Weird question I came up with, Inductors vs Capacitors energy storage

[OverlordCheese]

In general, our models say that inductors store magnetic fields, and capacitors store electric fields. My question is: which one is better at it? is there a "leakage current" equivalent for inductors?
basically I'm asking if there are any niche applications for an inductor integrator, or what advantages it can have.

[TimFox]

To maintain the field inside an air-core inductor, you need to keep the current flowing, which requires a short circuit across the terminals when the external power source is disconnected.  The total series resistance of that circuit is the analog of the leakage conductance in a capacitor.
With superconducting electromagnets (e.g., in MRI machines), the total series resistance is theoretically zero:  in practice, the current (and magnetic field) falls off very slowly.

[OverlordCheese]

Sorry, I think you misunderstood my question. Let's say I want to make a integrator circuit with a high accuracy. Does the inductor-integrator have any advantage over the capacitor integrator?

[TimFox]

In general, practical inductors have worse Q factors than can be obtained with capacitors.
If you build a circuit, the parasitic resistance of the inductor probably causes a higher error than the parasitic loss of a high-quality (polypropylene, etc.) capacitor.
Like most things, this question is quantitative.

[Benta]

To put it a bit differently:
Real capacitors are much closer to ideal capacitors than real inductors are to ideal inductors.

[SiliconWizard]

I suppose there is no inherent "difference" for ideal models. But real components are nothing ideal. Parasitics will all depend on construction and it's hard to give an answer without at least knowing the range of inductance or capacitance you're after and thus the kind of technology/package and so on. Inductors *may* have higher ESR depending on this, and of course if you consider inductors with ferrite cores, there's a whole range of potential issues, such as hysteresis.

One obvious factor is that inductors will be more susceptible to external magnetic perturbations, and just some metallic piece getting close to the inductor will throw off its inductance. Ways to protect such circuits are slightly different than protecting a capacitor-based topology.

[Benta]

You forgot interwinding capacitance, which is a major parasitic in inductors.
"Interelectrode inductance" (dunno if this is a valid term) is on the other hand easily avoidable in capacitors.

[TimFox]

You forgot interwinding capacitance, which is a major parasitic in inductors.
"Interelectrode inductance" (dunno if this is a valid term) is on the other hand easily avoidable in capacitors.

The parasitic series inductance of a capacitor determines its (first) self-resonant frequency (series resonance), as the parasitic parallel capacitance of an inductor gives it a parallel-mode self-resonant frequency.
For leaded capacitors, this inductance can depend mainly on the total length of the part from end to end, including leads, but even high-frequency MLCC capacitors have resonant modes.

[magic]

Sorry, I think you misunderstood my question. Let's say I want to make a integrator circuit with a high accuracy. Does the inductor-integrator have any advantage over the capacitor integrator?

That answer was exactly what you need to know.
Resistance of an inductor causes its current to decrease fairly fast even if the ends are shorted together.
Capacitors can hold charge for a long time.

It's easier to create an almost ideal open circuit than an almost ideal short.

[ejeffrey]

You forgot interwinding capacitance, which is a major parasitic in inductors.
"Interelectrode inductance" (dunno if this is a valid term) is on the other hand easily avoidable in capacitors.

That's ESL.  It's a problem in spiral wound electrolytic inductors (but those aren't good for high frequency anyway) but for most other inductors the ESL of the plates is negligible but the ESL of the leads is significant at higher frequency.

[Stray Electron]

  An inductor that stores roughly the same amount of energy as any given capacitor will be larger and much much heavier than a capacitor and with a LOT more copper (or other conductive metal) so it's also going to be more expensive than the capacitor. That's why you see fewer inductors than capacitors in AC filter circuits.

  To increase the power in a capacitor you must increase the area of the plates to increase capacitance or increase the thickness of the insulator to raise the voltage. In an inductor you must increase the number of windings (more metal) to increase the inductance or increase the size of the windings to increase the current. By now I'm sure that you're realized that the larger VERY thin capacitor plates are cheap as is the insulation and MUCH cheaper than the added amount of metal that would be required in a larger inductor. Large size inductors are rare in comparison to large size capacitors.

   That's not a bad question, it shows that you've been thinking about some of the practical aspects of circuit designs.

[oz2cpu]

I think it is a great question, and it is good you have been thinking about this,
the comments in this thread are good and usefull, and do explain it all.

I have only one minor "detail" to add..
the thread topic headline is : "Weird question I came up with"

this can mean anything, or nothing at all,
I simply and friendly suggest to try to use the full potential of this system,
it alow for much longer headlines,

for example : "Weird question I came up with, Inductors vs Capacitors energy storage"
I am sure it will attract more of the wanted people :-)

[Siwastaja]

Rule of thumb:
For mental equivalency:
* Swap "capacitor" and "inductor"
* Swap "current" and "voltage"
* Swap "series" and "parallel"
* Swap "open circuit" and "short circuit"
* Swap "zero" and "infinite" - i.e. scale numbers by 1/x


So it seems you are looking at longer-term (seconds or minutes or even more) energy storage capability.

Capacitor keeps the stored energy while open circuit. Leakage current is caused by parallel resistance (larger better).
Now repeat that sentence but do the above swaps:
Inductor keeps the stored energy while short circuit. Leakage voltage is caused by series resistance (smaller better).

With capacitors, it's perfectly possible to make parallel resistance in tens of megaohms. To make equally excellent inductors, the series resistance would need to be in 1 / tens of megaohms = below micro-ohms.

Why? Because materials like plastics and ceramics are excellent insulators, but copper is not equally excellent conductor.

With superconductors, storing energy in inductors for a long time is of course possible.

[Conrad Hoffman]

To keep things in perspective, energy density of either is lousy compared to a battery or a gallon of gasoline.

[TimFox]

Many years ago, ca. 1978, I attended a lecture by an engineer working on energy storage in very large superconducting solenoids, comparing this to very large flywheels.
The discussions about the strength of materials required to keep the solenoid from flying apart, compared with that required to keep flywheels intact was very detailed.
I think it involved the virial theorem (q.v.), but my memory so long after is not to be trusted.

[Conrad Hoffman]

AFAIK, forces and fields put a limit on what you can do with capacitors and inductors too.

[TimFox]

Yes.  For example, a charged vacuum capacitor that does not have insulating support to maintain the spacing between plates will collapse due to the mutual attraction of the opposite charges on the plates.

[Zero999]

You forgot interwinding capacitance, which is a major parasitic in inductors.
"Interelectrode inductance" (dunno if this is a valid term) is on the other hand easily avoidable in capacitors.

That's ESL.  It's a problem in spiral wound electrolytic inductors (but those aren't good for high frequency anyway) but for most other inductors the ESL of the plates is negligible but the ESL of the leads is significant at higher frequency.

The ESL is generally not much of a problem. Electrolytic capacitors still often have a low enough impedance to be useful, even at the frequency when they become purely inductive.  At higher frequencies multi layer ceramics are a better option and it's generally better to use the largest capacitance available, in the smallest case size, taking into account the effect of the capacitance being reduced at the operating voltage, due to saturation of the dialectic.

Inductors on the other hand often don't have a high enough impedance to be useful much above the resonant frequency. Using a larger component also pushes up the resonant frequency. The inductance of all cored inductance also goes down at high currents, due to saturation, which often occurs below the rated current.

[mawyatt]

Many years ago, ca. 1978, I attended a lecture by an engineer working on energy storage in very large superconducting solenoids, comparing this to very large flywheels.
The discussions about the strength of materials required to keep the solenoid from flying apart, compared with that required to keep flywheels intact was very detailed.
I think it involved the virial theorem (q.v.), but my memory so long after is not to be trusted.

Sperry (later acquired by Honeywell) had a facility in north Phoenix that produced large very high speed flywheels for space use. These were used for stored energy and controlled moment (satellite) movement. They had a test chamber where these were spun up that had very strong thick walls in case of failures which would disintegrate the wheel!

Porsche experimented with smaller flywheels for an experimental hybrid race car.

Best,

[Marco]

AFAIK energy density for inductive storage can actually be higher than capacitive even without superconductors. For certain pulsed power applications it can make sense, mostly railguns.

[Zero999]

AFAIK energy density for inductive storage can actually be higher than capacitive even without superconductors. For certain pulsed power applications it can make sense, mostly railguns.

For extremely short lengths of time yes, but efficiency is low, unless superconductors are used.

[tszaboo]

Actually, I would argue, that regular capacitors, like a film capacitor have energy storage properties much closer to an inductor.
The reason that electrolytic capacitors can store more energy, is because the dielectric layer is very thin, and the energy storage is inversely proportional. Chemistry turn is into nanotechnology. If we investigate inductors, for example a solenoid, L= turns^2 * area /length, we significantly increase the inductance, if we increase the turns, and reduce the length. For example flat wire inductors, or planar inductors. But that doesn't even get us into the ballpark or nanotechnology. So  the real question is, how do we make micrometer thickness wires, so we can increase the inductance significantly. And then how do we deal with the fact that the resulting magnetic field would saturate the core.

[Siwastaja]

Actually, I would argue, that regular capacitors, like a film capacitor have energy storage properties much closer to an inductor.
The reason that electrolytic capacitors can store more energy, is because the dielectric layer is very thin, and the energy storage is inversely proportional. Chemistry turn is into nanotechnology. If we investigate inductors, for example a solenoid, L= turns^2 * area /length, we significantly increase the inductance, if we increase the turns, and reduce the length. For example flat wire inductors, or planar inductors. But that doesn't even get us into the ballpark or nanotechnology. So  the real question is, how do we make micrometer thickness wires, so we can increase the inductance significantly. And then how do we deal with the fact that the resulting magnetic field would saturate the core.

Manufacturing of micrometer wire is not the problem. Core saturation is not the problem; if you can make a lot of turns, you can just use air core. (The only reason core is used today, is to reduce number of turns which need to be made of that crappy conductor called copper.)

The problem is the poor conductivity of the usual metals (like copper). We just don't have a simple, affordable material that enables storing energy in the form of sustained current ~ magnetic field, because the I²R losses are just huge. Compare this to capacitors which can store energy in form of sustained voltage ~ E field, because it's been found that even those high surface area "nano" structures in electrolytic capacitor SEI interface can be made with very little leakage (very high resistance).

Once again, it's possible to make a capacitor with 1Mohm of parallel equivalent resistance and still have 1F of capacitance and 10V voltage rating, but it's impossible* to make an inductor with 1µohm of series equivalent resistance and still have 1H of inductance and 10A current rating. These examples would be equal in energy storage.

*) without very cold temperatures enabling superconductors

Once someone invents a room-temperature superconductor which is also cheap to manufacture, this whole game changes (and it will be a huge revolution in electronics and computing, too).

Imagine if every capacitor came with a 100 Ohm - 1kOhm parallel resistor. You could still use the capacitor for many purposes, but not for longer term energy storage (microseconds OK - seconds not). This is the equivalent of the inductors of today, with many milliohms of series resistance because of copper.

It's just that we don't often even think how you would use an inductor for longer term storage, so it's unintuitive. The answer to that is: keep the current flowing all the time. If you don't want to use the energy right now but just keep it, you use a zero-resistance imaginary MOSFET (Magical Oxide Semiconductor Field Effect Transistor) to short-circuit the zero-ESR future inductor! We just intuitively think that "short circuit" means some uncontrolled, infinite current, but when you have inductance, that definitely is not the case: all current changes are controllable, if you can control the timing of what you do.

[TimFox]

Present-day superconductors require cold temperatures, but otherwise work well in their intended applications, when operated within their maximum parameters.
MRI magnets usually operate in a closed-cycle liquid helium environment, with a mechanical refrigerator keeping the helium below boiling.
So long as that temperature is maintained, the shorted inductor will maintain a steady current and magnetic field.
(In practice, imperfections at the joint where the short happens will produce a very slow decay of the current.)
A short piece of the superconductor can be heated above the T_C of the material to remove the short (leaving the normal resistance of the material, including its substrate) in the circuit.
This is how the current is injected into the circuit in the first place, with an external current source connected across this "hot" wire segment.
Way back in 1969, the famous "R²" Wilson gave a visiting lecture at my college on superconducting magnets (just before he took over the construction of Fermilab).
He passed around a six-inch length of the superconducting material;  one student asked about the silver plating over the superconducting layer.
The answer was "electrical insulation", but also for thermal conductivity, which superconductors are poor at.

[Doctorandus_P]

... but also for thermal conductivity, which superconductors are poor at.

Are you sure?
As far as I know superconductors do not only have zero electrial resistance, but also infinite thermal conductivity.

Maybe it's used in the initial phase, to cool the stuff down before it becomes a superconductor.