Chapter Conductance

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

  • Imagine that you have a 300-Ω television antenna, and you want the best possi-ble reception. You purchase “300-Ω” ribbon line, with a value of Zo that has been op-timized by the manufacturer for use with antennas whose impedances are close to300j0.For a system having an “impedance” of “R Ω,” the best line Zo is also RΩ. If R ismuch different from Zo, an unnecessary amount of power will be wasted in heating upthe transmission line. This might not be a significant amount of power, but it often is. Impedance matching will be discussed in more detail in the next chapter.ConductanceIn an ac circuit, electrical conductance works the same way as it does in a dc circuit.Conductance is symbolized by the capital letter G. It was introduced back in chapter 2.The relationship between conductance and resistance is simple: G1/R. The unitis the siemens. The larger the value of conductance, the smaller the resistance, and themore current will flow. Conversely, the smaller the value of G, the greater the value ofR, and the less current will flow.SusceptanceSometimes, you’ll come across the term susceptance in reference to an ac circuit con-taining a capacitive reactance or an inductive reactance. Susceptance is symbolized bythe capital letter B. It is the reciprocal of reactance. That is, B1/X. Susceptance canbe either capacitive or inductive. These are symbolized as BC and BL respectively.Therefore, BC1/XC, and BL1/XL.There is a trick to determining susceptances in terms of reactances. Or, perhapsbetter stated, a trickiness. Susceptance is imaginary, just as is reactance. That is, all val-ues of B require the use of the j operator, just as do all values of X. But 1/jj. Thisreverses the sign when you find susceptance in terms of reactance.If you have an inductive reactance of, say, 2 ohms, then this is expressed as j2 in theimaginary sense. What is 1/(j2)? You can break this apart and say that 1/(j2)(1/j)(1/2)(1/j)0.5. But what is 1/j? Without making this into a mathematical treatise,suffice it to say that 1/jj. Therefore, the reciprocal of j2 is –j0.5. Inductive sus-ceptance is negative imaginary.If you have a capacitive reactance XC10 ohms, then this is expressed as XCj10. The reciprocal of this is BC1/( j10)(1/ j)(1/10)(1/ j)0.1. What is1/ j? Again, without going into deep theoretical math, it is equal to j. Therefore, thereciprocal of j10 is j0.1. Capacitive susceptance is positive imaginary.This is exactly reversed from the situation with reactances.Problem 15-5 Suppose you have a capacitor of 100 pF at a frequency of 3.00 MHz. What is BC?First, find the reactance XC by the formulaXC1/(6.28fC)Susceptance275