Capacitors (5.1); Inductors (5.2); LC Combinations (5.3)

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Capacitors (5.1) Inductors (5.2) LC
Combinations (5.3)

• Prof. Phillips
• March 7, 2003

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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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Power Generation and Distribution

• Energy storage elements model information and
  power
• Capacitors are important components of
  electronics (logic circuits, filters and power
  supplies).
• Inductors are important for power and
  communications (motors, radio).

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Signal ProcessingCommunicationInstrumentation

• 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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Solid StateDigital 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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Electromagnetics

• For high frequency signals, inductance and
  capacitance are more significant effects than
  resistance.

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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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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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Capacitor
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Capacitor Voltage
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Energy Stored
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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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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) - Vs/A

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Inductor

The rest of the circuit
i(t)
v(t)
H

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Inductor Current
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Energy Stored
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Inductor Combinations

• Series inductors combine like series resistors
• Lser L1 L2 L3
• Parallel inductors combine like parallel
  resistors
• 1/Lpar 1/L1 1/L2 1/L3

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Capacitor Combinations

• Series capacitors combine like parallel resistors
  (opposite)
• 1/Cser 1/C1 1/C2 1/C3
• Parallel capacitors combine like series resistors
  (opposite)
• Cpar C1 C2 C3

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Class Examples