Chapter 11Chapter 11Inductors
The Basic Inductor
• When a length of wire is formed onto a coil, it
becomes a basic inductor
• Magnetic lines of force around each loop in the
winding of the coil effectively add to the lines of winding of the coil effectively add to the lines of
force around the adjoining loops, forming a strong
electromagnetic field within and around the coil
• The unit of inductance is the henry (H), defined as
the inductance when one ampere per second
through the coil, induces one volt across the coil
Factors that determine the inductance of a coil
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
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Inductors in DC Circuits
• When there is constant (DC) current in an
inductor, there is no induced voltage
• There is a slight voltage drop in the circuit • There is a slight voltage drop in the circuit
due to the winding resistance of the coil
• The coil basically appears as a short to DC
FIGURE 11-2 Symbol for the inductor.
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
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Basic Symbol for a Coil
FIGURE 11-9 Symbols for fixed and variable inductors.
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
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FIGURE 11-10 Inductor symbols.
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
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Typical Inductors
Winding resistance of a coil
•The small inherent wire resistance is called the dc
resistance or the winding resistance (RW)
•It is usually ignored
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Winding capacitance of a coil
•When many turns of wire are placed close
together in a coil, there is a winding capacitance
(CW)
•CW may become significant at high
frequencies
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Self-Inductance
• Inductance is a measure of a coil’s ability to
establish an induced voltage as a result of a
change in its currentchange in its current
• The induced voltage opposes the change in
current (vind)
Faraday’s and Lenz’s Laws
• Recall Faraday’s law:
– The amount of voltage induced in a coil is directly proportional to the rate of change of the magnetic field with respect to the coilwith respect to the coil
• Recall Lenz’s law:
– When the current through a coil changes:
• An induced voltage is created as a result of the changing electromagnetic field
• The direction/polarity of the induced voltage is such that it always opposes the change in current
Induced Voltage in the Series RL
Circuit
• At the instant of switch closure, the inductor
effectively acts as an open with all the source
voltage across it
• During the first 5 time constants, the current is • During the first 5 time constants, the current is
building up exponentially, and the induced coil
voltage is decreasing
• The resistor voltage increases with current
• After 5 time constants, all of the source voltage is
dropped across the resistor and none across the coil
Coil appears
as an open
Resistor and Coil Voltages in an Energizing Circuit
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Coil appears
as a short
10V instantaneously
induced in the coil
trying to keep current
flowing in same
direction
Resistor and Coil Voltages in a De-Energizing Circuit
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
After Vind decays,
there is no current
RL Time Constant
• Because the inductor’s basic action opposes
a change in its current, it follows that
current cannot change instantaneously in an current cannot change instantaneously in an
inductor
ττττ = L/R
where: τ is in seconds (s)
L is in henries (H)
R is in ohms (Ω)
Exponential Formulas
• RL Time Constant = L/R
• The special formula for determining instantaneous
current values for an RL circuit from zero is:
i =I (1 - e-Rt/L ) => I (1 - )i =IF (1 - e-Rt/L ) => IF (1 - )
• The special formula for determining instantaneous
current values an RL circuit to zero is:
i =Iie-Rt/L => Ii
Energizing Current in an Inductor
• In a series RL circuit, the current will increase to
approximately 63% of its full value in one time-
constant (τ) interval after the switch is closed
• The current reaches its final value in • The current reaches its final value in
approximately 5τ
Circuit Current in a an Energizing Circuit
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Energizing current in an inductor
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
De-energizing Current in an
Inductor
• In a series RL circuit, the current will decrease to
approximately 37% of its fully charged value one
time-constant (τ) interval after the switch is closed
• The current reaches 1% of its initial value in • The current reaches 1% of its initial value in
approximately 5τ; considered to be equal to 0
Circuit Current in a De-Energizing Circuit
At t = 0,
instantaneous
current
remains the
same
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
De-energizing current in an inductor
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Series Inductors
• When inductors are connected in series, the total
inductance increases
LT = L1 + L2 + L3 + … + Ln
Parallel Inductors
• When inductors are connected in parallel, the total
inductance is less than the smallest inductance
1/LT = 1/L1 + 1/L2 + 1/L3 + … + 1/Ln
Inductors in AC Circuits
• An increase in frequency induces more
voltage across the inductor in a direction to
oppose the current and causes it to decrease oppose the current and causes it to decrease
in amplitude
• The polarity of induced voltage is such that
the resulting induced current is in a
direction that opposes the change in the
magnetic field that produced it
Inductive Reactance
• Inductive reactance is the opposition to
sinusoidal current, expressed in ohms
• The inductor offers opposition to current, • The inductor offers opposition to current,
and that opposition varies directly with
frequency
• The formula for inductive reactance, XL, is:
XL = 2πf L
The current in an inductive circuit varies inversely with the frequency of the source voltage
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Higher Frequency = Higher XL
For a fixed voltage and fixed frequency, the current varies inversely with the inductance value
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
More Inductance = Higher XL
Phase Relationship of Current
and Voltage in an Inductor
• The voltage leads inductor current by 90° (ELI)
• The current lags inductor voltage by 90°
• The curves below are for a purely inductive circuit• The curves below are for a purely inductive circuit
Current is always lagging the inductor voltage by 90º
V
Current Lags
the Voltage by
90 Deg
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
IOr:
Voltage Leads
the Current by
90 Deg (ELI)
Power in an Inductor
• Instantaneous power (p) - the product of v and i
gives instantaneous power
• True Power (Ptrue) - ideally is zero, since all power
stored by an inductor in the positive portion of the true
stored by an inductor in the positive portion of the
power cycle is returned to the source during the
negative portion (is shifted back and forth). If
winding resistance is taken into account, the true
power is:
Ptrue = (Irms)2RW
Power curve for an inductor
Reactive
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
•Power is maximum when I and V are
equal (either positive or negative)
•Power is zero when either I or V are
zero
Instantaneous Values
Reactive Power
• The rate at which an inductor stores or
returns power is called its reactive power
(Pr), with units of VAR (volt-ampere (Pr), with units of VAR (volt-ampere
reactive)
Pr = VrmsIrms
Pr = V2rms/XL or
Pr = I2rmsXL
Quality Factor (Q) of a Coil
• The quality factor (Q) is the ratio of the reactive power in
the inductor to the true power in the winding resistance of
the coil or the resistance in series with the coil
• A theoretically perfect coil would have a Q of 1• A theoretically perfect coil would have a Q of 1
Q = (reactive power) / (true power)
Q = XL/RW
Checking a coil by measuring the resistance
Troubleshooting:
•Coils usually open
•Some windings short out from time to time effecting performance
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Basic capacitor power supply filter with a series inductor
Power Supply Application
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
An inductor used as an RF choke to minimize interfering signals on the power supply line
Power Supply Application
Thomas L. Floyd
Electronics Fundamentals, 6e
Electric Circuit Fundamentals, 6e
Copyright ©2004 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
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