Embedded Files
Background
Background
Figure 1: Fractal Iterations
Fractal Geometry
Fractal Geometry
The antenna design is based on a “fractal” geometry which is a geometry that repeats itself as you zoom in on any segment of the boarder. The Koch fractal antenna uses the snowflake concept, rather than a closed triangle which used in the Serpinski fractals. The practical use of this geometry is to reduce the overall line length by using more of the area earlier on rather than leaving it as free space.
Beginning with the top trace in figure 1, each preceding trace corresponds to an iteration. After each iteration the total perimeter increases by four thirds of the previous trace. This is achieved by dividing each equal side length into thirds then adding the top two sides of an equilateral triangle to the middle portion of the sectioned trace. For example, let the first trace have a perimeter length of L0, after the first iteration I obtain four different trace lines of length 1/3L0. This operation changes the total perimeter length to:
L1=4(1/3L0)=4/3L0
For the second iteration I obtain the third trace which will have a perimeter length of:
L2 =4/3L1=4/3(4/3L0)=16/9L0.
This process will continue for as many iterations that are desired.
Each iteration also creates another “resonant frequency” (𝑓0) in S11. In other words, the frequencies at which resonance occurs correspond to the center frequency of a bandwidth on which data can be received or transmitted. This geometry can be mathematically created utilizing “Affine Transformations”.
The affine transformations are mathematically illustrated above The affine transformation w1 scales the line by 1/3, w2 rotates a line segment by 60 degrees(this can change), w3 rotates at -60 degrees, and w4 translates the system. It is important to note that the angle that is chosen, for our case 60 degrees, can be altered depending on how the antenna is segmented. the equation, s=2(1+cos(Θ)), determines how the line is segmented where "s" is the divisor. In figure-1 "s" is 3. Again, it is important to remember that this transform does not create the antenna but instead creates the geometry used in the antenna.
Procedure & Steps
Procedure & Steps
Figure 3: Monopole Antenna Design in Sonnet
Sonnet Design
Sonnet Design
To begin, a monopole antenna is first designed for a specified frequency. For this design, the center frequency was 2.437GHz. One should note that this center frequency was not arbitrary but was determined by the center frequency of the filter that was attached to the antenna. To calculate the length of the dipole I must first determine the wavelength and divide that by a quarter. The monopole antenna is one based on a quarter wavelength overall length.
λ= speed of light/center frequency= 123.102mm λ/4=30.77mm
Using that information, I can model a monopole in Sonnet (units of mm). Be sure to set the Box parameters to free space on top and bottom and set the air gaps approximately a quarter wavelength of the given center frequency in size.
Taking the opportunity with a simpler antenna, I utilized dimension parameters. These parameters cycle through different lengths or widths while running frequency analysis on each. This saved time and quickly allowed me to modify the circuit. The large copper plate attached to the monopole acted as the ground plane.
Designing a monopole antenna and tuning it to meet the desired specifications was difficult to do in Sonnet. Therefore, I utilized a MATLAB toolbox that interfaced with Sonnet. With the help of the quick start guide, the process was much smoother ( https://www.sonnetsoftware.com/support/sonnet-suites/sonnetlab.html).
Recalling the equation 𝑠 = 2(1 + cos(θ)) and using the new length of 30.77mm I began creating our fractal antenna in the same manner that the monopole was created.
Figure 4: S11 of Monopole Antenna
Figure 5: S11 f Koch Fractal Antenna before Matching Network
As ideal a response that Figure 5 demonstrates, it was incorrect. The fractal design was created using a method of drag and drop of the same sized triangles. During the process not all of the triangles Ire connected, and thusly provided this false output. Furthermore, there was no ground and therefore the circuit is not performing like its produced counterpart.
This disconnect was discovered about 35mm along the antenna, which explained why S11 was such an ideal plot. During the process of making this initial antenna I kept extending the antenna to obtain a lower frequency output, even though it did not match calculations. So instead of creating a fractal antenna I created an oddly shaped monopole. The 4Ghz response are due to the small lengths produced by the triangles that remained connected.
After reconnecting all the components, I realized that I got a better radiation pattern using the larger size of the fractal antenna, and that I should be able to adjust its height and width slightly to obtain the frequency response I needed.
Furthermore, I created a ground plane on the back that did not reflect or impede any of the radiation patterns created by the fractal shape. The matching network was created using “Microstrip characteristic impedance as a function of width and height” found in figure 2-20 in Chapter 2 of “RF Circuit Design Second Edition”.
Figure 6: Characteristic Impedance of Microstrip Line as a Function of w/h Ratio
Figure 7: Finalized Koch Fractal Antenna in Sonnet
Figure 8: S11 of Designed Matching Network
Figure 9: Smith Chart Plot Over Stimulus Range of 2-3.5GHz
Manufacturing
Manufacturing
Figure 10: View of Trace Plane of Fabricated Antenna
Figure 11: View of Ground Plane of Fabricated Antenna
If you observe Figure 10 carefully, you will notice a small patch of copper tape. This was used to tune/modify the existing circuit as it was slightly off of the desired center frequency of 2.437Ghz. The ground plane worked Ill, and should not interfere with radiation patterns. HoIver, this was not confirmed as the software used does not have the proper licensing to observe those effects.
Figure 12: Wide View of S11 Response
Figure 13: Gain Values at Resonance Frequencies
Figure 12 is the S11 response of the circuit before performing modification via copper tape. It is important to notice that there are three dips or resonant points in the figure which matches the principle behind the creation of an Nth order fractal antenna. Thee should be "N" frequency ranges that can effectively utilized.
Figure 14: Narrow View of S11 Response Containing Desired Bandwidth
The antenna operated at a slightly higher center frequency than what was calculated in the design process (Figure 14). This being the case copper tape was added to the end to increase the length of the antenna to tune to the desired frequency. Doing so had major impacts on points 1 and 2, but since 3 operates around 5.4Ghz it’s created from the smaller antenna lengths that are not being changed and should therefore stay roughly the same.
Figure 15: Smith Chart of Fractal Antenna
Figure 16: Notable Smith Chart Data Points
Observing the smith chart in Figure 15 and the impedances at the three center frequencies in Figure 16, it becomes clearer as to why the S11 has a magnitude of 63dB for the 5.4 GHz resonant frequency. The antenna has a SWR of 1 which is due to the almost exact 50Ω impedance. That means that there are virtually no reflections at the port.
The 2.5 GHz resonant frequency has an S11 magnitude of 26dB and is slightly mismatched with an SWR of 1.12. Although the efficiency of the antenna is Ill above expectations, some fine tuning is required in order to meet the specified center frequency of 2.437GHz.
The standing wave ratio for the resonant frequencies can be calculated using the following equations of return loss and reflection coefficient: S11 = RL[dB] = -20log(|Γ|) |Γ|= 10-(RL[dB]/20) SWR=1+|Γ|/1-|Γ| However, the following table can also be utilized for quick, at a glance, conversions:
Figure 17: Return Loss, VSWR and Reflection Coefficient (Γ) Conversion Table
Antenna Tuning and Measurements
Antenna Tuning and Measurements
Figure 18: Narrow View of S11 Plot After Tuning
Figure 19: Gain Values at Resonant Points After Tuning
After appending a small amount of copper tape to the end of the antenna (Figure 10), the antenna met the center frequency specification of 2.4GHz. The obtained value is within 2% of the specified value of 2.437 which is adequate enough.
The antenna achieved approximately 16dB of gain, greater than 14dB which has a VSWR of less than 1.5 which was a required specification for our center frequency. This specification is used to calculate the appropriate bandwidth with respect to our center frequency. At 14dB (Figure 18), I obtain the following bandwidth approximation: BW= fH - fL = 2.486-2.3825 = 0.104GHZ = 104MHZ
Figure 20: Smith Chart after Tuning
Figure 21: Notable Data Points from Smith Chart after Tuning
However, using the copper tape to move the center frequency closer to what it needed altered the matching network requirements. The circuit becomes slightly inductive. Therefore, the matching network which is 2.8mm long and 6mm wide will also need to be altered. Decreasing the 6mm width should increase the impedance, and increasing the 2.8mm length should rotate the 2.4Ghz frequency by adding inductance. Doing so will lower the SWR and reduce reflections.
Conclusions and Improvements
Conclusions and Improvements
Matlab:
This project could be improved by creating a standalone MATLAB code that generates the Fractal Geometry with less room for human error. As it stands the code can create the x and y coordinates, but struggles to create a design that has any thickness to it. For instance, it can only create a 3x2mm shape, but you may need it to create a 3x3mm or 3x1mm line. Once this is achieved allowing the results to be directly input into the provided Sonnet MATLAB code only makes things easier. Having this created would decrease the amount of time spent creating the shape and tIaking its performance drastically.
Design:
The design I made was a lot larger than it needed to be to make creation of the antenna easier. This was due to constraints placed on the project by sonnet. The circuit could not have been tested accurately or quickly with sonnet-lite, due to the cell size and memory restrictions. I could have used the professional version of sonnet in the RF lab, but by focusing on other areas of the project I did not have time to redesign and test using the professional version. However, using the discoveries provided within this report creating the geometry and modeling it with smaller cell sizes would produce an accurate and smaller form factor design.
Impedance Matching:
A problem had with the impedance matching network was that it worked great on sonnet. But because I did not get a board file from eagle that exactly matched what was modeled, it threw off our impedance matching. HoIver, I would suggest finding a way to produce the board file directly off of Sonnet, with perhaps a different file type, and also doing a final test with extremely small cell sizes to more accurately gage the response before submitting the files to be manufactured.
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