barcode in vb.net 2010 The GB Plane in Software

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The GB Plane
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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 Fig. 15-9, with several points plotted.
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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.
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The GB Plane 241
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15-9 Some points in the
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complex admittance plane, and their conductive and susceptive components on the axes.
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Vector Representation of Admittance Complex admittances can be shown as vectors, just as can complex impedances. In Fig. 15-10, the points from Fig. 15-9 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.
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15-10 Vectors representing
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the points of Fig. 15-9.
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242 Impedance and Admittance
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Quiz
Refer to the text in this chapter if necessary. A good score is 18 or more correct. Answers are in the back of the book. 1. The square of an imaginary number (a) can never be negative. (b) can never be positive. (c) can be either positive or negative. (d) is equal to j. 2. A complex number (a) is the same thing as an imaginary number. (b) has a real-number part and an imaginary-number part. (c) is one-dimensional. (d) is a concept reserved for elite mathematicians. 3. What is the sum of 3 + j 7 and 3 j 7 (a) 0 + j0 (b) 6 + j14 (c) 6 j14 (d) 0 j14 4. What is ( 5 + j 7) (4 j5) (a) 1 + j2 (b) 9 j2 (c) 1 j2 (d) 9 + j12 5. What is the product ( 4 j 7)(6 j2) (a) 24 j14 (b) 38 j34 (c) 24 j14 (d) 24 + j14 6. What is the magnitude of the vector 18 j24 (a) 6 (b) 21 (c) 30 (d) 52 7. The complex impedance value 5 + j0 represents (a) a pure resistance. (b) a pure inductance.
Quiz
(c) a pure capacitance. (d) an inductance combined with a capacitance. 8. The complex impedance value 0 j22 represents (a) a pure resistance. (b) a pure inductance. (c) a pure capacitance. (d) an inductance combined with a resistance. 9. What is the absolute-value impedance of 3.0 j 6.0 (a) Z = 9.0 (b) Z = 3.0 (c) Z = 45 (d) Z = 6.7 10. What is the absolute-value impedance of 50 j235 (a) Z = 240 (b) Z = 58,000 (c) Z = 285 (d) Z = 185 11. If the center conductor of a coaxial cable is made to have a smaller diameter, all other things being equal, what will happen to the Zo of the transmission line (a) It will increase. (b) It will decrease. (c) It will not change. (d) There is no way to determine this without knowing the actual dimensions. 12. If a device is said to have an impedance of Z = 100 , you can reasonably expect that this indicates (a) R + jX = 100 + j0. (b) R + jX = 0 + j100. (c) R + jX = 100 + j100. (d) the reactance and the resistance add up to 100 . 13. Suppose a capacitor has a value of 0.050 F at 665 kHz. What is the capacitive susceptance, stated as an imaginary number (a) BC = j4.79 (b) BC = j4.79 (c) BC = j0.209 (d) BC = j 0.209
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