Rohedi, Ali Yunus (2017) Desain Microstrip Lines Menggunakan Metode Conformal Mapping Modular Baru Berbasis Logaritmik Fungsi Identitas Transformasi Joukowski. Doctoral thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Sistem komunikasi nirkabel lazim menggunakan microstrip lines karena
berbagai keuntungannya, antara lain strukturnya sederhana, berukuran kecil, gain
dan efisiensinya tinggi, serta biaya pembuatannya murah. Kelemahan microstrip
lines adalah masih sempitnya lebar pita frekuensi bila dibandingkan dengan fiber
optik.
Berbagai upaya teknis telah dikembangkan untuk mengatasi kelemahan
tersebut, namun dalam disertasi ini ditekankan pada aspek pendesainannya, yakni
sejauh mana tingkat akurasi dari formula-formula yang digunakan. Sedangkan
selama ini desain microstrip lines banyak bertumpu pada pemakaian formula umum
kapasitansi dan/atau impedansi karakteristik eksak dalam bentuk fungsi integral
eliptik yang diperoleh dengan metode conformal mapping. Oleh karena deret
takhingga integral eliptik lengkap macam pertama penyusun fungsi integral eliptik
adalah berkonvergensi rendah, maka desain microstrip lines umumnya dilakukan
menggunakan pendekatan dari fungsi integral eliptik tersebut. Fungsi integral
eliptik yang popular digunakan adalah yang diturunkan dengan pendekatan Hilberg.
Hingga kini hanya pendekatan Hilberg untuk tiga orde terendah saja yang
lazim digunakan. Hal ini disebabkan rumitnya pemakaian skema original iterasi
Hilberg dalam memformulasikan fungsi integral eliptik untuk pendekatan orde
tinggi. Penerapan fungsi identitas transformasi Joukowski melahirkan skema iterasi
baru pendekatan Hilberg yang dapat mengurangi langkah iterasi perumusan
argumen logaritmik fungsi integral eliptik. Dengan skema iterasi baru tersebut
argumen logaritmik pendekatan orde yang lebih tinggi dapat diformulasikan secara
eksplisit sebagai fungsi dari argumen logaritmik pendekatan orde yang lebih
rendah.
Implementasi formula modulus fungsi integral eliptik dari pendekatan
Hilberg orde tiga pada pendesainan microstrip lines jenis CPW (Coplanar
Waveguide) memberikan hasil perhitungan parameter geometri yang akurat untuk
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setiap nilai tetapan dielektrik bahan yang digunakan dan nilai impedansi
karakteristik yang dikehendaki.
Demikian pula, implementasi fungsi integral eliptik modular baru yang
dikembangkan dalam disertasi ini mengkonfirmasi bahwa hasil perhitungan
kapasitansi pendekatan Xiang untuk kapasitor pelat sejajar adalah tidak akurat
terhadap kapasitansi eksak Palmer, karena suku kapasitansi fringing fieldnya selalu
mendekati konstan untuk variasi rasio lebar dan jarak antar pelatnya. Hal ini
berbeda dengan konstribusi suku fringing field dari model kapasitansi empiris baru
yang diciptakan dalam disertasi ini, yang selain mendekati nilai kapasitansi eksak
formula Palmer juga lebih akurat dibandingkan semua formula kapasitansi dari
pendekatan yang ada. Kesesuaian model kapasitansi empiris baru terhadap
kapasitansi eksak Palmer tersebut menghasilkan hipotesa baru bahwa suku fringing
field kapasitor pelat sejajar dapat diformulasikan dalam fungsi integral eliptik.
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The wireless communications has commonly required the usage of
microstrip lines due to its advantages, namely simple structure, small size, high in
both of gain and efficiency, and low cost. The drawbacks of microstrip lines are
having narrow linewidth of frequency compared to optical fiber.
Some efforts have been developed to overcome the drawbacks, nevertheles
this dissertation is focused to explore the analytical aspect of designing, especially
to developed some methods to enhance the accuracy of the common formulas used
for designing the microstrip lines. As we know that the design of microstrip lines
were based on the usage of general formulas of capacitance and/or characteristic
impedance in the form of elliptic integral function obtained by using the method of
conformal mapping. Due to the infinite series of complete elliptic integral of the
first kind having low level of convergence, then the design of microstrip lines was
commonly performed by using approximation formulas of the eliptic integral
function.The approximations for the elliptic integral function that popularly used in
designing microstrip lines were due to Hilberg’s approximations.
Until now the only first three order of Hilberg’s approximations that were
commonly used for the application. This is because the usage of the original
Hilberg’s iteration schemes are so complicated in deriving high order of
approximations. Applying transformation function of Joukowski identity has
created the new iteration schemes for Hilberg approximations that can reduce the
iteration step of obtaining logarithmic arguments of the elliptic integral function.
By using the new iteration schemes, the logarithmic argument of the higher
approximation can be formulated explicitly as function of logaritmic argument of
the lower one.
The implementation of the approximate modulus formula of third order for
designing CPW (Coplanar Waveguide) gives the accurate geometric parameters for
both of the used dielectric constant and characteristic impedance.
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Applying the new modular of elliptic integral function developed in this
dissertation confirms that the capacitance calculation results of Xiang
approximation for parallel-plate capacitor is not accurate compared to the exact
capacitance due to Palmer, this is especially due to the fringing field term of the
capacitance is always constant for variation of the ratio width and plates separation.
It is diffrent with the constribution of the fringing field term of the new empirical
capacitance created in this dissertation, that besides approaching the value of exact
capacitance due to Palmer but also more accurate compared to all of available
approximate capacitance. The approriate of the new empirical capacitance formula
to the exact capacitance of parallel plate capacitor due to Palmer gives new hipotese
that the fringing field term of the capacitance can be presented in the form of elliptic
integral function.
| Item Type: | Thesis (Doctoral) |
|---|---|
| Uncontrolled Keywords: | microstrip lines, conformal mapping, transformasi Schwarz- Christoffel, integral eliptik, fungsi Joukowski |
| Subjects: | T Technology > TK Electrical engineering. Electronics Nuclear engineering > TK5105.546 Computer algorithms |
| Divisions: | Faculty of Mathematics and Science > Physics > 45001-(S3) PhD Thesis |
| Depositing User: | Rohedi Ali Yunus |
| Date Deposited: | 15 Aug 2017 03:30 |
| Last Modified: | 05 Mar 2019 03:43 |
| URI: | http://repository.its.ac.id/id/eprint/48565 |
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