Eşdeğer akımlar yöntemiyle yakın elektromanyetik alanı uzak alana dönüştürme
Near electromagnetic field to far field transformation with field equivalence principle
Yazar: DERYA HATİCE YİGİT
Danışman: PROF. DR. SELÇUK PAKER
İstanbul Teknik Üniversitesi / Bilişim Enstitüsü / İletişim Ana Bilim Dalı / Uydu Haberleşmesi ve Uzaktan Algılama Bilim Dalı
Derece: Yüksek Lisans, 2018
Konu: Elektrik ve Elektronik Mühendisliği = Electrical and Electronics Engineering

Özet:
Gelişen teknoloji sayesinde antenler, yüksek frekanslarda daha az kayıplı daha yüksek kazançlı olarak tasarlanıp üretilebilmektedir. Anten test sistemleri düzeneklerinin gereksinimleri de gitgide daha hassas sonuçlar gerektirmektedir.
Antenin uzak alanda ışıma modelinin ölçümü, daha gelişmiş antenlerin tasarlanması ve üretilmesinde önemli bir konudur. Anten uzak alan ışıma paterninin ölçümü için kullanılan teknikler doğrudan ve dolaylı ölçüm olarak iki gruba ayrılmaktadır. Doğrudan ölçümler bir yansımasız odada ya da dış ortamda yapılabilmektedir. Doğrudan ölçümde bulunan sonuçlar hiçbir dönüşüm gerektirmeksizin kullanılabilmektedir.
Bir antenden yayılan elektromanyetik alanın dağılımı antenden uzaklaştıkça kademeli olarak değişir. Antenin çevresindeki mesafe, temelde yakın alan ve uzak alan bölgeleri olarak iki ana bölgeye ayrılmaktadır. Antenlerin uzak alan testleri bir yansımasız odada ya da dış ortamda, çeşitli ön şartların sağlanması halinde yapılabilmektedir. Doğrudan ölçümler antenin uzak alanında yapılmaktadır.
Anten, yansımasız odada doğrudan ölçülmek istenirse ya oda boyutlarının çok büyük ya da anten çapının çok küçük olması gerekmektedir.
Anten, dış ortamda doğrudan ölçülmek istenirse, sağlanması gereken gereksinimler bazı zorlukları da beraberinde getirmektedir. Anten dış ortamda ölçüldüğünde çevreden gelecek interferanslar engellenmelidir. Antenin gönderdiği gücün anten etrafındaki objelere çarpıp geri yansıması engellenmelidir. Bu gereksinimin sağlanması için antenin, çapının dört katı büyüklüğünde bir platform üzerinde test edilmesi gerekmektedir. Ayrıca anten testi dış ortamda yapıldığında hava durumuna bağımlılık söz konusudur. Yağmurlu karlı havalarda yansıma ve kırılmalar fazla olacağından güneşli havalar tercih edilmelidir.
Tüm bu zorluklardan kaçınmak ve testlerin hassas sonuçlar vermesi istenmesi halinde antenler bir yansımasız odada, yakın alan bölgesinde test edilip, sonuçlar bazı matematiksel dönüşümler kullanılarak uzak alana taşınmalıdır.
Bu tez kapsamında antenlerin test gereksinimleri, uzak alan yakın alan bölgeleri açıklanmıştır. Yakın alan bölgesinde yüksek frekanslı antenlerin test edilmesi için gereksinimler tanımlanmıştır. Mekanik ölçüm sistemleri hakkında genel bilgi verilmiş olup, tez kapsamında düzlemsel ölçüm sistemi temel alınmıştır. Test sonuçları girdisi olarak, gerçek bir antenin testinden alınan yakın alan ve uzak alan verisi bulunmamaktadır. Bunun yerine matematiksel formülasyonu kullanılarak kolay ve pratik olarak paterni çizdirilebilecek teorik bir dipol anteni kullanılmıştır. Dipol anteninin paterni yakın alan ve uzak alan için çizdirilmiştir. Yakın alanda çizdirilen dipol anteninin yönlendiriciliği artırılmış, uzak alanda yönlü bir antenin test sonuçlarının transformu verilmiştir. Uzak alanda çizdirilen dipol anteninin paterni ile yakın alan uzak alan transformasyonu sonucu elde edilen patern karşılaştırılmıştır. Bu sonuçlar üzerinden metrik bir hata değeri bulunmuştur.
Yakın alanı uzak alana dönüştürürken eşdeğer alan prensibi (Huygens Prensibi) kullanılmıştır. Eşdeğer alan prensibi detaylı olarak tez kapsamında açıklanmıştır. Bu prensibe göre, yakın alanda bir S yüzeyinde ölçülen elektrik ve manyetik alanlar, yüzey akım yoğunluklarına çevrilmişlerdir. S yüzeyinin içinde elektrik ve manyetik alanların sıfır olduğu ve bulunan akım yoğunluklarının birer sanal kaynak olduğu Love teoremi temel alınarak tanımlanmıştır. Bu sanal kaynakların uzak mesafelere yaptıkları ışıma karakteristiğini veren formülasyon detaylı olarak açıklanmıştır. Dönüşüm işlemleri akış şemasında gösterilmiş, Matlab Programında geliştirilmiş kaynak kodu kullanılarak yakın alandan uzak alana dönüştürme işlemi tamamlanmıştır. Bunun sonucunda çıkan teorik değerler detaylı biçimde incelenmiş ve tez sonunda verilmiştir.

Abstract:
Thanks to the developing technology, previously unusable frequency bands are beginning to be used practically. The antennas used in these frequencies can be designed and manufactured with less loss and higher gain. Along with that, the requirements of the antenna test system arrangements require increasingly more precise results.
The purpose of this work is to find the characteristic of the far field using the electric and magnetic current densities that occur in the near field of an antenna.
The measurement of the antenna's far-field radiation pattern is an important issue in the development and production of high frequency antennas. Techniques for measuring the antenna far field radiation pattern can be divided into two groups as direct and indirect measurements.
Direct measurements can be made in a anechoic chamber or on the outside. Results from direct measurements can be used directly and do not need any conversion. Direct measurements are made in the far field area of the antenna.
Indirect measurements can be made in a anechoic chamber. The antenna under test is tested in near field region and far field charecteristics are calculated using near field measurement results.
The distribution of electromagnetic field components emitted from antenna changes as the distance from it increases. The distance in the vicinity of the antenna is divided into two main regions, mainly near field and far field fields. The near-field region is the region where the radiated reactive power density dominates over the active power density. The area where the active power density dominates is called the far field. In other words if the distance between the source and the antenna under test is greater than or equal to the distance boundary area, the phase difference on the spherical wave surface that is incident on the test antenna does not exceed 22.5̊ = π / 8.
The far field tests of the antennas can be carried out in a anechoic chamber or outdoor environment, provided various preconditions are met.
If the antenna is to be directly measured in anechoic chamber, the room size must be very large or the antenna diameter should be very small.
If the antenna is intended to be directly measured in the outdoor environment, the requirements to be met are accompanied by some difficulties. Any future interferences when the antenna is measured outside must be eliminated. The power transmitted by the antenna must be prevented to reflect back by hitting the objects around the antenna. To meet this requirement, the antenna must be tested on a platform that is four times the diameter of the antenna. Furthermore, when the antenna test is carried out in an outdoor environment, results obtained will be dependent on weather conditions. The sunny weather should be preferred because there will be more reflections and breaks in rainy and snowy weather. Also the distance between antenna under test and probe antenna must bee large enough to avoid coupling. This distance must be more than ten times the diameter of the antenna so that there are not coupling between the antenna under test and probe antenna. These conditions make difficult to establish a measurement setup for large diameter antennas.
To avoid all these difficulties and to obtain more precise results, the antennas can be tested in a anechoic chamber in the near-field area and the far field results can be calculated using some mathematical transformations from near-field results.
Within the scope of this thesis, the test requirements of the antennas and the definitions of near and far fields are given. Requirements for testing high frequency antennas in the near area are defined. General information about near field mechanical measurement systems is given and the details of the planar measurement system used in the thesis are explained. In general there are three types of near field measurement systems. They are: cartesian, cylindrical and spherical systems. These systems have cons and pros over each other. While cartesian systems can be used for measuring high gain antenna measurements they show poor performance in low gain antenna measurements. These systems also show good performance for high frequencies. In terms of the testing time cartesian near field measuring systems is best. Taking in mind all of these peformance results, in this thesis cartesian measuring system was chosen for the near to far field transformation.
As an input, no near field or far field data obtained from a real antenna test. Instead, a theoretical infinitally small dipole antenna data is used which can be easily and practically patterned using mathematical formulation as source data. Near field data of the dipole antenna for cartesian coordinate system is calculated from the theoretical formulas and the pattern of the dipole antenna is plotted for the near field. For the use in the cartesian near to far field transformation directivity of the dipole antenna has been increased.
The equivalent area principle (Huygens Prince) was used to convert the near field data to the far field pattern. Used equivalent area principle is explained in detail in the thesis. According to this principle, electric and magnetic fields measured on a surface in the near field are converted to surface current densities. It is defined on the basis of Love theorem that electric and magnetic fields within this surface are zero and that the current densities are a virtual source. The formulations that describe radiation of this virtual sources to far-field are described in detail.
First of all small dipole is placed in the origin of the cartesian coordinate system. Then electric and magnetic field components of the radiated field calculated on the surface of the theoretical cube. This is the basis of the equivalence are principle. This means that if we calculate all electric and magnetic field components in the all surfaces of the cube it means that we can define far field result of the dipole antenna. Then as a next step near field data will be calculated on the surface situated in Y=10*λ coordinate. Steps for the x and z scanning probes are 0.5*λ. After finding electric and magnetic fields they was transformed to the electric and magnetic surface currents. This procedure was done for all six surfaces.
Next step in the transformation is to chose observation point in the space in far field radiation area. This point is chosen in spherical system, then coordinates of the point are transfomed to the cartesian coordinates. Then electric and magnetic vector potantial components are calculated using previously found surface currents. Electric vector potential calculated from electric surface currents and magnetic vector potential calculated from magnetic surface currents accordingly. In this step integration is used for transformation.
Conversion from near field to far field is completed by using source code developed in Matlab Program. The resulting theoretical values are examined in detail and given at the end of the thesis. For pattern of the dipole antenna to be directional eights power of the components are taken. As a result high gain result is found in Y plane which is expected due to the nature of the antenna. Also results from Y plane surfaces are much bigger than other surfaces due to the our antenna is directive.
For the final result all the excited electric and magnetic field components from all six surfaces are summed up in the observation point. This result is our near to far field transfomation result. To measure performance of the transformation calculated data and the theoritical data calculated at the beginning of the thesis were compared. For comparison L2N metric was used. This norm also called Euclidean Norm. Value of the metric decreases as inputs to the metric is close to each other. L2N data fort his transformation is found to be 0.0018 which can be stated as a good result.
During thesis scanning parameters of the surfaces and directivities of the source antenna were changed to investigate the performance of the system under different situations. It is found that this system as stated in the theoritical part gives good performance for the antennas with high directivity. To measure this same procedure described above is performed for low directivity antenna. L2N metric was found in this situation is found to be 0.0040 which in worse. The main reason for this performance decrease is that power radiated from antenna transmits to the sides of the calculation cube. This problem can be solved by using cylindrical mechanical scanning system for near to far field tranformation system.
As a result it can be stated that this system works perfect for the high gain antennas and can be used in real life situations.