Periyodik olarak yüklü dikdörtgen dalga kılavuzlarında bloch empedansı ve uygulamaları
Bloch impedance of periodically loaded rectangular waveguides and its applications
- Tez No: 350633
- Danışmanlar: YRD. DOÇ. DR. SERKAN ŞİMŞEK
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2013
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Elektronik ve Haberleşme Mühendisliği Ana Bilim Dalı
- Bilim Dalı: Telekomünikasyon Mühendisliği Bilim Dalı
- Sayfa Sayısı: 75
Özet
Bilim insanlarının periyodik yapılar üzerindeki araştırma ve çalışmalarının başlangıcı 19. yüzyıl sonları olarak kabul edilmektedir. Birtakım avantajlarının yanında frekans spektrumunda seçici olmaya olanak sağlayan özellikleri düşünüldüğünde periyodik yapıların önemi gün geçtikçe artmış ve üzerinde daha fazla durulmaya değer görülmüştür. Periyodik yapılar günümüze kadar filtre tasarımı, yavaş dalga yapıları, faz kaydırıcıları, empedans uydurma cihazları, antenler ve anten besleme yapıları gibi muhtelif mühendislik uygulamalarında kullanılagelmiştir.Günümüzdeyse özellikle fotonik kristaller üzerinde sürdürülen araştırma ve çalışmalar periyodik yapıların literatürde halen güncelliğini koruyan bir çalışma alanı olmasını devam ettirmektedir.Bu çalışma kapsamında periyodik yapıların düzgün dikdörtgen dalga kılavuzlarındagöstermiş olduğu birtakım özellikler incelenmiştir.Çalışmanın tamamındaliteratürde sıklıkla tercih edilen standart WR-90 dikdörtgen dalga kılavuzu kullanılmıştır. İlk etapta çalışmaya ön hazırlık olması amacıyla dikdörtgen dalga kılavuzlarında elektromanyetik dalgaların göstermiş olduğu özellikler işlenmiştir. Elektrik ve manyetik alan ile kesim frekansı ifadeleri çıkartılmıştır. Daha sonra ise çalışmanın tamamında sıklıkla kullanılan Sparametreleri hakkında bilgi verilmiştir. Muhtelif durumlar için hesaplama yöntemleri üzerinde durulmuştur ve bununla ilintili olarak İletim Hattı Modeli incelenmiştir. Bir sonraki aşamada ise periyodik yapılar ve özellikleri irdelenmiştir. Buna bağlı olarakperiyodik yapılarınkarakteristik empedansı (Bloch empedansı) incelenmiştir. Durdurma bantlarının tespitinde daha önce kullanılan yöntemlerin yanı sıra Bloch empedansının sahip olduğu birtakım özellikler kullanılarak elde edilen sonuçların doğruluğu gösterilmiştir. Böylecebirim hücretasarımı yapılırkenBloch empedansından da istifade edilebileceği anlaşılmış olmaktadır. Çalışma kapsamında ele alınan bir diğer husus da kaskat yapılara ait verilerin doğruluğunu sınamak adına MATLAB üzerinde yapılan teorik analizlerin HFSS yardımıyla elde edilen simülasyon sonuçlarıyla tutarlılık arz ettiğini ortaya koymakoldu. Böylece bulunan sonuçların doğruluğunuteyit etmek adına kuvvetli bir kıstasa sahip olunmuştur.Çalışmanın son kısmında ise süreksizliğe sahip yapılar ele alınmıştır. İlk incelenen homojen yapılardan farklı olarak Sparametrelerinin tespitinde İletim Hattı Modeli?nin yetersiz kalmasından ötürüalternatif bir yöntem olan Modal Açılım Tekniği kullanılmıştır. Sonrasında ise benzer yaklaşımlarla bulunan sonuçlar verilmiştir.
Özet (Çeviri)
It is agreed that the beginning of research and studies on periodic structures by scientists goes back to late 19th century. Besides certain advantages, the importance of periodic structures, when the characteristics that allow them to be selective in the frequency spectrum considered, has increased day by day and began to be seen as worthy of research. Periodic structures have been widely used in different engineering applications such as filter design, slow-wave structures, phase shifters, impedance matching devices, antennas and antenna feeds. Today, especially the research and studies on photonic crystalsmaintain that periodic structures are still an up-to-date research area in literature.Thisstudy can be dividedtwo mainphase: The investigation about the subject and the analysis results of the subject. First phaseincludes the research on rectangular waveguides, scattering parameters, some analysis techniques, periodic structures and Bloch impedance. Second part contains the analysis, results, comparisons of results and comments.In the first phase of the study, in order to clarify the subject and to present necessary background information, waveguides, which are the structures that are used in order to transmit high power at GHzfrequencies, and their types are expressed. Periodic structures which have an important place in electromagnetics literature and particularly certain characteristics that are manifested by these structures on traditional rectangular waveguides are dealt with. The characteristics that electromagnetic wavesshow on the rectangular waveguides are treated. The expressions of electric and magnetic field and cut-offfrequency are extracted. After that, scattering parameters and their specifications, TransmissionLine Technique and scattering parameters of the cascaded structures are dealt with. In this context, obtaining the generalized scattering matrix for N-port circuits is discussed. Later, some inferences are made about circuits by using properties of thismatrix. Then, the specifications of the scattering matrix that must ensure for reciprocal, lossless or unreflecting circuits are investigated. Afterwards shift of the reference planes, which is another prominent issue for scattering parameters, is examined. To sum up, basic information is given about scattering parameters without too much detail. After that, Transmission Line Technique, which is a very important analysis technique regarding this issue, is examined so as to analyze the selected problem in the following sessions. In the context, getting the junction scattering matrix is explained. Then, finding the scattering parameters of the cascaded structures is examined due to finding the scattering parameters of the periodic structures. Computationmethods are discussed for various conditions and with regard to that Transmission Line Model is analyzed. The next step is about some characteristics shown by periodic structures.Periodic structures are described as the theoretically infinite transmission line or systems that occurred by adding the discontinuity elements to waveguides. These structures are designed as different forms and they can be made one, two or three dimension.Also, periodic structures can be microstrip line, waveguide or Electromagnetic Band-gap (EBG) and can be modeled by impedance during the transmission line. They support the properties of the slow wave propagation and have pass/stop band characteristics asfilters.After the explanation of the characteristics of the periodic structures,the notions like ABCD matrix and Bloch impedance and the necessary details are examined.In this context, expression the Bloch Impedance is extracted. Then, the properties that must be ensured in pass bands and stop bands of the Bloch impedance are indicated. After, the subject about terminating the periodic structures is dealtwith. Another significant topic about this study is determining the stop bands. Thus, this subject is considered and detecting the frequencies for the stop and pass bands by looking the ?and ?values is investigated.In the second phase of the study, the problem geometries and their solution results are revealed. The first problem which is examined in this respect is about a periodic structure used byWR-90 traditional rectangular waveguide. A certain discontinuous andhomogenousunit cell which has a material whose dielectric constant and dimensions are known is selected from literature. There existvariouswaysin order to find the pass and stop bands. One of theways from the literatureis determining the dispersion diagram of the model. Dispersion diagram of the selected model geometry can be easily found with some equations existing in the literature. When the scatteringparameters of the structure constituted by this unit cell is found and the dispersion diagram is put forward, the pass and stop bands in the frequency area are found out.Dispersion diagram of the selected model geometry can be easily found with some equations existing in the literature. This method can be summarized asfollows:First, scattering parameters of the junctions for the selected model geometry are found. Then, the junction scattering parameters are combined with the formulas for the cascaded structures. After computing the scattering parameters of the unit cell, reduced eigenvalue equation is solved in the selected frequency band. By looking the values of ?stop and pass bands of the model are determined. This technique is based on finding and examining the value of ?. The stop bands are determined by looking the values of ?and ?. On the dispersion diagram, the stop bands occurred when ?is equal to 0 or ?. In the pass bands,the absolute value ?is equal to 1 and always the product of the couple of the eigenvalues must be equal to 1. In other words, the eigenvalues are stated onunit circle in pass bands and onreal axisin stop bands.With the increasing of the differences between the dielectricconstants of the materials which compose the unit cell, how stop bands behave in the frequency area are also shown.When the contrast rises, the stop band regions expand.A MATLAB code which finds the ?values and detects the stop and pass bands, namely the dispersion diagram, of the chosen model geometry, is written and used. The pass and stop band boundaries aredetected by looking the ?is equal to 0 or ?. Also, eigenvalues ?1and ?2, which is obtained from the reduced eigenvalue equation, are examined. The results show the consistency of the properties that are expressed for the ? domain. After this investigation, the model is changedso asto observe the effect of the increasing contrast of the dielectric constants to the stop and pass bands.For the new dielectric value, stop band regions are found by using the dispersion diagram. Another way, which is specially focused on in this thesis, is the Bloch impedance approach. In this study, the expression of Bloch impedance is usedin MATLAB after finding scatteringparametersof the selected model geometry to obtain the stop band boundaries. Here when detecting stop bands, the characteristic of Bloch impedance which takes pure real value in pass bands and pure imaginary value in stop bands is used. Also, real parts are positive and imaginary parts are increasing function. Hence, the valid impedance values which provide both conditions must be selected. After that point, the change in stop bands according to the change in the dimensions of the dielectric materials is examined. A data set which contains stop bands obtained by various material dimensions is constructed by this way. After this step, the unit cell which is practically more important is designed. According to that, a central frequency determined for stop band and material dimensions for tolerance are detected. By this way, it is put forward that unit cell design can also be done by Bloch impedance.The new dielectric materialused in the selected geometry is also examined with Bloch impedance approach. Then, the results obtained from the dispersion diagram and Bloch impedance are compared and it is seen that the whole results are consistent and Bloch impedance approach is accurate. Therefore, this study shows that the same results can also be found by some characteristics shown by Bloch impedance. In the literature, a calculation method based on tensions over ABCD matrix is used to find Bloch impedance.Another case in this respect is to point out that the theoretical analyses carried out by using MATLAB to test the correctness of data related with cascadedstructures are consistent with the computer simulation results obtainedby HFSS. By this way, a robust criteria is obtained to confirm the correctness of the results. Furthermore, the minimum number of unit cells which is necessary to use in order to obtain satisfactory results can be determined by changing the number of cells that compose the cascadedstructure.At the end of the study, the condition in which the unit cell composing the periodic structure is discontinuous is examined. In such a case, Transmission Line Model which is fast in giving the scatteringparameters is inadequate. Therefore Modal Expansion Technique is used. After correctly computingthe scatteringparameters, the processes and analyses that are done before are repeated.As a result, the methods used when the unit cell is discontinuous are shown to be correct and valid.
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