CHAPTER 3. DESIGN OF LEAKY-WAVE ANTENNA
3.2. Simulation Results
Figure 3.4. Real and imaginary part of the Bloch impedance for the proposed unit cell as a function of frequency.
Where Z0 is set to 50. The real and imaginary values of Bloch impedance are dedicated in Fig. 3.4 so that the average of the real part throughout the entire radiating frequency range is calculated to 65.
For the impedance matching, the tapered line is used to convert the 50 micro-strip lines to 65 by calculating the proper width. The length lt and the width wt and wm of the tapered section are optimized to 16 mm, 0.5 mm, and 3 mm, respectively.
is chosen due to the limited space for the external sensor on the human body. Then, the whole proposed structure is depicted in Fig. 3.5, which consists of the array of 10 unit cells and two tapered sections for matching the impedance in two feeding points, so the overall length and the width of the antenna are 240 mm and 42.8 mm, respectively.
Figure 3.6. Simulated S-parameters of the proposed LWA
Figure 3.7. Normalized radiation patterns of the LWA in different frequencies.
The simulated S-parameters of the full length structure of our proposed LWA are indicated in Fig. 3.6.
As can be seen, both S11 and S21 are achieved lower than -9 dB in the range of frequency from 2.05 GHz to 2.38 GHz, then the S11 rises up to -2.5 dB but remaining very low S21 to maintain the good radiation.
The S11 result in RH frequency range shows not good impedance matching of the unitcell when the Im(ZB) is not near to 0.
Fig. 3.7 shows the normalized radiation patterns of the antenna in the radiating frequency range from 2.35 GHz to 2.65 GHz. It is clear to see that the scanning angle range is quite symmetric in accordance with the symmetry of the dispersion diagram. However, the broadside radiation occurs at 2.45 GHz rather than 2.5 GHz as the transition frequency in the dispersion diagram. That can be explained by the configuration of unit cell simulation being infinite, but the realized length of the antenna is limited. The scanning angle range is 95, from –45 at 2.35 GHz to 50 at 2.65 GHz without any stop band at 0 deg.
CONCLUSION AND FUTURE WORK
We investigated the out-folded patch antenna with the ZOR that is robust to the skin attachment, which helps to maintain a high-Q resonance with improved penetration toward body tissues. The operating principle of the antenna was interpreted as the open-ended CRLH TL, and the benefits of the tapered section and the ZOR were analyzed through parametric studies. In addition, the feasibility of the proposed antenna was validated by comparing it with the conventional patch antenna having the fundamental mode resonance. Two identical antennas were fabricated to measure reflection coefficients, coupling strengths, and near-field distributions. Despite the lossy properties of the human body, the proposed antenna maintained a high-Q resonance with the minimum |S11| of −20.2 dB and the peak |S21| of −46.2 dB at 2.5 GHz. Furthermore, the forward radiation was achieved with the measured FBR of 6.79, and the proposed concept was capable of achieving the MARD of 12.23% in the three trials of human experiments. The results demonstrated that the proposed antenna with the ZOR is suitable for more accurate estimation in non-invasive CGM systems as a replacement of the conventional patch antenna with the fundamental mode resonance. Our future scope includes additional experiments in a very restricted environment for multiple subjects to provide better validations of the proposed approach.
Based on the knowledge and data obtained from the restricted environments, we are also going to tune the proposed antenna for improved accuracy and sensitivity.
The proposed LWA operating from 2.35 GHz to 2.65 GHz is designed, can steer radiation direction with respect to frequency. With the wide scanning angle range from –45 to 50 in the simulation, the designed LWA has good characteristics to move forward following our approaches. For future work, the LWA is continued to be optimized and verified the interaction with the change of permittivity of the body tissue. In real life, the antenna should be placed on a specific human body part with different subjects and positions. Therefore, the antenna with conformal geometry, their position, and orientation should be considered because the electrical length of the antenna and scan angles will be changed in this case.
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ACKNOWLEDGMENT
First of all, I would like to express my deep gratitude to my advisor, Prof. Gangil Byun throughout my study program and completing my Master’s thesis. He is the first person who teaches me how to search for a good journal paper to study, comes to my desk to tell me about a hard time at the very first step of his research journey to boost my mood when I am feeling depressed, always raises my spirits and give me his comments about my attitude in the regular meetings for my better work. Without his guidance and patience, I could not have this good achievement and finished my course with more confidence in myself. I also would like to thank my committee members for taking the time to join my defense and give me brilliant comments on my research topic.
In addition, I would like to express my sincere thanks to the Technology Innovation Program (Development of sustained precision, semi-permanent, and low time lag 3rd generation CGMS for diabetes patients without blood sampling in glucose monitoring) funded by the Ministry of Trade, Industry and Energy (MOTIE) in Korea for the supporting.
My appreciation also extends to all my laboratory colleagues for their valuable mentoring and encouragement. Thank you for your warm heart to help an international student like me not only with the research but also with my daily activities. There are a lot of people surrounding me who give me the energy for each new day, I would like to show my acknowledgment to all of you.
Last but not the least, thank you, all my family members, for your unconditional love and support.
Thank you for always being my back, encouraging me, and listening to all my thoughts.
APPENDIX
To further research on metamaterial, I have been attracted to the metasurface application, specifically for the reflection phenomenon. In recent decades, the emergence of metasurface has attracted considerable attention due to the potential in controlling electromagnetic waves. Most gradient metasurface designs based on the generalized Snell’s law used proposed for both refractive and reflective metasurface. On the other hand, according to some theoretical studies, the generalized Snell’s law based on perfect anomalous reflection can never guarantee power conservation. Indeed, it needs a lossy surface to absorb the incident wave or active components in some areas. It was recently demonstrated that the bianisotropic metasurface has a robust potential to manipulate the phase, magnitude, and polarization state of an impinging wave with high efficiency.
The first research demonstrated the general theory for designing omega-type bianisotropic metasurface (O-BMS) based on field transformation. The author proved that once the desired fields below and above the metasurface are specified, the O-BMS properties can be calculated. Importantly, they can implement each meta-atom by analyzing an O-BMS unit cell as a two-port network, also known as the TL model.
From this point, many studies were introduced for both refractive and reflective metasurface designs.
Despite the challenges for the reflection case, the synthesis method presented the physical configuration assumption to achieve a “perfect” passive lossless refection metasurface. We present here an approach to implement a passive lossless bianisotropic metasurface design for high-efficiency anomalous reflection, using the general synthesis, and demonstrate such a metasurface in a practical design via numerical simulation.
1. Bianisotropic Metasurface Synthesis
(a)
(b)
Apx Figure 1. 1. Anomalous reflection (a) A schematic diagram of anomalous reflector, (b) Physical configuration of an O-BMS for anomalous reflection.
As shown in Apx Fig. 1(a), multiple diffraction modes will appear when incident waves impinge to the periodic metasurfaces because of the Floquet-Bloch theorem. That would be a chance to generate reflection fields with other directions that differ from a specular angle, known as anomalous reflection.
The deep sub-wavelength of meta-atom can be homogenized to provide useful physical insight, which allows the metasurface formed by discrete unit cells. The synthesis provides an idea that the assumption of surface waves with decaying power in +z-direction in the top facet of the metasurface matches the local power profile without affecting the whole metasurface function. The first step in designing an O- BMS is specifying two electromagnetic fields at the top and bottom of the metasurface. Based on the physical configuration presented in Apx Fig. 1(b), the equation for the fields in both the top and bottom facets of the metasurface can be defined as follows:
,1 ,2
1 2
,1 ,2
1 2
, ,1 ,2
1 ,1 2 ,2
,
( , ) ( , )
t t
t t
jk y jk y
z z
x top sw sw
jk y jk y
sw z sw z
y top
E y z E e e jE e e
E E
H y z j e e e e
k k
(1) (2)
cos s cos s
,
cos s cos s
,
( , ) ( , ) ( , )
( , )
i i r r
i i r r
jkz jky in jkz jky in
x bot inc ref in out
jkz jky in jkz jky in
in out
y bot
in out
E y z E y z E y z E e e E e e
E E
H y z e e e e
Z Z
(3) (4) where the amplitudes of the incident and reflected waves are denoted as Ein and Eout, respectively. The surface waves in the top facet have decay coefficients α1 and α2 along the +z-direction. The transverse wave numbers kt,1 and kt,2 are chosen at will as long as kt,2 = kt,1 + k(sin θr − sin θi) and kt n, k with n = 1,2. The amplitude for the reflected wave is set to Eout E ein jXout Zout Zin , where Xout is an arbitrary phase shift.
In the next step, three parameters of O-BMS should be determined which are electric surface impedance Zse, magnetic surface impedance Ysm, and electromagnetic coupling coefficients Kem. The bianisotropic sheet transition conditions show that the bianisotropic metasurface constituents can be solved when the fields in the top and the bottom facets of the metasurface are specified. Note that the metasurface is passive and lossless, so that ℜ(𝑍𝑠𝑒) = ℜ(𝑌𝑠𝑚) = ℑ(𝐾𝑒𝑚), for the case of TE polarization, they can be formulated as:
* *
, , , ,
*
, , , ,
, , , ,
, , , ,
, ,
, ,
1 ,
2
1 ,
2 1 2
x top y bot x bot y top em
x top x bot y top y bot
y top y bot y top y bot
sm em
x top x bot x top x bot
x top x bot se
y top y bot
E H E H
K
E E H H
H H H H
Y j K
E E E E
E E
Z j
H H
, ,
, ,
x top x bot ,
em
y top y bot
E E
K H H
(5)
(6)
(7)
(a) (b)
Apx Figure 1. 2. (a) 2-ports network for an unit cell, (b) an unitcell constructed by 3 impedance sheets separated by substrates.
After that, the structure can be considered as a microwave network to calculate the impedance properties.
The transmission line model in Apx Fig. 1.2(a) shows the 2-ports network corresponding to a unit cell of the metasurface. The equivalent impedance matrix is given via:
, 11 12 ,
, 21 22 ,
y bot x bot
x top y top
E Z Z H
E Z Z H
(8)
Owing to the three unknowns in the equation above, the unit cell structure consists of three impedance sheets in the top, mid, and the bot is introduced, as shown in Apx Fig. 1.2 (b). The impedance sheets
are separated by dielectric substrates with the thickness t. Based on the cascade structure, the value of each impedance sheet can be calculated by:
Z Zbot ZTL Zmid
ZTL Ztop (9)The period of the structure depends on the operating frequency, incident and desired reflected angles, which are formulated as:
sin i sin r,
P
(10)
(a) (b)
(c) (d)
(e) (f)
Apx Figure 1. 3. Numerical trials: (a)(c)(e) the metasurface constituents values, (b)(d)(f) the full-wave simulation for E fields.
The synthesis is investigated by numerical simulation in Ansys HFSS for different situations, as shown in Apx Fig. 1.3. Apx Fig. 1.3 (a), 3(c), and 3(e) show the numerical metasurface constituents for three phenomenons in Apx Fig. 1.3 (b), (d), and (f), respectively. The structure is designed with 20 supercells in +y-direction and set as infinite in +x- direction. We use the Gaussian beam which has a specific beam waist to observe the incident and reflected fields. It is worth noting that the propagation constants kt,1
and kt,2 of two surface waves should be chosen properly to achieve high anomalous reflection magnitudes. While the first case indicates the electric fields that normal incident waves can reflect 70, the two cases below show the oblique impinging waves with the incident angle of 40 and 60 toward normal reflection. All the trials proved the synthesis has a great potential in reflective metasurface design.
2. Physical Implementation for Metasurface Design
Apx Figure 1. 4. Proposed unitcell structure with I-shaped.
Based on the synthesis illustrated in the previous section, a bianisotropic metasurface for high-
efficiency reflection is designed. The I-shaped structure is introduced to realized physical implementation is defined by the longitude length lt, transverse length dl, and the width w, as shown in Apx Fig. 1.4. The variation of three parameters determines the corresponding impedance range for each layer, and the key parameter can be considered as dl. Our purpose is to design an O-BMS which can reflect an incident angle of 60◦ to the normal direction at 10 GHz. Three metallic I-shaped layers indicate three impedance sheets in the top, middle, and bottom, respectively. They are separated by Taconic RF-60 substrates (εr = 6.15) with the thickness t = λ0/30. The proposed supercell is composed of 6 unit cells. The size of the unit cell can be calculated, and then divided to the number of unit cells per supercell, known as λ0/5.
(a) (b) (c)
Apx Figure 1. 5. Comparison between numerical and optimized results for electric surface impedance of (a) top layer, (b) middle layers, and (c) bottom layers.
(a) (b)
Apx Figure 1. 6. Comparison between numerical and optimized results for reflection coefficients in (a) magnitude and (b) phase.
Despite the proper value of dl for the impedance sheet, the coupling between layers is extremely strong.
Then, each unit cell was optimized by using Floquet ports with periodic boundaries in HFSS. The impedance values of all three layers in simulation should be tuned to match with the calculation by each unit cell, as shown in Apx Fig. 1.5. Once the impedance values are matched, the magnitude and phase of scattering parameter are also followed,presented in Apx Fig. 1.6. The reflected magnitude of each