Calculation of Circuit Losses

Author: Edmund A. Laport

In solving for the reactance required in a network of given performance, the choice of potential and current values at the beginning of the problem is immaterial and determined by convenience only. For definite design applications, however, it may be best to work the problem with potential and current values corresponding to the power expected in reality.

Fig. 5.42:

The values derived from the completed vector diagram then not only provide the necessary network solution but show the currents and potentials existing at all points in the circuit. On this basis, the power loss and circuit efficiency can be computed with little effort, provided that the dissipation factors (Q's) of the reactive elements are known approximately. The vector diagrams are worked out on the assumption that the reactive elements are lossless. less the Q of a reactance is less than 20, this is correct enough for drawing the diagrams. Finally, to determine the losses which were previously neglected, it is necessary only to calculate the energy in each reactance by multiplying the potential across it by the current through it. This reactive energy in volt-amperes, divided by the Q of the reactance, gives the power loss in watts for the element. With synthesis made easy, many networks can be examined with the view of obtaining minimum energy storage and therefore minimum circuit loss.