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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.

I

B

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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.

The is meant to imply that the current is going into the slide.

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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.

I

BB B Note the magnetic fields are all up inside the ring in this picture.

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Current flowing through a coil

• 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

B

B

B

B

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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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DemoConnect 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

• Decreasing current leads to an induced current that adds to the original current, tending to keep it the same.

I<I0

B<B0

iInduced current

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Increase current flowing through a coil

• Increasing current leads to an induced current that subtracts from the original current, tending to keep it the same.

I>I0

B>B0

iInduced 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 Henry 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 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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+++++++ ++++++++

- - - - - - - - - - - - - - -

Let’s get out of here

Slow down. Not

so fast.

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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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I’m happy now.

Keep that current coming.

+ +

+

+

+ +

+

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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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- - - - - - - - - - - - - - -

+++++++ ++++++++

Let’s get out of here

Slow down. Not

so fast.

It’s deja-vu 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. The times faster than the time constant are smoothed over but times longer than the time constant remain.

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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 in the “transition” phase – between the on and off we usually use in logic circuitry.

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References

• Electronics The Easy Way, Miller and Miller

• http://electronics.howstuffworks.com/inductor.htm/printable

• http://electronics.howstuffworks.com/oscillator.htm/printable

• http://electronics.howstuffworks.com/radio.htm/printable