Modern Characterization of Electromagnetic Systems and its Associated Metrology
Finally, it is shown that the probe correction can be useful when the size of the probes is that of a resonant antenna and it is shown then how to carry it out.
In Chapter 7, two methods for spherical near‐field to far‐field transformation are presented. The first methodology is an exact explicit analytical formulation for transforming near‐field data generated over a spherical surface to the far‐field radiation pattern. The results are validated with experimental data. A computer program involving this method is provided at the end of the chapter. The second method presents the equivalent source formulation through the SRM described earlier so that it can be deployed to the spherical scanning case where one component of the field is missing from the measurements. Again the methodology is validated using other techniques and also with experimental data.
Two deconvolution techniques are presented in Chapter 8 to illustrate how the ill‐posed deconvolution problem has been regularized. Depending on the nature of the regularization utilized which is based on the given data one can obtain a reasonably good approximate solution. The two techniques presented here have built in self‐regularizing schemes. This implies that the regularization process, which depends highly on the data, can be automated as the solution procedure continues. The first method is based on solving the ill‐posed deconvolution problem by the iterative conjugate gradient method. The second method uses the method of total least squares implemented through the singular value decomposition (SVD) technique. The methods have been applied to measured data to illustrate the nature of their performance.
Chapter 9 discusses the use of the Chebyshev polynomials for approximating functional variations arising in electromagnetics as it has some band‐limited properties not available in other polynomials. Next, the Cauchy method based on Gegenbauer polynomials for antenna near‐field extrapolation and the far‐field estimation is illustrated. Due to various physical limitations, there are often missing gaps in the antenna near‐field measurements. However, the missing data is indispensable if we want to accurately evaluate the complete far‐field pattern by using the near‐field to far‐field transformations. To address this problem, an extrapolation method based on the Cauchy method is proposed to reconstruct the missing part of the antenna near‐field measurements. As the near‐field data in this section are obtained on a spherical measurement surface, the far field of the antenna is calculated by the spherical near‐field to far‐field transformation with the extrapolated data. Some numerical results are given to demonstrate the applicability of the proposed scheme in antenna near‐field extrapolation and far‐field estimation. In addition, the performance of the Gegenbauer polynomials are compared with that of the normal Cauchy method using Polynomial expansion and the Matrix Pencil Method for using simulated missing near‐field data from a parabolic reflector antenna.
Typically, antenna pattern measurements are carried out in an anechoic chamber. However, a good anechoic chamber is very expensive to construct. Previous researches have attempted to compensate for the effects of extraneous fields measured in a non‐anechoic environment to obtain a free space radiation pattern that would be measured in an anechoic chamber. Chapter 10 illustrates a deconvolution methodology which allows the antenna measurement under a non‐anechoic test environment and retrieves the free space radiation pattern of an antenna through this measured data; thus allowing for easier and more affordable antenna measurements. This is obtained by modelling the extraneous fields as the system impulse response of the test environment and utilizing a reference antenna to extract the impulse response of the environment which is used to remove the extraneous fields for a desired antenna measured under the same environment and retrieve the ideal pattern. The advantage of this process is that it does not require calculating the time delay to gate out the reflections; therefore, it is independent of the bandwidth of the antenna and the measurement system, and there is no requirement for prior knowledge of the test environment.
This book is intended for engineers, researchers and educators who are planning to work in the field of electromagnetic system characterization and also deal with their measurement techniques and philosophy. The prerequisite to follow the materials of the book is a basic undergraduate course in the area of dynamic electromagnetic theory including antenna theory and linear algebra. Every attempt has been made to guarantee the accuracy of the content of the book. We would however appreciate readers bringing to our attention any errors that may have appeared in the final version. Errors and/or any comments may be emailed to one of the authors, at [email protected], [email protected], [email protected].
Acknowledgments
Grateful acknowledgement is made to Prof. Pramod Varshney, Mr. Peter Zaehringer and Ms. Marilyn Polosky of the CASE Center of Syracuse University for providing facilities to make this book possible. Thanks are also due to Prof. Jae Oh, Ms. Laura Lawson and Ms. Rebecca Noble of the Department of Electrical Engineering and Computer Science of Syracuse University for providing additional support. Thanks to Michael James Rice, Systems administrator for the College of Engineering and Computer Science for providing information technology support in preparing the manuscript. Also thanks are due to Mr. Brett Kurzman for patiently waiting for us to finish the book.
Tapan K. Sarkar
Magdalena Salazar Palma ([email protected])
Ming‐da Zhu ([email protected])
Heng Chen ([email protected])
Syracuse, New York
Tribute to Tapan K. Sarkar by Magdalena Salazar Palma, Ming Da Zhu, and Heng Chen
Professor Tapan K. Sarkar, PhD, passed away on 12 March 2021. The review of the proofs of this book is probably the last task he was able to accomplish. Thus, for us, his coauthors, this book will be always cherished and valued as his last gift to the scientific community.
Dr. Sarkar was born in Kolkata, India, in August 1948. He obtained his Bachelor of Technology (BT) degree from the Indian Institute of Technology (IIT), Kharagpur, India, in 1969, the Master of Science in Engineering (MSCE) degree from the University of New Brunswick, Fredericton, NB, Canada, in 1971, and the Master of Science (MS) and Doctoral (PhD) degrees from Syracuse University, Syracuse, NY, USA, in 1975. He joined the faculty of the Electrical Engineering and Computer Science Department at Syracuse University in 1979 and became Full Professor in 1985. Prior to that, he was with the Technical Appliance Corporation (TACO) Division of the General Instruments Corporation (1975–1976). He was also a Research Fellow at the Gordon McKay Laboratory for Applied Sciences, Harvard University, Cambridge, MA, USA (1977–1978), and was faculty member at the Rochester Institute of Technology, Rochester, NY, USA (1976–1985). Professor Sarkar received the Doctor Honoris Causa degree from Université Blaise Pascal, Clermont Ferrand, France (1998), from Polytechnic University of Madrid, Madrid, Spain (2004), and from Aalto University, Helsinki, Finland (2012). He was now emeritus professor at Syracuse University. Professor Sarkar was a professional engineer registered in New York, USA, and the president of OHRN Enterprises, Inc., a small business founded in 1986 and incorporated in the State of New York, USA, performing research for government, private, and foreign organizations in system analysis.
Dr. Sarkar was a giant in the field of electromagnetics, a phenomenal researcher and teacher who also provided an invaluable service to the scientific community in so many aspects.
Dr. Sarkar research interests focused on numerical solutions to operator equations arising in electromagnetics and signal processing with application to electromagnetic systems analysis