The GB plane

Chapter The GB plane

Teach Yourself Electricity and Electronics Third Edition Book
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Summary of Contents

Teach Yourself Electricity and Electronics Third Edition Book

  • Admittance is the complex composite of conductance and susceptance. Thus, ad-mittance takes the formYGjBThe j factor might be negative, of course, so there are times you’ll write YGjB.Parallel circuitsRecall how resistances combine with reactances in series to form complex impedances?In chapters 13 and 14, you saw series RL and RC circuits. Perhaps you wondered whyparallel circuits were ignored in those discussions. The reason is that admittance, ratherthan impedance, is best for working with parallel ac circuits. Therefore, the subject ofparallel circuits was deferred.Resistance and reactance combine in rather messy fashion in parallel circuits, andit can be hard to envision what’s happening. But conductance (G) and susceptance (B)just add together in parallel circuits, yielding admittance (Y). This greatly simplifies theanalysis of parallel ac circuits.The situation is similar to the behavior of resistances in parallel when you workwith dc. While the formula is a bit cumbersome if you need to find the value of a bunchof resistances in parallel, it’s simple to just add the conductances.Now, with ac, you’re working in two dimensions instead of one. That’s the only dif-ference.Parallel circuit analysis is covered in detail in the next chapter.The GB planeAdmittance can be depicted on a plane that looks just like the complex impedance (RX)plane. Actually, it’s a half plane, because there is ordinarily no such thing as negativeconductance. (You can’t have something that conducts worse than not at all.) Conduc-tance is plotted along the horizontal, or G, axis on this coordinate half plane, and sus-ceptance is plotted along the B axis. The plane is shown in Fig. 15-9 with several pointsplotted.Although the GB plane looks superficially identical to the RX plane, the differenceis great indeed! The GB plane is literally blown inside-out from the RX plane, as if youhad jumped into a black hole and undergone a spatial transmutation, inwards out andoutwards in, turning zero into infinity and vice-versa. Mathematicians love this kind ofstuff.The center, or origin, of the GB plane represents that point at which there is noconduction of any kind whatsoever, either for direct current or for alternating current.In the RX plane, the origin represents a perfect short circuit; in the GB plane it corre-sponds to a perfect open circuit.The open circuit in the RX plane is way out beyond sight, infinitely far away fromthe origin. In the GB plane, it is the short circuit that is out of view.The GB plane277