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Theoretical foundations of electrical engineering

# Problems solving in electrical engineering – Construction of the operator equivalent circuit

The essence of the operator method is that functions of a real variable t which is called the original, is assigned to the complex variable p which is called the image. As a result, derivatives and integrals of the originals are replaced with algebraic functions of the corresponding images (differentiation is replaced with multiplying by the operator p and integration is replaced with dividing by it) which in turn determines the transition from a system of integral-differential equations to a system of algebraic equations for images of variables. In solving these equations it is necessary to find images and then originals by the reverse transition.

The main principle of the transient processes solution by the operator method is transformation of the usual electrical circuit to the operator equivalent circuit of the variable p. The received scheme is calculated by any known method (by nodal potential method, loop method or equivalent transformation method).

The figures below show the electric circuit diagram and its operator equivalent circuit, respectively:

Thus there are rules of the main elements transformation in the electrical circuit:

• Active resistance remains unchanged;
• Capacitor with capacity C is replaced with two elements – capacitor 1/pC and EMF source Uc(0)/p, which characterizes the initial charge on the capacitor;
• Inductor L is replaced with two elements – inductor pL and EMF source L·iL(0), which characterizes the initial current through the inductor;
• Constant source of EMF or current J, E are replaced with J/p and E/p, respectively.
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