Lecture Notes 9_Reactive

The switch s closes for a fraction a of the time a is

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Unformatted text preview: 717) Capacitors and Inductors: 9 – 9 / 12 Average Current/Voltage 9: Capacitors and Inductors • Capacitors • Types of Capacitor • Inductors • Passive Components • Series and Parallel For a capacitor i = C dv . Take the average of both sides: dt 1 t2 −t1 Inductors • Series and Parallel Capacitors • Current/Voltage Continuity • Average Current/Voltage • Buck Converter • Power and Energy • Summary t2 t1 idt = = C t2 −t1 1 t2 −t1 t2 t1 v (t ) C dv dt = dt 2 [v ]v(t1 ) = C t2 −t1 C t2 −t1 v (t2 ) v (t1 ) dv (v (t2 ) − v (t1 )) (1) If v (t1 ) = v (t2 ) then the average current exactly equals zero. (2) If v is bounded then the average current → 0 as (t2 − t1 ) → ∞. The average current through a capacitor is zero and, likewise, the average voltage across an inductor is zero. The circuit symbols remind you of this. “Average” can either be over an exact number of periods of a repetitive waveform or else the long-term average (provided v and i remain bounded). “v is bounded” means |v | always stays less than a predefined maximum value. E1.1 Analysis of Circuits (2013-3717) Capacitors and Inductors: 9 – 9 / 12 Buck Converter 9: Capacitors and Inductors • Capacitors • Types of Capac...
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