The GB Plane

Some points in the complex admittance plane, and their conductive and susceptive components on the axes.
Admittance can be depicted on a plane similar to 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 a component 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 GB plane is shown in above figure, with several points plotted. It’s Inside Out.

The GB plane looks superficially identical to the RX plane. But mathematically, the two could not be more different! The GB plane is mathematically inside out with respect to the RX plane. The center, or origin, of the GB plane represents the point at which there is no conduction for dc or for ac. It is the zero-admittance point, rather than the zero-impedance point. In the RX plane, the origin represents a perfect short circuit, but in the GB plane, the origin corresponds to a perfect open circuit.

As you move out toward the right (east) along the G, or conductance, axis of the GB plane, the conductance improves, and the current gets greater. When you move upward (north) along the jB axis from the origin, you have ever-increasing positive (capacitive) susceptance. When you go down (south) along the jB axis from the origin, you encounter increasingly negative (inductive) susceptance.

Vector Representation of Admittance

Complex admittances can be shown as vectors, just as can complex impedances. In below figure, the points from above figure are rendered as vectors.

Generally, long vectors in the GB plane indicate large currents, and short vectors indicate small currents. Imagine a point moving around on the GB plane, and think of the vector getting longer and shorter and changing direction. Vectors pointing generally northeast, or upward and to the right, correspond to conductances and capacitances in parallel. Vectors pointing in a more or less southeasterly direction, or downward and to the right, are conductances and inductances in parallel.
Vectors representing the points of above figure


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