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!
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