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Unformatted text preview: LECTURE 4. TRANSIENT ANALYSIS MAE307 Applied Electronics Instructor: Prof. Inkyu Park Department of Mechanical Engineering Korea Advanced Institute of Science and Technology (KAIST) Review of Lecture #3 MAE307 Applied Electronics Ideal Capacitor Device that can store energy in the form of a charge separation when polarized by an electric field (i.e. voltage). Two electrodes separated by dielectric material in between (eg. air, mica, or Teflon). CV Q = MAE307 Applied Electronics Capacitor acts as an open circuit in the presence of DC current (no flow of current due to dielectric materials). Capacitance (C): a measure of the ability of the device to accumulate (i.e. store) charge. Unit=F (farad) Ideal Capacitor (cont’d) Current flows in the presence of changing electric field (i.e. voltage). ) ( ) ( t Cv t q = dt t dv C dt t dq i ) ( ) ( = = t d t i t d t i t d t i t v t C t C t C C ′ ′ + ′ ′ = ′ ′ = ∞ ∞ ) ( 1 ) ( 1 ) ( 1 ) ( Voltage across the capacitor is obtained by the integration of current. ) ( ) ( t Cv t q = MAE307 Applied Electronics C C C t ∫ ∫ ∫ ∞ ∞ ) ( ) ( 1 t v t d t i C t t C + ′ ′ = ∫ Energy stored in the capacitor: ∫ ∫ ∫ ′ ′ ′ ′ = ′ ′ ′ = ′ ′ = t d t d t dv C t v t d t i t v t d t P t W C C C C C C ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 1 ) ( ) ( 2 t Cv t Cdv t v C C C = ′ ′ = ∫ Ideal Inductor Element that has the ability to store energy in a magnetic field. Magnetic field around a current carrying conductor tends to resist changes in the current (electromotive force; EMF) Typically made by winding a coil of wire around a core (insulator or MAE307 Applied Electronics ferromagnetic material). In ideal inductor, the wire has zero resistance. → In case of DC bias, it works as a short circuit. dt t di L v L ) ( = IV relation: Inductance (unit: Henry, H) Ideal Inductor (cont’d) Inductor current ) ( ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ( t i t d t v L t d t v L t d t v L t d t v L t i L t L L t L t L L + ′ ′ = ′ ′ + ′ ′ = ′ ′ = ∫ ∫ ∫ ∫ ∞ ∞ Energy storage in inductors ∫ ∫ ∫ ′ ′ ′ ′ = ′ ′ ′ = ′ ′ = t d t d t di L t i t d t v t i t d t P t W L L L L L L ) ( ) ( ) ( ) ( ) ( ) ( = ′ ′ = ) ( 1 ) ( ) ( 2 t Li t Ldi t i L L L MAE307 Applied Electronics ∫ 2 L L L Example dt t di L v L L ) ( = ) ( ) ( 1 ) ( t i t d t v L t i L t t L L + ′ ′ = ∫ Solution of (Dynamic) Circuits Containing Energy Storage Elements Apply KVL / KCL / node voltage method / mesh current method (SAME) But the circuit analysis now becomes differential equations. dt t dv C t i R t v t v t i C C C S R ) ( ) ( ) ( ) ( ) ( 1 = = = ) ( 1 ) ( 1 ) ( t v RC t v RC dt t dv S C C = + A * KCL at node A MAE307 Applied Electronics * KVL around mesh ) ( ) ( ) ( 1 = t v t Ri t v C R S ) ( 1 ) ( ) ( = ′ ′ ∫ ∞ t C C S t d t i C t Ri t v ) ( ) ( 1 t i t i C R = ∫ ∞ ′ ′ = t C C t d t i C t v ) ( 1 ) ( In differential equation form, dt t dv...
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This note was uploaded on 11/21/2010 for the course MECHANICAL mae302 taught by Professor Jang during the Spring '10 term at Seoul National.
 Spring '10
 jang
 Mechanical Engineering

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