Methods of Electromagnetic Field Analysis* 



By S. A. SCHELKUNOFF 



This paper presents a discussion of ideas involved in various mathematical 

 methods of electromagnetic field analysis and of the inter-relations between 

 these ideas. It stresses the points of contact between circuit and field theories 

 and their mutually complementary character. While the field theory focuses our 

 attention on the electromagnetic state as a function of position in space, the 

 generalized circuit theory is preoccupied with the electromagnetic state as a 

 function of time. The points of contact between the field and circuit theories are 

 many. Thus, Maxwell's equations are identical with Kirchhoff's equations 

 (really Lagrange-Maxwell equations) of certain three-dimensional networks in 

 which only the adjacent meshes are coupled. The integral equations for the 

 electrical current in conductors embedded in dielectric media are also Kirchhoff 

 equations of certain networks containing infinitely many meshes with a coupling 

 between every two meshes. 



From the point of view of electrical performance the difference between a 

 physical network of lumped elements and a continuous network, such as a 

 resonator, is due to a certain difference in the distribution of the zeros and poles 

 of associated impedance functions in the complex impedance plane. Similarly, 

 the difference between ordinary transmission lines and wave guides is due to a 

 difference in the distribution of natural propagation constants. 



The paper ends with a general discussion of the discontinuities in wave guides, 

 idealized boundary conditions for simplification of electromagnetic problems, 

 and the analytical character of field vectors regarded as functions of the complex 

 oscillation constant. 



IX THE last few years engineering applications of electromagnetic field 

 theory have been greatly expanded. Field theory has become essential 

 for the solution of many practical problems and in planning engineering 

 experiments. Xew applications have influenced the theory itself and have 

 led to new conceptions. The chasm between the circuit theory of low 

 frequency electrical phenomena and the field theory of high-frequency 

 phenomena has disappeared. The two theories have met in wave guides 

 and their merger has become essential. This paper is a discussion of the 

 essential ideas underlying various mathematical methods of analysis of 

 electromagnetic oscillations and waves in the light of new applicatipns and of 

 the merger of the originally distinct circuit and field theories. 



CiRcurr Theory 



Circuit theory is a mathematical method and it should not be confused 

 with circuits. Empty space is neither a circuit nor a network; but as we 

 shall soon see, for the purposes of analysis the empty space can be treated as 

 a network. It is perfectly true that until recently circuit theory was con- 



* This paper was originally delivered as a lecture at a meeting sponsored by the Basic 

 Science Group of the American Institute of Electrical Engineers, April 12, 1945. 



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