Advanced Electric Circuits by A. M. P. Brookes and P. Hammond (Auth.)

By A. M. P. Brookes and P. Hammond (Auth.)

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Once more a single frequency equivalent is easily found and may be as shown in Fig. 8(a) and (b). c 60 ADVANCED ELECTRIC CIRCUITS In a good inductor r should be much less than the reactance a>L and therefore coL/r is a useful measure of the efficiency of the inductor. Cl)L\ QL = For the capacitor, coC\r (b) (o) F I G . 8 At audio and radio frequencies, QL = 10-300 for wound inductors and at audio and radio frequencies Qc> 100 for normal capacitors. The relations between the equivalent circuits (a) and (b), Fig.

10. —T— c ^REtotol parallel loss >r=totol series loss F I G . 9 F I G . 10 If the circuit is a smey resonant one we should compound the series equivalent circuits, so that total loss = rL + r^ If it is a parallel resonant one we compound the parallel equivalents.

In Fig. 1 be replaced by sinusoidal alternating voltage sources which all have the same frequency, and the resistance R±, R2. . by complex impedances Z i , Z 2 . . , the proofs of the superposition theorem and the reciprocity theorem remain valid for steady-state conditions. NETWORK THEOREMS 27 If the alternating voltage sources have different frequencies, we cannot use complex impedances because impedance is a function of frequency. However, by writing down the mesh equations in the form of differential equations, we can prove that the superposition theorem is still valid for steady-state conditions.

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