# Theory: With an AC circuit adding capacitors will cause the current trend towards leading

so if you add enough caps can you emulate what an inductor is doing, ie. Lead the current so far that it appears to be lagging?

I assume this doesn't work, why not?

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You can simulate an inductor with capacitors, but you need additional circuitry to invert its impedance, and there are limitations on what you can simulate with it:

http://en.wikipedia.org/wiki/Gyrator

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Because with a resistive / capacitive parallel load, the total current is the vector sum of pure resistive current (current in phase with voltage) and pure capacitive current (current 90 degree lead from voltage). If the two components are Ir and Ic then the lead angle is atan2(Ic,Ir) which is 0 for Ic = 0, Ir > 0, and pi/2 = 90 degrees for Ir = 0, Ic > 0. So you are always between 0 and 90 degrees lead for RC parallel loads. It's not like the lead angle is proportional to the capacitance.

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The gyrator thing is a lot less useful than it looks in theory (I have never encountered one in an application).

Jason is right that you can only get +/-90 phase shift from one capacitor/inductor. On the other hand you can easily make a chain by combining several such RC/RL networks and get a phase shift of any angle (just be aware that in a passive network the stages influence each other so calculating the required circuit may not be an easy task).

The real problem is that you cannot change the frequency dependency of a capacitor so you can always easily discriminate between them by changing the input signal frequency.

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You've never encountered a "land line" telephone? {insert funny generation gap saying here, preferably using inherently funny words such as "whippersnappers"} –  davidcary Jul 20 '12 at 19:10
Gyrator circuits were used in telephone networks? Could you elaborate a little on this? –  jpc Jul 27 '12 at 9:30
Most telephone-line modems have a gyrator circuit -- it's in the DAA.a. I've been told that a similar circuit is in most "electronic" telephones that plug into a land line. According to Wikipedia, the line card at the other end of that twisted pair -- inside the telephone company building -- usually includes a gyrator circuit. –  davidcary Jul 28 '12 at 6:11
@davidcary Thanks. So in the end gyrator-type circuits are in fact really common but they don't look like 4-terminal elements we know from circuit theory. Their usage is also a little tricky so they are not as universal as normal inductors. –  jpc Jul 30 '12 at 13:13