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ECE201 Lect-171 Capacitors (6.1); Inductors (6.2); LC Combinations (6.3) Dr. Holbert April 5, 2006

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ECE201 Lect-172 Energy Storage Elements Capacitors store energy in an electric field. Inductors store energy in a magnetic field. Capacitors and inductors are passive elements: –Can store energy supplied by circuit –Can return stored energy to circuit –Cannot supply more energy to circuit than is stored.

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ECE201 Lect-173 Power Generation and Distribution Energy storage elements model electrical loads: –Capacitors model computers and other electronics (power supplies). –Inductors model motors.

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ECE201 Lect-174 Signal Processing Communication Instrumentation Capacitors and inductors are used to build filters and amplifiers with desired frequency responses: –Instrumentation amplifiers. Capacitors are used in analog-to-digital (A/D) converters to hold a sampled signal until it can be converted into bits.

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ECE201 Lect-175 Solid State Digital Design Integrated circuits (ICs) have layers of conductors (metal, silicon with impurities) with insulators (glass) between. This is a capacitor! This capacitance is one of the limiting factors in processor speeds. This capacitance is used to create RAMs.

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ECE201 Lect-176 Electromagnetics For high frequency signals, inductance and capacitance are more significant effects than resistance.

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ECE201 Lect-177 Capacitance Capacitance occurs when two conductors (plates) are separated by a dielectric (insulator). Charge on the two conductors creates an electric field that stores energy. +- - - - - - - - - - - - + + + + + + + +

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ECE201 Lect-178 Capacitance The voltage difference between the two conductors is proportional to the charge: q = C v The proportionality constant C is called capacitance. Units of Farads (F) – Coulomb/Volt

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ECE201 Lect-179 Capacitor i(t) + – v(t) The rest of the circuit

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ECE201 Lect-1710 Capacitor Voltage

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ECE201 Lect-1711 Energy Stored

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ECE201 Lect-1712 Class Examples Learning Extension E6.2 Learning Extension E6.3

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ECE201 Lect-1713 Inductance Inductance occurs when current flows through a (real) conductor. The current flowing through the conductor sets up a magnetic field that is proportional to the current. The voltage difference across the conductor is proportional to the rate of change of the magnetic field.

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ECE201 Lect-1714 Inductance The voltage difference across the inductor is proportional to the rate of change of the current. The proportionality constant is called the inductance, denoted L Units of Henrys (H) - V·s/A

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ECE201 Lect-1715 Inductor i(t) + – v(t) The rest of the circuit H

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ECE201 Lect-1716 Inductor Current

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ECE201 Lect-1717 Energy Stored

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ECE201 Lect-1718 Class Examples Learning Extension E6.4 Learning Extension E6.5

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ECE201 Lect-1719 Inductor Combinations Series inductors combine like series resistors L ser = L 1 + L 2 + L 3 + · · · Parallel inductors combine like parallel resistors 1/L par = 1/L 1 + 1/L 2 + 1/L 3 + · · ·

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ECE201 Lect-1720 Capacitor Combinations Series capacitors combine like parallel resistors (opposite) 1/C ser = 1/C 1 + 1/C 2 + 1/C 3 + · · · Parallel capacitors combine like series resistors (opposite) C par = C 1 + C 2 + C 3 + · · ·

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ECE201 Lect-1721 Class Examples Learning Extension E6.7 Learning Extension E6.8

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