3-Lesson_Notes_Lecture18_ee205 - Lecture 18 Parallel...

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Lecture 18 Parallel Resonant Circuit with Non-ideal Circuit Elements The following items are covered: Conversion of a practical tank circuit, with coil resistance, to an equivalent parallel resonant circuit with ideal elements Derivation of the expression for resonant frequency for the practical tank circuit Analysis of the effect of approximating the practical tank circuit Solve numerical example with the practical tank circuit Parallel Resonance with Practical Tank circuit The circuit for a practical tank circuit is shown in Figure 18-1 R l represents the resistance of the coil, having inductance L. R l X L X C Fig. 18-1 Practical tank circuit The resistance R l can no longer be included in a simple series or parallel combination with the source resistance and any other resistance for design purposes. Even though R l is usually relatively small in value compared with other resistance and reactance levels of the network, it does have an important impact on the parallel resonant conditions, as will be demonstrated through numerical example.
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First, our effort will be to find a parallel network equivalent of the series R-L branch of Fig.18-1. Now we will learn that a resistance R l in series with X L , as shown in Fig. 18-2 can be converted to an equivalent resistance R p in parallel with X Lp . 22 L l L R X X + = L l L R X R + = l R l X p R Lp X Fig.18-2 Parallel equivalent of two impedances in series The expressions of R p and X Lp in terms of R l and X L can be written as, L l p L RX R R + = L l Lp L X X + = Proof: optional The admittance of the series R l and X L
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This note was uploaded on 01/16/2010 for the course EE ee205 taught by Professor Profsyed during the Spring '09 term at King Fahd University of Petroleum & Minerals.

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3-Lesson_Notes_Lecture18_ee205 - Lecture 18 Parallel...

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