496 BELL SYSTEM TECHNICAL JOURNAL 



determined from the law of force exerted by a moving charge on a sta- 

 tionary charge. This approach leads to one or two integral equations which 

 can be approximated by a system of linear algebraic equations. M hile the 

 latter may seem much simpler than the differential ecuations obtained 

 from the natural network model, in reality their solution would often consti- 

 tute a much more difficult analytical problem. The natural network model 

 in which each mesh is coupled only to the adjacent meshes is in harmony 

 with the idea of continuous propagation of electromagnetic disturbances; 

 while the reduced network model conforms to the action at a distance 

 philosophy. The difference is merely in the language and ideas and not in 

 substance. 



Fig. 4 — Two possible modes of propagation in a symmetrically shielded parallel pair.* 



Finally, the third method is based on the idea that at certain frequencies, 

 called the natural frequencies, various parts of a closed system oscillate in 

 phase or 180° out of phase, that the most general natural oscillation is the 

 sum of such oscillations, and that the most general forced oscillation can be 

 expressed in terms of fields aszociated with the natural modes of oscillation. 

 We may call this the normalized network model of the electromagnetic field. 

 Thus far we have described it with reference to closed systems or cavity 

 resonators. In effect we have assumed that the amounts of magnetic and 

 electric energy are finite or else we could not talk about T and U functions. 

 The method can be extended to open systems of wave guides. 



Modes of Transmission 



Let us begin with a coaxial transmission line. Everyone is familiar with 

 the particular mode of transmission in which equal and opposite currents 

 flow in the two conductors. The circuit is completed through the dielectric 

 where the displacement current flows from one conductor to the other. 

 Next, consider a shielded parallel pair. If the structure is symmetric, we 

 shall recognize at once two modes of transmission, Fig. 4. In one mode, the 

 balanced mode, the currents in the wires are equal and opposite; there are 



* In the upper part of this figure one of the directional arrows should be reversed. 



