Parallel resonance

Chapter Parallel resonance

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

  • R0, that is, the resistor is a short circuit, then the circuit is called a series LC circuit,and the impedance at resonance will be extremely low. The circuit will offer practicallyno opposition to the flow of alternating current at the frequency fo. This condition is se-ries resonance.Parallel resonanceRefer to the circuit diagram of Fig. 17-12. This is a parallel RLC circuit. You rememberthat, in this case, the resistance R is thought of as a conductance G, with G1/R. Thenthe circuit can be called a GLC circuit.Calculating resonant frequency31917-12A parallel RLC circuit.At some particular frequency fo, the inductive susceptance BL will exactly cancelthe capacitive susceptance BC; that is, BL−BC. This is inevitable for some frequencyfo, as long as the circuit contains finite, nonzero inductance and finite, nonzero capaci-tance.At the frequency fo, the susceptances cancel each other out, leaving zero suscep-tance. The admittance through the circuit is then very nearly equal to the conductance,G, of the resistor. If the circuit contains no resistor, but only a coil and capacitor, it iscalled a parallel LC circuit, and the admittance at resonance will be extremely low.The circuit will offer great opposition to alternating current at fo. Engineers think moreoften in terms of impedance than in terms of admittance; low admittance translates intohigh impedance. This condition is parallel resonance.Calculating resonant frequencyThe formula for calculating resonant frequency fo, in terms of the inductance L in hen-rys and the capacitance C in farads, isfo0.159/(LC)1/2The1/2 power is the square root.If you know L and C in henrys and farads, and you want to find fo, do these calcu-lations in this order: First, find the product LC, then take the square root, then divide0.159 by this value. The result is fo in hertz.The formula will also work to find fo in megahertz (MHz), when L is given in mi-crohenrys (µH) and Cis in microfarads (µF). These values are far more common thanhertz, henrys, and farads in electronic circuits. Just remember that millions of hertz gowith millionths of henrys and millionths of farads.This formula works for both series-resonant and parallel-resonant RLC circuits.