Hi Gang! I'm going to talk about selecting a coil and
capacitor for a parallel LC resonant circuit. Basically, that's this coil and this capacitor
used in many crystal radios. This is something I get asked about a lot
in the comments to my crystal radio videos. Hopefully this video will help with that,
and with other projects that have parallel coils and capacitors. What do we mean by a parallel LC resonant
circuit? First, here's some background. We'll use this model of the crystal radio. We'll ignore the rest of it for now. This is the coil, and this is the capacitor. What do we mean when we say they're in parallel? The end of the coil
is connected to this end of the capacitor. And this wiper blade connects the other end
of the coil to the other end of the capacitor. You can ignore this section here
since it amounts to just an unpowered loop of wire. So connecting in parallel
means that the opposite ends of the coil and capacitor
are connected together. That's important here
because that allows them to resonate at a specific frequency. Let's illustrate that. Let's pick a point in time when the capacitor
is charged, positive charge on one side
and negative charge on the other. Since the coil is just a wire with low resistance,
the capacitor is basically shorted out. At first it's almost as if we'd connected the
two sides with a simple wire. And so it'll begin to discharge. The charge will begin flowing from one capacitor
plate, through the coil,
to the other. Current flowing in a coil creates a magnetic
field around that coil. Notice that the magnetic field lines have
a direction indicated by arrows. That's determined by the direction of the
current. The current won't be constant though,
because capacitors don't discharge at a constant rate. The current will gradually increase,
and as a result, so will the magnetic field's strength. The current will exist until there's no more
charge on the capacitor. But a magnetic field exists only
when there's a current flowing through the coil. Since the capacitor is discharged,
there's no more current, and so the magnetic field starts to collapse. The magnetic field collapsing
then causes current to flow in the wire. That current flows in the same direction
as it did when the magnetic field was expanding. And notice now that that current is charging
the capacitor. But also notice that the charges on the capacitor
plates are the opposite of what they were before. That makes sense
since the current was flowing in the same direction as it was before. Eventually the magnetic field is fully collapsed. We're also back to where we started with a
charged capacitor, no current and a short circuit. The energy that was in the magnetic field
is now stored in the electric field in the capacitor. And since we essentially have a short circuit,
the capacitor starts to discharge. But since the capacitor was charged the opposite
way, the current flows in the opposite direction
from before. That again creates a magnetic field around
the coil, which reaches its maximum just as the capacitor
is discharged. With no more energy in the capacitor to drive
the current, the magnetic field collapses,
charging up the capacitor again, but with the charges on opposite sides this
time, back the way it was when we started. The whole thing repeats again,
and so on. But it doesn't go on forever. When the current is flowing through the wires,
there's a little heating going on. That heat is energy
and is a loss to the surroundings. So each time the magnetic and electric fields
will be weaker, and the current will be lower, Except that in this crystal radio,
there's this short coil here, called an antenna coil,
which is connected to an antenna, which is receiving energy from the incoming
radio waves. Those waves create current in the antenna,
and in the short coil, which creates an expanding and collapsing
magnetic field that moves across some of our resonant coil's
wires, causing current to flow. It's adding a little energy
to make up for the energy lost to heat, and keeps the cycle going. Each time the current flows in one direction
and then reverses and flows in the other direction is considered one complete cycle. That complete cycle always takes the same
amount of time. And so there are a specific number of cycles
happening per second. That cycles per second is the frequency. We further call it the resonant frequency. And instead of saying it's the cycles per
second, we say it's some number of Hertz. Change some things about either the coil or
the capacitor and the frequency will change too. Those things are the inductance of the coil
and the capacitance of the capacitor. If we want this parallel circuit
to resonate at different frequency then we'll need change either the coil's inductance
or the capacitor's capacitance. Knowing that,
we can finally talk about selecting the coil and capacitor. This example is of a crystal radio
which receives AM radio. The radio station we're trying to listen to
has a specific frequency. That's the number you see in the radio station's
name: 1310 NEWS,
or TSN 1200. It's also what you see on the radio dial. That 1200 is actually 1,200 kilohertz. One kilohertz is 1000 hertz,
or 1000 cycles per second. Typical AM radio frequencies for medium waves
are in the range 525kHz to 1700kHz. So we need to select a coil and capacitor
combination that will resonate somewhere in that frequency
range. To do so we start with this formula. It's the formula for the resonant frequency
of a coil and capacitor connected in parallel. The L is the coil's inductance
and the C is the capacitor's capacitance. It's for that reason we call this a parallel
LC circuit. We have a coil's inductance, L,
in parallel with a capacitor's capacitance, C. A typical capacitor for these radio circuits
has a capacitance of 365pF, which is often adjustable from 40pF to 365pF. In my How to Make a Crystal Radio video
I show how to make one of these adjustable capacitors
in the shape of two cylinders. You can also buy variable capacitors that
have that range and there are links for that in the video
description. I also have a video all about capacitance
and making capacitors and there'll be a link for that at the of
this video. All links are also in the video description. But let's say our capacitor is adjusted for
somewhere in between its range, say it's set for 250pF. Instead we'll do the adjusting to select a
frequency using this wiper blade on the coil. The capacitor is in parallel with the coil
by connecting to one end of the coil and to the wiper blade. The wiper blade can be moved across the top
of the coil, making contact in different places. The section on this side isn't involved and
doesn't matter. So the section of the coil that's in use
is the section between this end and the wiper blade. By moving the blade along,
you change the inductance, L, and therefore the resonant frequency. This is the formula for the inductance of
a coil. Notice it includes things like the number
of turns, the cross sectional area,
the length of the coil, and something representing the material the
wires are wrapped around. I have a video all about designing coils for
specific inductances and I'll give a link to it at the end of this
video. I also have a calculator on my website for
calculating the inductance. Again, all links are also in the video description. For this coil,
using the inductance formula, with the wiper blade out here so that we're
using the full coil, the inductance is 369 microhenries. Plugging that and the 250pF capacitance
into the resonant frequency formula we get that the parallel LC circuit will resonate
at 524 kilohertz. Remember, we wanted to be able to adjust for
a range of 525 kilohertz to 1700 kilohertz,
so that handles the bottom end of the range. Next, we move the wiper blade all the way
to here where there are just 10 turns in this section. This time,
using the induction calculator on the coil design webpage,
we put in the values for the coil we're designing, but only 10 turns. If we don't know how long the coil will be
then we can put in the wire diameter and it'll figure out the length on its own. The inductance is 43 microhenries. Switching to the webpage with the LC resonance
calculator, we plug that in,
and get 1535 kilohertz, which is less than the 1700 kilohertz we want. So we go back to the inductance calculator
webpage and put in 8 turns instead. That gives us 35 microhenries,
and putting that in the LC resonance calculator we get 1701 kilohertz. Perfect. So our coil and capacitor will give us
the full 525 kilohertz to 1700 kilohertz range. Well, thanks for watching! See my youtube channel for more informative
videos like this. You can support these videos either through
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