This video gives visual demonstrations of how inductors and high pass filters work. It shows the circuit, the equations, the time-varying inputs and outputs, and the frequency response plot.

The inductor is sort of 'storing up the current'

Current eventually flows through like it's a wire or short circuit

This is of course opposite of a capacitor, which initially allows current, then stops it

Now if we disconnect the inductor from the source and connect to a resistor instead

That sort-of-stored up current is released into this other resistor

Now instead of a DC input here let's go with a square wave with 20 Hz

This is going to cycle between -5 V to 5 V 20 times a second (slowing time down here though to show it), but this would be one cycle every 50 ms.

So lets see here what the voltage source looks like on a graph

It starts at 5, then down to -5, then back to 5, etc..

Now let's look at the voltage across the inductor

This is important because for a high pass RL filter, which I'm showing here, we use the voltage across the inductor as our 'output voltage'.

Notice as 5 volts is sourced, the voltage across the inductor initially follows this, but then quickly goes back to 0 as the inductor starts letting all the current through

When the voltage source drops to -5, the inductor voltage drops to –10 to account for the full 10 V swing, but then quickly goes back to 0.

When the voltage source rises to 5 again, the inductor voltage rises to 10 to again account for the full 10 V swing, but then quickly goes back to 0.

So most of the time here, or most of this 50 ms duty cycle, the voltage across the inductor is 0.

That means this signal at a frequency of 20 Hz would not 'pass', it would be 'blocked' for the most part, because, for the most part, our output voltage is tending towards 0, not the voltage of our source

Let's save this screenshot for a frequency response comparison later

Now let's crank this up to 85 Hz, which happens to be the cutoff frequency of this filter.

We know that’s the cutoff based on the equation

Notice the inductor starts off by matching the source voltage, then trails off to 0 like before

But before it gets too close to 0, the source switches again

So at this frequency, the source signal sort of passes, but it will be attenuated since the voltage across the inductor tending towards 0 for a good portion of the 50 ms duty cycle

Let's save this screenshot for a frequency response comparison later

Now let's crank this up to 1000 Hz, which is beyond the cutoff frequency.

Now you can see the inductor voltage never has enough time to drop or rise to 0

The voltage across the inductor matches, for the most part, the source voltage

This is because the inductor is not given enough time between the switching source voltages to act like a wire,

it acts more like an open circuit at higher frequencies

So we would say the voltage across the inductor is 'passing' the high frequencies

Thus, it acts as a 'high pass filter'

But lets take this screenshot here and compare how the voltage across the inductor responds at varying frequencies

Now let's visualize what we've shown on a frequency response graph.

So here the x axis represents frequencies in a log scale, and the y axis represents how much of the source signal gets through to the ouput.

So if we go on this graph to the frequency we just showed at 1 kHz, you can see the the loss is small, and this is where our output signal was pretty close to the input signal.

Then we go down to 85 Hzand you can see this curve has gone down a bit, this repsresents the –3dB where our output has lost about half the power of the input signal.

Then we go down to 20 Hz and you can see it's further down to around –13 dB, representing more attenuation of our source square wave

So you can see how using the voltage across the inductor as our output voltage yields a high-pass filter,

because it will pass the higher-frequency 1 kHz signal pretty closely

but will mostly reject the 20 Hz squarewave.

So this is how a high pass RL filter works

and as discussed this is due to the time delay inductors have with storing electrical energy.

If you're interested in how a low pass RL filter works, check out that video which goes a little bit quicker than this.

I also did videos on low and high pass RC filters, so you're of course welcome to check those out too.

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