Periyodik olarak yüklü dikdörtgen dalga kılavuzlarında bloch empedansı ve uygulamaları
Bloch impedance of periodically loaded rectangular waveguides and its applications
Yazar: FATİH AKIN BAYRAKTAR
Danışman: YRD. DOÇ. DR. SERKAN ŞİMŞEK
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Elektronik ve Haberleşme Mühendisliği Ana Bilim Dalı / Telekomünikasyon Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2013
Konu: Elektrik ve Elektronik Mühendisliği = Electrical and Electronics Engineering

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.

Abstract:
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.