Gyrator

The gyrator or positive impedance inverter is an electric circuit which inverts an impedance. In other words, it can make a capacitive circuit behave inductively, a bandpass filter behave like a band-stop filter, and so on. It is primarily used in active filter design and miniaturization.

Simulated inductor

The primary use of a gyrator is to simulate an inductive element in a small electronic circuit or integrated circuit. Before the invention of the transistor, coils of wire with large inductance might be used in electronic filters. A real inductor can be replaced by a much smaller assembly containing a capacitor, operational amplifiers or transistors, and resistors. This is especially useful in integrated circuit technology.

Additionally, real capacitors are often much closer to "ideal capacitors" than real inductors are to "ideal inductors". Because of this, a synthetic inductor realized with a gyrator and a capacitor "may", for certain applications, be closer to an "ideal inductor" than any real inductor can be. Thus, use of capacitors and gyrators may improve the quality of filter networks that would otherwise be built using inductors. Also, the Q factor of a synthesized inductor can be selected with ease.

Since gyrators use active components, they only function as a gyrator within the power supply range of the active element. Hence gyrators are usually not very useful for situations requiring simulation of the 'flyback' property of inductors, where a large voltage spike is caused when current is interrupted.

Operation of the circuit

The circuit works by inverting the effect of the capacitor. The desired effect is an impedance of the form of an ideal inductor "L" with a series resistance "R_L":

$Z\; =\; R\_mathrm\{L\}\; +\; j\; omega\; L\; ,!$

From the diagram, the input impedance of the op-amp circuit is:

$Z\_mathrm\{in\}\; =\; left(\; R\_mathrm\{L\}\; +\; j\; omega\; R\_mathrm\{L\}\; R\; C\; ight)\; |\; left(\; R\; +\; \{1\; over\; \{j\; omega\; C\; ight)$

With R_LRC = L, it can be seen that the impedance of the simulated inductor is the desired impedance in parallel with the impedance of C and R. If R is much greater than R_L, though, this comes close to:

$Z\_mathrm\{in\}\; =\; R\_mathrm\{L\}\; +\; j\; omega\; R\_mathrm\{L\}\; R\; C\; ,!$

This is the same as a resistance R_L in series with an inductance L = R_LRC. It differs in function from a true inductor due to the parallel RC term, and because R_L is large compared to a real inductor. A real inductor has low internal resistance caused only by the wire it is made of. This limits the Q factor, or accuracy, of filters that can be made with the simulated inductor.

Applications

The primary application for a gyrator is to reduce the size and cost of a system by removing the need for bulky, heavy and expensive inductors. For examples, RLC bandpass filter characteristics can be realized with capacitors, resistors and operational amplifiers without using inductors. Thus hi-fi graphic equalizers can be achieved with capacitors, resistors and operational amplifiers without using inductors because of the invention of "gyrator".

Gyrator circuits are extensively used in telephony devices that connect to a POTS system. This has allowed telephones to be much smaller, as the gyrator circuit carries the DC part of the line loop current, allowing the transformer carrying the AC voice signal to be much smaller, due to the massively reduced current. Circuitry in telephone exchanges has also been affected with gyrators being used in line cards. Gyrators are also widely used in hi-fi graphic equalizers, parametric equalizers, discrete bandstop and bandpass filters (such as rumble filters), and FM pilot tone filters.

There are many applications where it is not possible to use a gyrator to replace an inductor:
* High voltage systems utilizing flyback (beyond working voltage of transistors/amplifiers)
* RF systems (RF inductors are usually small anyhow)
* Power conversion, where a coil is used as energy storage.

External links

* [http://sound.westhost.com/dwopa.htm#inductor Good description of this form of the simulated inductor — Elliot Sound Products]
* [http://www.analogzone.com/avt08063.htm Another description, with the same circuit]
* [http://www.forsselltech.com/schematics/Gyrator1.htm LC filter design using equal value R gyrator, an alternative design]
* [http://www.linkwitzlab.com/images/graphics/inductr1.gifAn alternative circuit]
* Webarchive backup: [http://web.archive.org/web/20060610130156/g.irisz.hu/~leto/elektro/girator2.jpgAnother alternative circuit]
* [http://www.spectrum-soft.com/news/winter97/gyrator.shtm Discussion of the gyrator in general and a macro for Micro-Cap V]
* [http://www.falstad.com/circuit/ex-gyrator.html Java simulation of this circuit]
* [http://www.epanorama.net/documents/telecom/gyrator.html Single transistor gyrator for telephony applications]
* [http://www.rowetel.com/blog/?p=51 SPICE Analysis of gyrator for telephony applications]

References