C.T. Tai

Plane wave reflection and refraction involving a finitely conducting medium

In this work the structure of electromagnetic field in a lossy conducting medium is studied in detail. The meaning of the complex angle of refraction is explained in terms of real parameters involved in this problem. The concepts are illustrated with a wave refracting from air into pure water at a frequency of 95 GHz and an incidence angle of 60/spl deg/. The approach is similar to that used to derive refraction in many electromagnetic textbooks, such as Stratton (J. A. Stratton, 1941), which has been cited in many of the textbooks published since. Our results agree with his for the real angle of the equiphase surface of the refracted fields, but we explore further subjects, including the instantaneous and time-averaged Pointing vectors.

Direct integration of field equations

Summary form only given. The integral equations of the field equations in electrostatics, magnetostatics, and electrodynamics are derived with the aid of a scalar-vector Greens theorem which can be obtained by several different approaches. One of them is to start with the vector Greens theorem first formulated by Stratton. The steps lead to the scalar-vector Greens theorem is outlined. The integration of the field equations can then be executed readily using that theorem. The results can be interpreted in terms of potential functions if so desired but they are not necessary. In fact, these interpretations are not unique. The second part of this work consists of a review of Stratton and Chus (1939) famous formula. It is shown that the diffraction integrals obtained by Franz (1948) with the aid of the dyadic Greens functions can be derived readily from Stratton and Chus formula by means of some simple vector identities. Schelkunoffs (1951) claim that his formulas are stronger than Stratton and Chus formula is without foundation. In the first place he never demonstrated where his strength is. In fact, it can be shown that his expressions are equivalent to Franzs expressions which are derivable from Stratton and Chus formula. Finally, it should be pointed out that the line integral deliberately added by Stratton and Chu to compensate for the discontinuity of the fields across the edge of an aperture is really not necessary because this line integral as a result of Meixners edge condition is a null integral.

A critical study of the circuit relations of two distant antennas

In this work, we present a critical study of the circuit relations for two distant coupled antennas: either both are transmitting, or one is transmitting and one is receiving. We found that Carters two mutual impedances, Z/sub 12/ and Z/sub 21/, are not applicable to these two cases. Two sets of circuit relations have been formulated, with two sets of wave impedances, to characterize these new circuit relations. It is shown that the coupled wave impedances are not equal to each other, and they satisfy a conjugate relation with a negative sign. Such a relation also applies to Carters Z/sub 12/ and Z/sub 21/.

A new theory of receiving antennas

We have made a thorough examination of the existing theory of receiving antennas, particularly its equivalent circuit and we have formulated a new theory. The formulation is based on the classical theory of scattering, and by revising the well-known circuit relations for coupled antennas formulated by P.S. Carter (see Proc. IRE, vol.20, p.1004-41, 1932). The new theory enables us to revise not only the equivalent circuit but many related parameters, such as the impedance matching factor, the polarization matching factor, the receiving cross-section, and the generalized Friiss transmission formula.

Notation in vector analysis

After a brief comment on the work by Chen et al. (IEEE Transactions on Education, vol.41, no.1, p.61-9, February 1998), the author suggests a vector notation system for the electromagnetics community. The concepts of gradient, divergence and curl together with matrix operators are discussed.

From the Historian-another matter of history (scalar product)

The basic incorrectness of the scalar product approach to deriving the differential expression for the divergence of a vector function in the Cartesian system is demonstrated. The origin of the approach is traced, and its ubiquity in the literature is documented.<<ETX>>

A comparison of the classical theory and the scattering theory of receiving antennas

The theory of receiving antenna is one of the subjects developed in the early period of radio engineering. We will designate the theory formulated by A.F. Stevenson in 1948 as the classical theory and the theory formulated recently by the present author as the scattering theory of receiving antennas. The two theories we quite different. We will review the classical theory first and point out a useful feature of that theory. An outline of the new theory will then be presented. In the new theory we treat the receiving antenna as a lossy scattering body. Poyntings theorem is applied to the transmitting/receiving system to derive the equivalent circuit relations. Unlike the classical theory, the power relation of the system is automatically satisfied. One important feature of the new theory shows that the mutual impedances between the transmitting antenna and the receiving antenna are not equal to each other.

Teaching electrodynamics without magnetism

This communication is based on a lecture note that was written by this author 35 years ago, for a course in electromagnetic theory given at the University of Michigan. The original note was passed to some students and a few personal friends over the years. There are several aspects of the note that may be of interest to professionals teaching EM theory, and to students who have not been exposed to the relativistic foundation of EM theory. This work can also be treated as a supplement to the works of Page [ 11 and Elliott [2 ] , wherein Maxwell’s equations are obtained from the electrostatic equations with the aid of Einstein’s special theory of relativity 131. In our presentation, we follow closely the work of Sommerfeld [4] to describe the transformation of the field quantities in two inertial systems. In this writing, we have adopted the new operational notation for the divergence and the curl. The rationale and the logic of introducing this new notation are explained fully in Chapter 8 of the author’s book on vector analysis [SI.

Loaded transmission line as a two-port network

A college homework problem, dealing with a loaded transmission line, is reviewed. The setup is then treated as a two-port distributed network. The law of conservation of power is explained with the aid of a scattering theory. Two coupled circuit relations are then formulated. One, associated with the load terminals, is quite different from the conventional equation involving the self impedance and the mutual impedance. An effective impedance function, designated as the scattering impedance, is introduced to facilitate the formulation. The result of applying the Rayleigh/Carson reciprocity theorem to find the expression of the load current is also discussed.

A fundamental theorem on the maximum frequency of coherent oscillations by Robert S. Elliott

Summary form only given. Elliott (J. Appl. Phys. 23, 812-18, 1952) enunciated an important theorem on the maximum frequency limit for electron beam oscillators. The theorem is based on several physical laws. The first law states that the average power supplied by an electron beam to the field must be equal to the total average power lost by the resonant structure, including the useful output power and the ohmic loss. The second law states that the product of the frequency of oscillation and the average stored energy of the device must be greater than the average output power. The third law invokes the quantum theory of radiation. It implies that the minimum stored energy should be at least equal to the average noise energy level. With these laws at his disposal, Elliott was able to formulate his theorem. The author reviews Elliotts paper, showing the key formulation, and the proof of the theorem and its application to the design of klystrons and magnetrons. The author points out the inherent limitations of these devices in generating coherent oscillations in the optical spectra.<<ETX>>