Inductors and Tuners
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Currents lead to magnetic fields
• One law of physics states that an electric
current gives rise to (is the source of) a
magnetic field.
– There are various versions of this law
associated with the following people
• André-Marie Ampère
• Jean-Baptiste Biot and Felix Savart
• James Clerk Maxwell
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A straight wire
• A current I flowing through a wire produces
a magnetic field B that encircles the wire.
B
I
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Right-hand rule
• If you are looking along the wire from the
source of the (positive) current, then the
magnetic field would go around the wire in
a clockwise direction.

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The  is meant
to imply that
the current is
going into the
slide.
4
A ring of current
• If the current goes around a ring, then the
magnetic field punches through the center of the
ring in one direction and wraps around to head in
the opposite direction on the outside of the ring.
B
B
I
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B Note the magnetic
fields are all up
inside the ring in
this picture.
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Current flowing through a coil
B
B
B
B
• A coil can be approximated
as a stack of rings. The
magnetic fields of all of the
rings add up to one big
magnetic field emanating
through the center of the
coil.
I
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Changing magnetic fields lead to
electric fields
• Another law of physics states that a
changing magnetic field gives rise to (is
the source of) a voltage difference. This
voltage can lead to an “induced” current.
– There are various versions of this law
associated with the following people
• Michael Faraday
• Heinrich Lenz
• James Clerk Maxwell
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Demo
Connect a coil of wire to an
ammeter. Move a magnet
near the coil. This changing
magnetic field will produce
a current in the circuit.
The current is proportional
to the rate of change of the
magnetic field as well as the
area of the coils – think of as
the area of a loop times the
number of loops.
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Why UTP is twisted
• UTP – unshielded twisted pair wire that is
used for standard Ethernet connections
twists the wires to have the opposite effect
as our coil. Our coil has a large area, UTP
is twisted to minimize the area and thus
reduce any induced current due to magnetic
fields in the environment.
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Don’t go changing
• The current in our coil led to a magnetic field.
• If the current changes then that magnetic field
changes, and that leads to a voltage.
• That voltage leads to its own current in the coil.
• That induced current opposes the change in the
current that caused.
• Analogous to “inertia” objects in motion tend to
remain in motion.
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Reduce current flowing through a coil
B<B0
I<I0
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• Decreasing current leads to
an induced current that
adds to the original current,
tending to keep it the same.
i
Induced current
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Increase current flowing through a coil
B>B0
I>I0
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• Increasing current leads to
an induced current that
subtracts from the original
current, tending to keep it
the same.
i
Induced current
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Inductor
• A circuit element that opposes changes in the
current is known as an inductor.
• They are also known as coils (since they tend to
have that shape) and chokes.
• The units of inductance is the henry.
– Named after Joseph Henry, an American scientist who
studied electricity and magnetism discovering a number
of effects independent of Michael Faraday. Joseph was
also the first Secretary (director) of the Smithsonian
Institution.
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A circuit with just a resistor
With just a resistor, when the
switch is flipped the current
(immediately) jumps up to
the value given by Ohm’s
law I = V/R.
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An LC Circuit: an inductor (L) and a
resistor (R) in series
With an inductor in
series, the current
changes more slowly
eventually reaching
the value given by
Ohm’s law.
The circuit
above has an
unusually high L
and low R to
achieve a large
effect.
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Effect of Inductor
• Recall that the effect of an inductor is to
oppose changes in current.
• It does not stop the change in the long run,
but rather smoothes out its effect over time.
• The LR circuit obeys mathematics similar
to that of an RC circuit.
– V(t) = Vs (1 – e-t/)
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Also slows down the decrease in current
V(t) = V0 e –t/
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The circuit shown below is an RC when the
switch is on the upper setting and an LC
circuit on the lower setting.
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Behavior of previous circuit
RC
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LC
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Time base changed to examine the
LC circuit behavior
LC
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The period (time from maximum to maximum) is 6.5904 ms
or 0.0065904 s. The frequency is the reciprocal of the
period 1/0.0065904 s  152 Hz.
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Periodic Behavior of LC Circuit
• The charged capacitor wants to get rid of its
charge (i.e. to get the charge on the positive
plate to travel around and meet up with the
negative charge or vice versa).
• To do this, there must be a current.
• Since there was not previously a current, the
inductor will tend to keep the current from
growing too quickly.
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Slow
down. Not
so fast.
Let’s get
out of here
+++++++ ++++++++
------- --------
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Periodic Behavior of LC Circuit (Cont.)
• The current ultimately gets established and the
capacitor discharges.
• But the inductor will not let the current diminish
very quickly.
• Thus the current continues and the capacitor
begins to charge again. This time the plate that
was positive now becomes negative.
• The current will diminish but it the time it takes
the capacitor will again become charged.
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Keep that
current
coming.
+
+
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+
I’m happy
now.
+
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Periodic Behavior of LC Circuit (Cont.)
• Eventually we reach the same situation we started
with – a charged capacitor and no current (just that
the plates have the opposite charge from before)
and the process starts over again.
• Another way to view the process is in terms of
energy. The capacitor stores energy in an electric
form and the inductor stores energy in a magnetic
form. The energy switches back and forth
between electric and magnetic.
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Slow
down. Not
so fast.
Let’s get
out of here
------- -------+++++++ ++++++++
It’s dejavu all over
again
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Natural frequency
• The LC circuit has a periodic behavior. Period
behavior is characterized by a frequency – the
number of cycles exhibited per second (measured
in Hertz).
• We call the frequency exhibited by the LC circuit
by itself the LC circuit’s “natural frequency” to
distinguish it from the “driving frequency” which
we introduce next.
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In the circuit shown above we add a signal generator that
applies a periodic voltage to the system. It is said to “drive” the
system.
Since the applied voltage is periodic, it has its own frequency,
known as the “driving frequency.”
In the case shown above, the driving frequency is 60 Hz.
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Some
transient
behavior
The resulting frequency is 1/0.0164062 s  61 Hz is
essentially the driving frequency.
Note that the resulting amplitude is 0.442 V.
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Let us take the same circuit and drive it at a frequency
that is close to its natural frequency and see what
happens.
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The resulting frequency is 1/0.0067014  149 Hz (again the
driving frequency).
But look at the amplitude 7.2 volts. Much larger than the
previous amplitude of 0.442 V.
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For completeness, let us drive the circuit at a frequency
that is higher than its natural frequency and see what
happens.
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The resulting frequency is 1/0.005 = 200 Hz (again the
driving frequency).
But look at the amplitude 1.95 volts, smaller than the
amplitude obtained at the natural frequency.
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Resonance
Note the meaningless definition followed by a reasonable explanation.
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Radio: Transmitter
• Now we are in a position to understand
radio.
• In the transmitter a carrier signal (simple
sine wave) is modulated (usually at a lower
a frequency than the carrier.
• This modulated signal is amplified and fed
into an antenna so that the transmitting
antenna has a large varying current in it.
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Radio: Wave
• The varying current in the antenna produces a
varying magnetic field.
• That varying magnetic field produces a varying
electric field.
• That varying electric field produces a varying
magnetic field.
• And so on.
• This is an electromagnetic or radio wave
propagating through space and carrying our
information away from the source/transmitter.
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Radio: Receiver
• Our radio wave happens by an antenna. Because
of the varying electric field, a current is
established in our antenna.
• We are receiving/detecting the signal.
• But lots of other people are sending signals and
we are receiving their signal as well.
• Fortunately there is a large range of possible
carrier frequencies and we can use these to
distinguish one signal from another.
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Electromagnetic Spectrum
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Radio: Tuner
• Our LC circuit serves as a simple tuner.
• Using the notion of resonance, we can pick out a
particular frequency by making an LC circuit with
a natural frequency that matches the carrier
frequency.
• Signals close to the natural frequency emerge from
the LC tuner with a large amplitude, any signal
much higher or lower in frequency is suppressed.
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Radio: Filter/Demodulator
• Another step is required. The information
must be stripped away from the carrier.
• We can use the time constant associated
with an RC circuit here in a way the times
faster then the time constant are smoothed
over but times longer than the time constant
remain.
• We saw a circuit like this in our last lab.
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Filter Circuit
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Final Step
• The final step, now that we have the
original (demodulated) signal is to amplify.
• Amplification uses transistors which we
have not introduced yet.
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References
• Electronics The Easy Way, Miller and
Miller
• http://electronics.howstuffworks.com/induct
or.htm/printable
• http://electronics.howstuffworks.com/oscilla
tor.htm/printable
• http://electronics.howstuffworks.com/radio.
htm/printable
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