Electrical and Electronic circuits simulation using Maxwell's equations

Question

How can the Maxwell equations be used for developing exact mathematical model of electrical and electronic circuits?

Answer 1

Circuit theory uses lumped element models connected by idealized lines. Maxwell's equations are used to model the lumped elements: inductors, capacitors, resistors. The same physical circuit may have to be modeled by more and more complicated combinations of such lumped as the frequency of operations increases. For example, a coil of wire at its simplest, i.e., at dc is just a resistor representing the wire's ohmic resistance, at some non-zero frequency it may be an inductor in series with that ohmic resistance, at some even higher frequency you have to take into account the capacitance between the neighboring windings, as well, etc. All that is from Maxwell's equations.

Depending on the size of the circuit and its operational frequency the connecting lines may also need to be modeled as distributed transmission lines, together with the parasitic inductive or capacitive couplings between the several circuit elements. And finally, to make the design engineer's life even more difficult, at some even higher frequency, your circuit will also be radiating as a lousy antenna would.