Time-Domain Characterization of Radio Links (download)

Dr. Colin C. Bantin

Thales Group

Abstract:

The performance of radio links can be characterized in the time domain by the convolution of three functions of the antennas involved; a y function, which is the inverse Fourier transform of the admittance at the feed point, an h function, which is the inverse Fourier transform of the time derivative of the effective length of the antenna, and the source excitation voltage, v. The first two functions, when convolved together, form a response, or r function, specific to each antenna. These are functions of the orientation angles of the antennas and the distance between them. The response function gives the electric field due to an impulse voltage source. It therefore characterizes the antenna as a transmitter. The response function also represents the time derivative of the received current due to an incident electric field impulse. It therefore it also characterizes the antenna as a receiver. A link between two such antennas is characterized by a convolution of the respective transmit and receive response functions, an integration with respect to time, and the multiplication by a scale factor inversely proportional to the separation distance. This gives the impulse response of the entire link, which, when convolved with the source function, gives the received current in the load due to an applied source voltage. It is instructive to explore the y, h and r functions for different elementary antennas. We can do this analytically for some cases, or by using detailed moment method modeling in other cases.  

An isolated current element has, by definition, a y function that is a delta function in time. The h function is the time derivative of a delta function, which can be deduced from the inverse Fourier transform of the frequency-domain expression for the electric field. Therefore the r function of a current element is the time derivative of a delta function. A short dipole, which has a triangular current distribution at all frequencies, has an admittance that is dominated by a capacitance, therefore the y function is the time derivative of a delta function. The h function, also deduced from the frequency-domain electric field expression, is again the time derivative of a delta function. Therefore the r function of a short dipole is the second time derivative of a delta function. A long dipole, with a reflection-matched source resistor, has a y function that is essentially a positive impulse function followed by a lesser magnitude negative impulse function separated by the source-to-tip travel time. The h function is a series of impulses of alternating sense and decreasing amplitude. Therefore the r function of a finite length dipole, by convolution, is a triplet of impulse functions, two positive pulses separated by twice the source-to-tip travel time, and one negative pulse centered between them. The response function approaches that of a short dipole as the length decreases. An infinite dipole has y, h and r functions consisting of only a single impulse, in each case equivalent to the first of the pulses for a finite length dipole. This is an exact representation for a tapered thin-wire and approximate for a constant (thin) radius wire. A dipole with an imposed sinusoidal current filament cannot be evaluated directly, but functions related to the y and h functions illustrate the impossibility of achieving this case physically.

Biography:

Dr. Colin C. Bantin received the MaSc and PhD degrees in Electrical Engineering from the University of Toronto, Toronto, Canada in 1969 and 1972 respectively, and was a Postdoctoral Fellow at the University of Cambridge, Department of Applied Mathematics and Theoretical Physics from 1971 to 1973. He was a co-recipient of the Antennas & Propagation Group 1971 G-AP Best Paper Award.  From 1974 to 1978 Dr. Bantin was with Telesat Canada, in Ottawa, Ontario, Canada, working on the 6/4 GHz and 12/14 GHz earth station programs. From 1978 to 1983 he was Vice President and Chief Engineer for Digital Telecommunications Ltd., in Mississauga, Ontario, Canada, helping to pioneer the use of digital satellite and fibre optic communications systems in Canada. In 1983 he established the consulting firm of C.C.Bantin & Associates Ltd. From 1993 to 1995 he was an Associate Professor at the Etisalat College of Engineering in Sharjah, U.A.E. where he developed and taught courses in telecommunications, digital communications and radio systems. He has also taught a radio systems course at the University of Toronto. Since 2002 he has been with Thales Rail Signalling Systems designing, developing and installing radio communication networks for urban rail systems.   Dr. Bantin has maintained an active research program in electromagnetics, antennas and radio propagation. His major areas of interest are wave propagation, antennas, and time domain analysis.