the elements used have an influence on the length of the elements. Although these parameters were calculated from a predetermined table, there is a margin for error which needs to be calculated if a metallic boom is used. Since a wood boom was used, this consideration is not necessary.

The length of the boom is calculated using the formula below:

C. Signal Consideration In order to generate a signal to test the parameters that were used to design the antenna, a balun connection was used. See below in Figure 1. The outer coaxial cable shield of our RG-58 coaxial cable are tied together to act as a common ground for our antenna. Where the inner copper core of the coaxial cable forming the loop are each tied to one end of the folded dipole while the transmission line that carries our signal is tied

to one end to the folded dipole as well as this can be seen in Figure 3.

Fig. 1. – Balun Connection

Fig. 2. 6 Element Yagi-Uda Antenna

Fig. 3 Close up of folded dipole and balun connection

D. Performance

Using the constructed antenna, it was then tested to determine the efficiency and effectiveness of our antenna. After testing we came up with the following data using the Hewlett Packard 8753D Network Analyzer. Looking at Figure 4 can give some

information about the performance of our antenna. Looking at the measurement we are measuring S21. The antenna was connected to port 1 and the receiving antenna connected to port 2. S21 is measuring the power received on port 2 relative to the power input at port 1. At marker 1 is 1.23GHz and it is -47.4dB. So the 3 dB point would be approximately -50dB. The reference angle of -47.4dB is at 252°. The determination angle if found by subtraction 230° which is the angle that we hit -50.4dB. To determine the first angle we will subtract 252-230 = 22° which is just one side of our radiation pattern. The second determination angle is at an angle of 261° so to find the second angle we will do the following 261 – 252 = 9° which gives us the second part of our radiation pattern. Ideally these are to be equal to get a symmetrical radiation pattern. So the span for our 3dB beam width is 31°.

Fig. 4. S21 Measurement If we look at Figured 5 we have the plot for the S11 measurement which is representative of the power that is reflected back from our antenna. This happens because we do not have a perfect impedance match between our transmission line and our antenna. We can see here at marker two that which is for our 1.2Ghz that we reflect back -13.507dB. But looking back at our measurement for Figure 4 we measured the performance of our antenna at 1.25Ghz and comparing that to figure 5 we can see at marker one that we reflect back -31.13dB which is a lot less power. So even though we designed our antenna for 1.2Ghz it function better at 1.25GHz.

Fig. 5. S11 Measurement

Looking at Figure 6, the exact match for our antenna can be determinied and will give a better idea of how the antenna would perform. In figure 6, the antenna has an impedance of 88.734Ω. Using thing we could also look at the VSWR and the Reflection Coefficent.

Γ= (ZL-Zo)/(ZL+Zo)=(88.734-50/88.734+50)=.279

As seen, the reflection coefficient is not 0 but on the scale of 1 to zero it is still fairly low. Now we can look at the Voltage Standing Wave Ration.

VSWR= (1+ Γ)/(1- Γ)=(1+ .279)/(1- .279) =1.77 The VSWR is not perfect it is still fairly low but we would like it to be a closer match.

Fig. 6. Matching

E. Conclusion So for the performance of the antenna, it can be said that it did not perform as well as initially planned but it performed at a decent rate. The biggest flaw with the antenna was the unequal radiation pattern that was displayed from the antenna with most of the power on one side of the antenna. The performance could be increased by using more precise cutting tools and taking more accurate measurements of the elements of the antenna and devising a better matching system to lower our reflection coefficient and VSWR.

REFERENCES

[1]C. Balanis, Antenna theory. Hoboken, NJ: Wiley Interscience, 2005, pp. 595-597.

[2]P. Bevelacqua, 'The Yagi-Uda Antenna - Yagi Antennas', Antenna-theory.com, 2015. [Online]. Available: http://www.antenna-theory.com/antennas/travelling/yagi.php. [Accessed: 20- Nov- 2015].