Vector representation of admittance

Chapter Vector representation of admittance

Teach Yourself Electricity and Electronics Third Edition Book
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Teach Yourself Electricity and Electronics Third Edition Book

  • When you move upwards (“north”) along the jB axis from the origin, you haveever-increasing capacitive susceptance. The formula for this quantity, BC, isBC6.28fL siemenswhere f is in Hertz and C is in farads. The value of B is in siemens. Alternatively, you canuse frequency values in megahertz and capacitances in microfarads. The complex valueis jB = j(6.28fC).Moving upwards along the jB axis indicates increasing capacitance values.Formula for inductive susceptanceWhen you go down (“south”) along the jB axis from the origin, you encounter increas-ingly negative susceptance. This is inductive susceptance; the formula for it isBL1/(6.28fL) siemenswhere 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 jBj(1/(6.28fL).Moving downwards along the jB axis indicates decreasing values of inductance.Vector representation of admittanceComplex 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, longer vectors indicate greater flow of current, and shorter ones indicateless current.Imagine a point moving around on the GB plane, and think of the vector gettinglonger and shorter, and changing direction. Vectors pointing generally “northeast,” orupwards and to the right, correspond to conductances and capacitances in parallel.Vectors pointing in a more or less “southeasterly” direction, or downwards and to theright, are conductances and inductances in parallel.Why all these different expressions?Do you think that the foregoing discussions are an elaborate mental gymnastics rou-tine? Why do you need all these different quantities: resistance, capacitance, capacitivereactance, inductance, inductive reactance, impedance, conductance, capacitivesusceptance, inductive susceptance, admittance?Well, gymnastics are sometimes necessary to develop skill. Sometimes you need to“break a mental sweat.” Each of these expressions is important.The quantities that were dealt with before this chapter, and also early in this chap-ter, are of use mainly with series RLC (resistance-inductance-capacitance) circuits. Theones introduced in the second half of this chapter are important when you need to an-alyze parallel RLC circuits. Practice them and play with them, especially if they intimi-date you. After awhile they’ll become familiar.Why all these different expressions ?279