# Why is it that we use capacitors in Differentiator & Integrator circuits (comprising Op Amps) & not inductors?

One of the possible reasonsI know is that capacitors are available in wide range of values and can be made more accurate than inductors. What other factor leads to the use of capacitors over inductors?

• Have you considered any of the fundamental differences between inductors and capacitors? – Samuel Dec 16 '15 at 18:39
• Simple: to keep an inductor charged current must keep flowing, to do that without powerloss series resistance must be 0 ohm, this is unfeasible. To keep a capacitor charged a voltage needs to be kept constant: simple, make sure it does not discharge so prevent leakage. How much do real capacitors leak, if you choose the right type (ceramic for example): not much. So a capactitor is much more practical as an integrator. – Bimpelrekkie Dec 16 '15 at 19:52

A lot of circuits require medium/high impedance values for even moderately low frequencies such as audio and a capacitor of say 10 nF at 1 kHz has an impedance of 15.9 kOhm. An inductor having this impedance at 1 kHz would have a value of 2.53 henries.

Now that isn't a small value to fit in a space for a surface mount component. That's one reason and the next is cost - try finding a 2.5 henry coil in farnell, digikey or mouser and see how much change you have out of a dollar or a pound. The 10nF will cost you about a couple of pennies maximum.

So, it's not small and it's not cheap and a side effect of it not being small is that it will possess significant parasitic capacitance (several pico farads if not more) and this makes it less than perfect. I'm certainly not saying caps are perfect but they are a couple of orders of magnitude more perfect than an inductor.

Also it will have a significant DC resistance as it is made as small as it can be. It won't be good at handling currents like capacitor is and the core will probably saturate.

• Worth adding: the reason a 2.5H coil is expensive is because it's huge. Henries are like farads: their derived units (µF, µH, etc) are more often seen than the base units. – duskwuff -inactive- Dec 16 '15 at 19:53
• Seems worth adding: if I needed a huge inductor for a filter (for whatever reason), I would use a gyrator. en.wikipedia.org/wiki/Gyrator – Peter Smith Dec 17 '15 at 11:49

Generally speaking inductors are much more lossy than capacitors. They depart much more from the ideal models that people learn at college, and in a poorly specified fashion. In other words a circuit having inductors instead of caps is more likely to need tweaking.

Also inductors, depending on how they are constructed, are more prone to picking up stray fields, which means more PCB layout constraints. The whole process from hand sketched circuit diagram to working PCB is more predictable when inductors are not there.

Finally, if you need to substitute a part, you are more likely to have problems with an inductor than a cap, as many inductors use non-standard footprints.

• +1 for mentioning stray fields pickup; especially for precision circuitry, shielding an inductor is much more troublesome than shielding a cap. – Lorenzo Donati -- Codidact.com Dec 16 '15 at 21:10
• +1 for "ideal". Real capacitors are more like ideal capacitors than real inductors are like ideal inductors. – Nick T Dec 17 '15 at 2:27

Both coils (inductors) and capacitors differentiate or integrate something w.r.t. time.

I think, in almost any context, an active circuit (one with op-amps or some kind of transistor amplifier) with inductors will cost more than one with the equivalent number of capacitors. It takes more to manufacture a coil than it takes to manufacture a capacitor.

It would be possible to build integrator or differentiator circuits using inductors, but these would integrate current instead of voltage.

You would need a current amplifier (low input impedance, high output impedance) instead of a voltage amplifier in this case as well. These are somewhat more impractical to build.