Antenna Design Project:

(1)

Antenna Design Project:

A Helical Antenna Analysis

April 2014

Kevin Blosser Test #2: ECE 434

Introduction

The purpose of this project was to design, simulate, fabricate and test an antenna of our choosing. The specifications for the antenna were to have resonance at 500 MHz, have high gain, high bandwidth, and VSWR less than 2:1. For these reasons, a helical antenna was chosen, because if constructed properly it would excel in the design specifications, and it could be made of accessible materials.

Theory

The theory behind the helical antenna has many facets to it. The important design attributes are the input impedance, gain, bandwidth, and VSWR. Another factor critical to the design of the helical antenna is its array factor, or AF. The structure of the antenna is given by Figure 1, where D is the diameter, S is the spacing between the coils, H is the height of the antenna, C is the circumference, L is the length of one loop, and α is the angle the coil makes with the ground plane, or pitch angle. In Figure 1 you see the coaxial feed coming up from the ground plane in the +Z direction to connect to the helix shaped wire acting as the antennas radiating structure with the aforementioned dimensional variables.

Figure 1: Helical Antenna Dimensionality

The first important attribute of the antenna was its input impedance. Input impedance is a measure of the resistance that the power source sees when it is connected to the antenna. The helical antennas input impedance is based on handbook data which is given by equation 1, where is the input

(3)

2

impedance, C is the circumference of the helix projected onto a circle at the ground plane, and λ is the wavelength of the current being fed into the antenna from the coaxial feed. Because the wavelength of the current is fixed for the project, the circumference must be varied to create the desired input

impedance of 50Ω, to allow matching of the coaxial feed impedance, thus creating create maximum power transfer to the antenna.

Equation 1: Input Impedance

The next important attribute of the helical antenna is its gain. The gain of an antenna is its ability to have more power density in one direction at the expense of other directions. The helical antennas dB gain equation given in equation 2 shows that the gain is related to the circumference C , the spacing between the coils S, the wavelength of the current λ, and the number of turns that the helix has, N. The antenna needs as high a gain possible for the assignment. To maximize that gain, the circumference, the spacing between the coils, and the number of turns need to be as large as possible.

( ) log( ( ) ( ) ) Equation 2: Gain in dB

Another figure of merit important to the project is bandwidth. Bandwidth is the range of frequencies where the antenna meets its design specifications, whereas the fractional bandwidth of an antenna is the ratio of the antennas bandwidth to center frequency it operates at. The fractional bandwidth equation is given in Figure 2, where is the upper frequency limit, is the lower frequency limit, and

is the center frequency. Figure 2 shows how the fractional bandwidth of the helical antenna remains relatively constant, because handbook data shows that the ratio of the upper and lower bandwidth frequencies remain relatively constant. To get the actual bandwidth based off of the antennas dimensional parameters, Equation 3 shows the acceptable operational range of wavelengths λ that correspond to the circumference of the antenna C.

Equation 3: Circumference to Acceptable Wavelength Range

(4)

3

⁄

Figure 2: Fractional Bandwidth Equation Block

The last figure of merit important to the project is VSWR, or the voltage standing wavelength. The VSWR of an antenna is a measure of how well the input impedance is matched to the feeding structure.

Equation 4 shows the equation for the VSWR of any circuit, where is the reflection coefficient, which is a measure of how close the input impedance is to the source impedance . Because is a function of frequency as seen in Equation 1, the VSWR is often used to calculate the bandwidth of antennas, where the bandwidth is the range of consecutive frequencies that the VSWR is less than 2.

, Equation 4: VSWR and Γ

The last factor to consider for a helical antenna is the array factor. Traditional modeling of the helical antenna uses an array factor, where each turn in the helix counts as an element in an array.

The array factor is important because it is a good approximation of the antennas radiation pattern.

The array factor given in Equation 5 shows how N number of turns affects the radiation pattern.

The variables in Equation 5 are defined where is the proportionality constant, is the attenuation constant, L is the length of one turn, k is the spherical wave constant, and S is the spacing between the coils.

∑ ^{( )}

, ( ) ( ) (

) cos Equation 5: Array Factor

(5)

4

Design and Design Methodology

When designing the antenna the first calculations involved matching the input impedance of the antenna to the 50Ω coax cable connection, so that maximum power transfer was occurring from the coaxial connection to the antenna. Designing for matching impedances also has the benefit that no matching network will be used to implement the antenna design. Using Equation 1 in the theory section, the desired input impedance is = 50Ω, therefore the circumference of the helix calculates to C=.213m. This circumference violates the acceptable wavelength range from Equation 3, because λ=

.6m is outside the allowable range, but the assumption was made that violating this equation will not affect the input impedance significantly, so the equation remained violated in my final design.

The next thing considered was the antennas height. This influenced the antenna design such that too tall would make construction unpractical and difficult. Two things are factors of total height ,H, the spacing between coils ,S, and the number of turns ,N. This relationship is given in Equation 6. The total number of turns had to be at least 6 so the attenuation factor α would be approximately 0, making it negligible. Also, since gain is a priority, the more turns on the helix the better. For the spacing between the coils handbook data suggests that ⁄ , which, with the given wavelength, put the spacing to . With and , the total height was , which is practical.

Equation 6: Total Height

Table 1 shows all of the dimensional attributes of the antenna that were used for construction after.

Table 1: Antenna Dimensions Dimension Size H (Total Height) 1.08m D (Diameter) .068m S (Coil Spacing) .18m C (Circumference) .213m L (One Loop) .281m α(Pitch Angle) 40.2°

N(Number of Turns)

6 turns

The last design element to consider was the ground plane was considered. Because it was used to support the antenna, the biggest flat piece of wood was used to serve as its base.

Knowing the dimensional attributes of the antenna, the construction went underway. First the support for the radiating structure was built. Using PVC pipe for a cylindrical base, drywall repair tape was used to increase the circumference of the structure to get the desired input impedance. Copper wire was

(6)

5

used for the conducting wire. The wire was attached to a male BNC connector that passed through a hole drilled into the ground plane, and winded up the support structure in the designed helix shape.

The ground plane was made of a piece of plywood that was .8m x .5m, and covered in aluminum foil.

The plywood also had a wooden dowel screwed into it to support the radiating structure. Figure 3 shows the final construction of the antenna. Because all of the parts were found, the antennas effective cost was $0, but an estimated cost for components would be $10 max.

Figure 3: Final Antenna Construction

Simulation Results

For simulations, since the helical antenna was not on the PCAAD software provided, an online calculator was used¹. Matlab simulations were also used to see the array factors performance. To use the

calculator, the antennas center frequency, number of turns in the helix, and the spacing between those turns must be known. The performance metrics it returned are as follows in Table 2.

Table 2: Simulation Results Performance Metric Value

Gain 10.51 dBi

Bandwidth (@ -3dB) 452.7 - 552.3 MHz Beamwidth(@-3dB) 38.7°

The software also calculated what the suggested dimensions of the antenna would be. Because the design violated the wavelength range in Equation 3, they were different dimensions then what was proposed. Table 3 shows the values converted from the outputted dimensions of the calculator.

1 The online calculator used can be found at http://jcoppens.com/ant/helix/calc.en.php

(7)

6

Table 3: Simulation Dimensions Dimension Size H (Total Height) 1.08m

D (Diameter) .2m

S (Coil Spacing) .18m C ( Circumference) .628m

L (One Loop) .666m

α(Pitch Angle) 16°

N(Number of Turns) 6 turns

Because the suggested circumference is different than the one calculated, the performance metrics on the antenna were different. The simulation circumference is bigger than calculated; from Equation 2, it is surmisable that the calculators predicted gain is going to be bigger. From Equation 3, the calculators bandwidth is going to be lower than the actual value.

Matlab was used to simulate the array factor for the designed helical antenna. Using Equation 5 where α was assumed to be zero because , Matlab produced Plot 1, a polar plot of the

approximate normalized array factor.

Plot 1: Polar Plot of Array Factor

From the plot it’s visible that the antenna does not radiate in the +Z direction, but rather slightly off to the sides, this is the result of a violation of a handbook data suggestion where ⁄ , this creates a h(ϴ) term from Equation 5 which is non-ideal. The array factor plot is similar to the canonical traveling wave structure, which suggests that it still will have high bandwidth properties.

(8)

7

Measurement Results

To obtain the gain measurements for the antenna, the antenna was attached to an AC generator with a 50Ω coax cable, a variable frequency source of 100mW passed into the antenna. From there the radiation traveled down approximately 30’ of hallway, where a receiving log periodic antenna was used to obtain the gain in dBm. Using the array factor plot, the antenna was oriented in the direction of maximum directivity. Figure 4 shows the gain and frequency at which the antenna resonated best, as received by the log periodic antenna. It shows that the antennas maximum gain is -20dBm at 520 MHz.

Because the helical antenna radiation is circularly polarized, the log periodic antenna only received half of the power that was transmitted. If another circularly polarized antenna was used to receive, the gain would increase by about 3dB.

Figure 4: Gain Measurement

Plot 2 shows a graph of VSWR vs Frequency, the lowest VSWR close to 500 MHz was at 520 MHz, which matched the frequency where the antenna achieved maximum gain. Also on Plot 2 the bandwidth can be visualized and calculated. By looking at when the VSWR is less than 2, with the center frequency being 520 HZ, the bandwidth approximately ranges from 518-522 MHz, which is very small.

Plot 2: VSWR vs Frequency

(9)

8

Antenna Assessment

After analyzing the results, it seems that the assumption made about the wavelength range violation not affecting the input impedance needed reevaluation. That assumption changed the input impedance enough that the it did not match the coaxial cables. Even so with more turns the antennas gain increase while holding the assumption. Even with the bad assumption, an analysis of Plot 2 shows that the circumference needed to be bigger to match input impedances, but it is impossible to design for because of the wavelength range violation. Also with the assumption the antenna had fairly good gain, and may have large bandwidth at a higher frequency range around 1.06 – 1.88 GHz. If adjustments were to be made to the original antenna design and methodology, they would be to ensure the diameter is within the acceptable wavelength range and a matching network compensates for the load and source impedance mismatch.

Conclusion

In conclusion, the designed antenna performed fairly well despite its design flaws. It had resonance close to 500 MHz, decent gain, the VSWR was less than 2:1, but the bandwidth was terrible. Trying to balance the different factors during design was both intellectually stimulating and challenging.

Antenna Design Project: