barcode in vb.net 2005 The j factor might be negative, of course, so there are times you ll write Y in Software

Encoder Quick Response Code in Software The j factor might be negative, of course, so there are times you ll write Y

The j factor might be negative, of course, so there are times you ll write Y
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Parallel circuits
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Recall 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 why parallel circuits were ignored in those discussions. The reason is that admittance, rather than impedance, is best for working with parallel ac circuits. Therefore, the subject of parallel circuits was deferred. Resistance and reactance combine in rather messy fashion in parallel circuits, and it 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 the analysis of parallel ac circuits. The situation is similar to the behavior of resistances in parallel when you work with dc. While the formula is a bit cumbersome if you need to find the value of a bunch of 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 difference. Parallel circuit analysis is covered in detail in the next chapter.
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The GB plane
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Admittance 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 negative conductance. (You can t have something that conducts worse than not at all.) Conductance is plotted along the horizontal, or G, axis on this coordinate half plane, and susceptance is plotted along the B axis. The plane is shown in Fig. 15-9 with several points plotted. Although the GB plane looks superficially identical to the RX plane, the difference is great indeed! The GB plane is literally blown inside-out from the RX plane, as if you had jumped into a black hole and undergone a spatial transmutation, inwards out and outwards in, turning zero into infinity and vice-versa. Mathematicians love this kind of stuff. The center, or origin, of the GB plane represents that point at which there is no conduction 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 corresponds to a perfect open circuit. The open circuit in the RX plane is way out beyond sight, infinitely far away from the origin. In the GB plane, it is the short circuit that is out of view.
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278 Impedance and admittance
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15-9 Some points in the GB plane, and their components on the G and B axes.
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Formula for conductance
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As you move out towards the right ( east ) along the G, or conductance, axis of the GB plane, the conductance improves, and the current gets greater, but only for dc. The formula for G is simply G 1/R
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where R is the resistance in ohms and G is the conductance in siemens, also sometimes called mhos.
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Formula for capacitive susceptance
It won t hurt to review the formulas for susceptance again. They can get a little bit confusing, especially after having worked with reactance.
Why all these different expressions 279 When you move upwards ( north ) along the jB axis from the origin, you have ever-increasing capacitive susceptance. The formula for this quantity, BC, is BC 6.28fL siemens
where f is in Hertz and C is in farads. The value of B is in siemens. Alternatively, you can use frequency values in megahertz and capacitances in microfarads. The complex value is jB = j(6.28fC). Moving upwards along the jB axis indicates increasing capacitance values.
Formula for inductive susceptance
When you go down ( south ) along the jB axis from the origin, you encounter increasingly negative susceptance. This is inductive susceptance; the formula for it is BL 1/(6.28fL) siemens
where f is in Hertz and L is in henrys. Alternatively, f can be expressed in megahertz, and L can be given in microhenrys. The complex value is jB j(1/(6.28fL). Moving downwards along the jB axis indicates decreasing values of inductance.
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