If electromagnetic theory is 'science' then circuit theory is 'engineering'. One can appreciate how Ohm's circuital law follows from Ohm's electromagnetic law and Joule's loss of circuit theory from the concept of Poynting vector. Moreover, it is exciting to see that the dispersion relation of a hollow-pipe waveguide, that supports electromagnetic waves of RF phase velocity greater than the speed of light, can be derived not only by the electromagnetic theory but also by the circuit theory. Similarly, the dispersion relation of a helix slow-wave structure, used in a TWT that supports electromagnetic waves of RF phase velocity less than the speed of light, can be derived not only by the electromagnetic theory but also by the circuit theory. It turns out that the electromagnetic theory gives the interaction impedance of the structure measuring the RF electric field available for interaction with, say, electrons in a vacuum electron device, which cannot be provided by the circuit theory. On the other hand, the circuit theory has an advantage over the electromagnetic theory in that it uses a less number of boundary conditions at a time to derive a circuit parameter and that it can provide the characteristic impedance of the structure for the design of RF input and output couplers in an electron device.

Retd Professor of Electronics, IIT-BHU