Gyrator calculator

How a gyrator acts like a coil

The cap and Rg split the signal at the coil's end, so the follower's input lags behind it at low frequencies and catches up at high ones. The follower copies that lagging voltage and feeds it back through Rs. The current through Rs then lags the voltage, the way a coil's current does. With a perfect follower the inductance is L = Rs × Rg × C, with Rs in series and roughly Rg across it.

It acts like a coil between two frequencies. Below fLo = 1 / (2π Rg C) it's mostly Rs. Above fHi = 1 / (2π Rs C) it's mostly Rg. Its Q is best halfway between them on a log scale, at about half the square root of Rg / Rs. So a big ratio between the two resistors makes a cleaner coil.

Op-amp follower. The op-amp's speed adds a third limit, near the square root of its gain-bandwidth times fLo. Around there the impedance peaks and then swings the wrong way. With a TL072 and the starting values that's about 3.9 kHz, well below fHi. Fine for bass and mids, where most gyrators sit. The op-amp also has to drive the coil's whole current through Rs, so a small Rs on a big coil runs out of current at a low level.

Transistor follower. Same formula, but a single transistor falls short of a perfect follower two ways. Its gain is short of 1 by about 26 mV divided by the voltage across the emitter resistor, and that adds loss that grows with frequency. And the coil's current runs through the transistor, so the base needs that current divided by beta, which comes through Rg. In this model a 2N5088 at about 1.7 mA tops out near Q 4, with Rg around half of beta × Rs. On the way down it can only pull as much current as its emitter resistor carries at idle. Fine for broad, gentle peaks. For a narrow one, use an op-amp. The transistor's end of the coil sits at its emitter's DC voltage, so it needs a cap in series, as it usually has.

With a cap in series. Most gyrators are used this way, as a graphic EQ band or a power amp's resonance control. The cap and the coil resonate at f = 1 / (2π √(L C)), and the Q is √(L / C) divided by the series resistance. Put any other resistance in the branch in the second field.

How this tool works. We solve the circuit with the same engine and the same op-amp and transistor models as the circuit bench, and work out the impedance from 10 Hz to 50 kHz. The grey curve is a plain coil with the same inductance and series resistance, for comparison. Stock values are E24 for resistors and E12 for caps. The op-amp's current limit of about 10 mA is typical of a TL072, not measured.

Spot an error, or want a circuit added? Email info@swellamps.com. A schematic or a clear photo of one helps. Anything you send may be used to improve these models and our desktop app.

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