3-Lesson_Notes_Lecture15_ee205 - Lecture 15 The analysis of...

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Lecture 15 The analysis of the RLC series resonant circuit is continued. This lecture covers: The dependence of impedance and current on frequency Concepts of band frequency, cut-off frequency and half power frequency Expressions for band frequencies Relationship of quality factor with bandwidth Expressions for selectivity Total impedance (Z T ) versus frequency C RL E s I Z T Fig. 15-1: Series resonant circuit We have seen that the total impedance of a series RLC circuit at any frequency is, TL L C Z RJ X J X =+ The magnitude and phase angle of impedance as a function of frequency can be written as, 22 ( ) [ ( )] [ ( ) ( )] C Zf R f X f X f
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Here, Z T (f) means the total impedance as a function of frequency. The changes of the various terms R, X L , X C , total X, Z T as a function of frequency are shown in the following figures. f 0 R(f) R Fig. 15-2(a) R as function of frequency We know the resistance of a circuit does not change with frequency
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2 L Xf L π = 2 y Lm x == () L y x f 0 Fig. 15-2 (b) X L as function of frequency Inductive reactance is 2 times pi times f times L. Hence the plot of X sub L is a straight line as a function of frequency
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1 2 C X fC π = () C Xf f 0 Fig. 15-2 (c) X C as function of frequency Capacitive reactance is reciprocal of 2 times pi times C . Hence plot of X sub C is a hyperbolic curve
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C X L X L C X X > L C XX > X 0 f s f Fig. 15-2 (d) Net X as function of frequency At low frequency X sub C is very high and X sub L is very small. At
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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_Lecture15_ee205 - Lecture 15 The analysis of...

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