Equivalent Circuits for Two-Dimensional Magnetic Fields: I - The Static Field

These papers describe electric circuit analogs for the 2-dimensional magnetic fields of synchronous machines. Although finite difference solutions of the differential equations are introduced to establish the mathematics, equivalent circuits are also deduced from elementary field and circuit theory familiar to electrical engineers. A simple resistive circuit is constructed to represent the static magnetic field with the ability to introduce any known currents and iron saturation. For the sinusoidally time-varying case, an RC analog is shown to represent the usual coupled circuit, and provides a most versatile tool for predicting eddy currents. Both the static and time-varying equivalent circuit should prove useful in the design of synchronous machines for the solution of magnetic problems for which numerical methods are necessary.