Complex admittances in parallel

Chapter Complex admittances in parallel

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

  • Megahertz and microhenrys go together in the formula. As for XC, recall the formulaXC1/(6.28fC). Convert 220 pF to microfarads to go with megahertz in the formulaC0.000220 µF. ThenjXCj(l/(6.28× 7.15× 0.000220))j101Now, you can consider the resistance and the inductive reactance to go together, soone of the impedance vectors is 330 j4490. The other is 0 j101. Adding these gives330j4389; this rounds off to Z 330j4390.Problem 16-8A resistor, coil, and capacitor are in series. The resistance is 50.0 Ω, the inductance is10.0 µH, and the capacitance is 1000 pF. The frequency is 1592 kHz. What is the com-plex impedance of this series RLC circuit at this frequency?First, calculate XL6.28fL. Convert the frequency to megahertz; 1592 kHz 1.592 MHz. ThenjXLj(6.28× 1.592× 10.0)j100Then calculate XC1/(6.28fC). Convert picofarads to microfarads, and use megahertzfor the frequency. Therefore,jXCj(l/(6.28× 1.592× 0.001000))j100Let the resistance and inductive reactance go together as one vector, 50.0 j100. Letthe capacitance alone be the other vector, 0 j100. The sum is 50.0 j100j10050.0j0. This is a pure resistance of 50.0 Ω. You can correctly say that the impedanceis “50.0 Ω” in this case.This concludes the analysis of series RLC circuit impedances. What about parallelcircuits? To deal with these, you must calculate using conductance, susceptance, andadmittance, converting to impedance only at the very end.Complex admittances in parallelWhen you see resistors, coils, and capacitors in parallel, you should envision the GB(conductance-susceptance) plane.Each component, whether it is a resistor, an inductor, or a capacitor, has an admit-tance that can be represented as a vector in the GB plane. The vectors for pure conduc-tances are constant, even as the frequency changes. But the vectors for the coils andcapacitors vary with frequency, in a manner similar to the way they vary in the RX plane.Pure susceptancesPure inductive susceptances (BL) and capacitive susceptances (BC) add together whencoils and capacitors are in parallel. Thus, BBLBC. Remember that BL is negativeand BC is positive, just the opposite from reactances.In the GB plane, the jBL and jBC vectors add, but because these vectors point in ex-actly opposite directions—inductive susceptance down and capacitive susceptanceup—the sum, jB, will also inevitably point straight down or up (Fig. 16-5).Complex admittances in parallel289