Capacitors (6.1); Inductors (6.2);
LC Combinations (6.3)
Dr. Holbert
April 5, 2006
ECE201 Lect-17
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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 electrical
loads:
– Capacitors model computers and other
electronics (power supplies).
– Inductors model motors.
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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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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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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=Cv
• The proportionality constant C is called
capacitance.
• Units of Farads (F) – Coulomb/Volt
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Capacitor
The
rest i(t)
of
the
circuit
+
v(t)
–
dv (t )
i (t )  C
dt
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Capacitor Voltage
t
1
v(t )   i ( x)dx
C 
t
1
v(t )  v(t 0 )   i ( x)dx
C t0
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Energy Stored
1 2
wC (t )  Cv (t )
2
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Class Examples
• Learning Extension E6.2
• Learning Extension E6.3
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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) - V·s/A
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Inductor
The
rest i(t)
of
the
circuit
+
H
v(t)
–
di (t )
v(t )  L
dt
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15
Inductor Current
t
1
i (t )   v( x)dx
L 
t
1
i (t )  i (t 0 )   v( x)dx
L t0
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Energy Stored
1 2
wL (t )  Li (t )
2
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Class Examples
• Learning Extension E6.4
• Learning Extension E6.5
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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
• Learning Extension E6.7
• Learning Extension E6.8
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