# Inductor as insulator?

My question may seem a little controversial, but as I've been studying electronics for a short time, this question arose and I imagine that many of those who read it were able to help me.

From what I have studied, one of the properties of the inductor is to store energy in the form of a magnetic field when a current is applied to it.

According to the formula that determines the inductive reactance of inductors, the higher the frequency, the greater the impedance it presents.

If an inductor were subjected to a very high frequency, would it be possible for it to behave close to an insulator, due to the fact that its resistivity increases exaggeratedly?

• If you're asking whether inductors can form low-pass filters (filters which pass low frequencies and reject high frequencies), yes, they can. People don't usually refer to this filtering as "insulation" though. Feb 26 at 16:55
• I think you're conflating the impedance of the inductor at some frequency with its overall resistivity . Feb 26 at 16:55
• Yes, it can be thought as an "AC insulator". Feb 26 at 16:55
• If you consider a varying signal as an AC and DC component together, the DC component still gets through. And lower frequency components get through easier. Feb 27 at 11:32

# Looking for imaginative explanations

Your question is interesting and thought provoking. So I suggest we forget for a moment the traditional boring textbook explanations and try to answer it with only the help of our imagination. We can test our ideas step by step through CircuitLab. Here is a possible scenario.

# Stopping current through resistance

Looking at it in a more "philosophical" way, your question is actually about how we can stop the current in a circuit.

## Perfect conductor

If we close the circuit of a voltage source through a piece of wire, a huge current will flow through this perfect conductor. Since CircuitLab does not like such a short connection, I have set a very low (1 Ω) internal resistance of the ammeter. So the current is limited to 1 A according to Ohm's law I = Vin/RA.

simulate this circuit – Schematic created using CircuitLab

If we sweep (linearly change) Vin, the current changes linearly.

## Imperfect conductor

Then, if we close the circuit through a resistor R, the current meets with another opposition according to Ohm's law I = Vin/R (here the ammeter is perfect with zero resistance). Therefore, the resistor is an imperfect conductor.

simulate this circuit

The current changes linearly as above.

## Real insulator

If we start increasing the resistance all the way to infinity, it will increasingly interfere with the current and eventually cut it off altogether. We have effectively removed the resistor, and there is no current because air is a real insulator. So this was one possible way to break the current with a real insulator.

simulate this circuit

# Stopping current through voltage

Is it possible to interrupt the current in any other way than by increasing the resistance? Can we close the circuit with an element that is not an insulator but behaves as such? Let's think.

## Virtual insulator

Indeed current is controlled by resistance but created by voltage. So if we want no current, there must be no voltage. The input voltage is independent of us so we cannot change it. However, we can neutralize the input voltage by an equal but opposite voltage, and the result would be the same - no current. Eureka!

For this purpose, we can insert another but opposing voltage source in the place of the resistor and adjust its voltage VL so that to make it equal to the input voltage. If we are too lazy to do it, we can take a behavioral voltage source and set its voltage to be equal to Vin.

simulate this circuit

The result is amazing - the current stops flowing as if the circuit is broken! The additional voltage source acts as a virtual insulator (open circuit or simply, "nothing").

This trick is known as "bootstrapping" and is widely used to virtually increase resistance.

## Virtual AC&DC insulator

We can apply an AC input voltage or even a combination of AC & DC voltage, and the "copying voltage source" will continue behaving as an "insulator".

simulate this circuit

## Inductor AC insulator

This is how an inductor behaves - it produces a voltage that opposes the input AC voltage and neutralizes it. As a result, the current does not change. In this sense, the inductor can be considered as a "virtual insulator".

simulate this circuit

(Ignore the yellow graphic; it is only to "cheat" CircuitLab autoscaling).

# Stopping vs diverting

Having decided to reveal the "philosophy" behind circuits, let's note that this way of stopping current by a resistance or opposing voltage source in series is only possible if the input source is an imperfect current source (made by a voltage source and a resistor in series).

If it is "ideal" (perfect), its current, like the water of a raging mountain river, cannot be stopped because the source will raise (theoretically to infinity) its internal voltage with the idea of overcoming the obstacle. In this case, the current can only be diverted through another device in parallel. This technique is known as "current steering".

• A good example of dumbing down: it produces a voltage that opposes the input AC voltage and neutralizes it. It opposes the voltage just as much as the volt drop across a 628 kohm resistor would (the current being circa 1.6 uA peak). Your statement propagates the falsehood that the back-emf from an inductor dictates the current flow into that inductor. Clearly, a 100 uH inductor produces the same back emf but, the current will be 1.6 amps peak. Feb 27 at 11:09
• @Andy aka, Here I have set myself the goal of roughly showing the two ways of "stopping" the current - by resistance and by voltage. My view of the inductor is that it does it the second way, and instantly. How else but with "counter voltage" could it do it since it's obviously not a resistor? The capacitor does it in the same way - through "counter voltage" , only with a delay. Feb 27 at 16:23

If an inductor were subjected to a very high frequency, would it be possible for it to behave close to an insulator

Yes. Inductors are used widely in RF circuits to block RF signals while allowing DC to pass. For example in a bias tee circuit, or to provide power to various kinds of amplifiers and other circuits.

due to the fact that its resistivity increases exaggeratedly?

The resistivity of the inductor doesn't change. It's the reactance that changes. "Resistivity" implies that energy is consumed (turned into heat) by the device. Reactance only stores and then later releases electrical energy. They are different concepts and you should be sure not to confuse them.

Also resistivity is the intensive property of a material that makes it useful for constructing a resistor. Resistance is the extensive property of a device made from a resistive material that gives the ratio of voltage across it to current through it at DC.

There are devices (ferrite beads) that have frequency-dependent resistance, but that doesn't seem to be what you're asking about.

Reactance isn't resistivity, but yes, this is a common technique. The term is "RF choke".

An inductor gives "inertia" to current. When a voltage is applied across an inductor, current gradually starts flowing. When you want it to stop flowing, you have to apply the opposite voltage to make it gradually slow down. If you force the current to stop flowing, the inductor will create the opposite voltage. (The equation does not say which one is cause and which one is effect.)

We say that inductors let DC through, because the current eventually gets up to whatever it would be if the inductor wasn't there.

simulate this circuit – Schematic created using CircuitLab

The yellow chart shows the current in the circuit without the inductor. The blue chart shows the current in the circuit with the inductor. It takes about 5 seconds to reach the same current that it would be if the inductor wasn't there.

I used a 1-Henry inductor in the simulation for simplicity, but realistic inductors are more like micro-Henries to milli-Henries and they will reach the full current in microseconds to milliseconds.

So that's what an inductor does. What's this stuff about "blocking AC"? If you think about it, if you use AC power, the voltage will start going down before the current has gone all the way up, so the current never gets to the full amount. You can see in the DC experiment, the voltage is only about 60% after 1 second. If the voltage reversed after 1 second (this would be a 0.5Hz square wave) the current would never be able to get higher than 60%. In fact, here's the simulation of that:

simulate this circuit

Not only does the current only get to 60% (the first time, then it stabilizes at about 50%), the current is going in a kind of curvy triangular wave instead of a square one. That makes sense, since it's the first part of the last graph repeated over and over.

It should be easy to see that if we increase the frequency, the current will get less high, too. If the frequency is 5 times higher than before, now the current only gets to about 10% of the full amount, before the square wave flips and the current decreases again:

This is what people mean when they say inductors block AC, and they block higher frequencies better. If we apply a voltage but the current doesn't flow, the current is blocked - that's what blocked means. If we apply an AC voltage but the AC current doesn't flow, the AC current is blocked. And you can see that an inductor lets through DC (eventually) but mostly blocks AC (depending on the frequency and other things).

I'm using a square wave because I think it makes for a better basic understanding since you can see how the current is just parts of the first graph stitched together. If the AC voltage is a sine wave, the current also works out to be another sine wave:

simulate this circuit

Notice, though, that the highest current doesn't happen at the same time as the highest voltage. The highest current comes when the voltage is zero and just about to go negative. And once the current stabilizes, the current is zero when the voltage is highest. This is called a phase shift.

If you divide the voltage by the current in a resistor, you calculate its resistance. If you divide the AC voltage by the AC current in an inductor, or a capacitor, or anything else for that matter, you calculate something that is a lot like resistance, that we call impedance. If you do it in complex numbers, it also magically accounts for phase shifts properly. I won't go into the details of that. As you can see, as the frequency gets higher, so does the impedance.

There's one more thing I want to show you. What if we use AC and DC at the same time? Or more than one AC frequency? You ready for a complicated graph? Here we go:

simulate this circuit

So we put in a 1 volt DC, and 1 volt of low frequency AC, and 1 volt of high frequency AC. (Well, relatively low and relatively high. They're both pretty low since I'm still telling it to simulate a huge 1-Henry inductor.)

And if you don't get intimidated by the orange wave being all over the place you can see that all of the DC got through just fine, after several seconds. You can see that the low frequency got reduced to about 10% of its normal value, and you can see that the high frequency is barely there at all. All at the same time!

Yes, that's right: if you put several frequencies in at the same time, each one gets "processed" separately. Weird how that is, but the math just works out that way.

So can you apply high frequency voltage to an inductor and then block DC with it because its impedance is high? Absolutely not. But can you still block the high frequencies? Yes. An inductor has low impedance to DC and high impedance to high frequency AC at the same time.

Even though it sounds kind of lame that you can't make an adjustable insulator, this is actually way cooler when you realize what it means. This lets you separate different frequencies out of a single combined wave. With combinations of inductors to block low frequencies and capacitors to block high frequencies, you can make a kind of "frequency filter" that only lets through the exact frequencies you want. This is how radios (including things like Wi-Fi) tune to specific radio stations instead of hearing all of them at the same time. Without this, wireless communication would be impossible.

IRL, an inductor will have a self resonant frequency SRF.
From DC to, say, one decade below the SRF its impedance will rise pretty much in proportion to frequency.
From one decade above, impedance is bound to fall for a couple of decades.
Behaviour at SRF depends on the "Quality Factor" QF of the resonance circuit it should be considered at this frequency.
With a high QF, I'm inclined to see impedance increases exaggeratedly here.
I wouldn't call it isolation / insulator even where used to block unwanted HF.

• Beware SRF depends on assembly in addition to component properties. Feb 27 at 16:43