Capacitors and Inductors Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C.

Contents Introduction Capacitors Series and Parallel Capacitors Inductors Series and Parallel Inductors Applications

Introduction Ideal capacitors and inductors are storage elements that dissipate no energy during operation Both exhibit frequency-dependent characteristics

Capacitors A capacitor consists of two conducting plates separated by an insulator (or dielectric) The energy is stored in its electric field

Cont’d Types of capacitors –Electrolytic: low-frequency and high-capacitance (10 4  F) applications –Ceramic: high-frequency and small-capacitance (~1pF) applications –Polyester, mica, film, etc Capacitors are used to select RF channel, block dc, pass ac, shift phase, store energy, start motor, and suppress noise

Linear Capacitors Slope = C q q vv Linear Nonlinear

I-V Characteristic of Capacitor (a) fixed capacitor (b) variable capacitor

Power and Energy in Capacitor 0

Cont’d v t i t v +_+_ v +_+_ ISIS ISIS ISIS ISIS Charging Discharging ii

Properties of Capacitor A capacitor is an open circuit to dc. The voltage on a capacitor cannot change abruptly. Not allowedAllowed

Cont’d An ideal capacitor dose not dissipate energy. Capacitors can be used as memory devices –Volatile: DRAM –Nonvolatile: EPROM, Flash, etc The circuit model of a practical capacitor is shown below (100M  ) ()()

Example Find energy stored in each capacitor under dc conditions Capacitors replaced by open circuits

Parallel Capacitors

Series Capacitors

Inductors An inductor consists of a coil of conducting wire The energy is stored in its magnetic field

I-V Characteristic of Inductor (a) air-core (b) iron-core (c) variable iron-core

Power and Energy in Inductor 0

Properties of Inductor An inductor acts like a short circuit to dc. The current through an inductor cannot change abruptly. Not allowedAllowed

Cont’d An ideal inductor dose not dissipate energy. The circuit model of a practical inductor is shown below : winding capacitance : winding resistance

Example

Series Inductors

Parallel Inductors

Summary Parallel connectionsSeries connections

Linearity Investigations Homogeneity property: Additivity property: Both exhibit linearity properties

Applications: Integrator

Alternative Integrator Problem: Large i L due to small L under dc

Applications: Differentiator

Alternative Differentiator Problem: Large L is difficult to realize