Introduction to Energy Storage Elements: The Capacitor

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Introduction to Energy Storage ElementsThe
Capacitor
2
Review

• So far, we have talked about two kinds of circuit
  elements
• Sources (independent and dependent)- active, can
  provide power to the circuit.
• Resistors-passive, can only dissipate power.

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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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Energy Storage is Fun!

• Voltages and currents in a circuit without energy
  storage elements are linear combinations of
  source voltages and currents.
• Voltages and currents in a circuit with energy
  storage elements are solutions to linear,
  constant coefficient differential equations!

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Even More Fun!

• Practicing engineers almost never solve the
  differential equations directly. They also
  almost never use the techniques in Chapter 6.
• Instead, they use
• LaPlace transforms (covered in EEE 302)
• AC steady-state analysis
• These techniques convert the solution of
  differential equations into algebraic
  problems-circuit analysis (eg the voltage
  divider) can be applied directly.

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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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Signal ProcessingCommunicationInstrumentation

• Capacitors and inductors are used to build
  filters and amplifiers with desired frequency
  responses
• RF and IF amplifiers in a superhetrodyne
  receiver.
• Instrumentation amplifiers.

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Signal ProcessingCommunicationInstrumentation

• Capacitors are used in A/D converters (PCM
  encoders) to hold a sampled signal until it can
  be converted into bits.

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Solid StateDigital Design

• Integrated circuits 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.
• The voltage difference between the two conductors
  is proportional to the charge
• q C v

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Capacitance

• The proportionality constant C is called
  capacitance.
• Units of Farads (F) - C/V

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Capacitor
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Capacitor Voltage
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Energy Stored
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Example
i(t)
The rest of the circuit

0.2F
v(t)
-
17
Find v(t)Find wc(t)
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Solution
wc(t)
2.5J
2s
1s
t