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===Simulated inductor=== [[File:Op-Amp Gyrator.svg|right|thumb|300px|An example of a gyrator simulating inductance, with an approximate equivalent circuit below. The two ''Z''<sub>in</sub> have similar values in typical applications. Circuit from {{Harvtxt|Berndt|Dutta Roy|1969}}]] A gyrator can be used to transform a load capacitance into an inductance. At low frequencies and low powers, the behaviour of the gyrator can be reproduced by a small [[op-amp]] circuit. This supplies a means of providing an [[inductor|inductive]] element in a small [[electrical network|electronic circuit]] or [[integrated circuit]]. Before the invention of the [[transistor]], coils of wire with large [[inductance]] might be used in [[electronic filter]]s. An inductor can be replaced by a much smaller assembly containing a [[capacitor]], [[operational amplifier]]s or transistors, and [[resistor]]s. This is especially useful in integrated circuit technology. ==== Operation ==== In the circuit shown, one port of the gyrator is between the input terminal and ground, while the other port is terminated with the capacitor. The circuit works by inverting and multiplying the effect of the capacitor in an [[RC circuit#Differentiator|RC differentiating circuit]], where the voltage across the resistor ''R'' behaves through time in the same manner as the voltage across an inductor. The op-amp follower buffers this voltage and applies it back to the input through the resistor ''R<sub>L</sub>''. The desired effect is an impedance of the form of an ideal inductor ''L'' with a series resistance ''R<sub>L</sub>'': <math display="block">Z = R_L + j \omega L.</math> From the diagram, the input impedance of the op-amp circuit is <math display="block">Z_\text{in} = (R_\text{L} + j \omega R_L R C) \parallel \left(R + \frac{1}{j \omega C}\right).</math> With ''R<sub>L</sub>RC'' = ''L'', it can be seen that the impedance of the simulated inductor is the desired impedance in parallel with the impedance of the RC circuit. In typical designs, ''R'' is chosen to be sufficiently large such that the first term dominates; thus, the RC circuit's effect on input impedance is negligible: <math display="block">Z_\text{in} \approx R_L + j \omega R_L R C.</math> This is the same as a resistance ''R<sub>L</sub>'' in series with an inductance ''L'' = ''R<sub>L</sub>RC''. There is a practical limit on the minimum value that ''R<sub>L</sub>'' can take, determined by the current output capability of the op-amp. The impedance cannot increase indefinitely with frequency, and eventually the second term limits the impedance to the value of ''R''. ==== Comparison with actual inductors ==== Simulated elements are electronic circuits that imitate actual elements. Simulated elements cannot replace physical inductors in all the possible applications as they do not possess all the unique properties of physical inductors. '''Magnitudes.''' In typical applications, both the inductance and the resistance of the gyrator are much greater than that of a physical inductor. Gyrators can be used to create inductors from the microhenry range up to the megahenry range. Physical inductors are typically limited to tens of henries, and have [[parasitic resistance|parasitic series resistances]] from hundreds of microhms through the low kilohm range. The parasitic resistance of a gyrator depends on the topology, but with the topology shown, series resistances will typically range from tens of ohms through hundreds of kilohms. '''Quality.''' Physical capacitors are often much closer to "ideal capacitors" than physical inductors are to "ideal inductors". Because of this, a synthesized inductor realized with a gyrator and a capacitor may, for certain applications, be closer to an "ideal inductor" than any (practical) physical 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. The [[Q factor|Q]] of an LC filter can be either lower or higher than that of an actual LC filter β for the same frequency, the inductance is much higher, the capacitance much lower, but the resistance also higher. Gyrator inductors typically have higher accuracy than physical inductors, due to the lower cost of precision capacitors than inductors. '''Energy storage.''' Simulated inductors do not have the inherent energy storing properties of the real inductors and this limits the possible power applications. The circuit cannot respond like a real inductor to sudden input changes (it does not produce a high-voltage [[Counter-electromotive force|back EMF]]); its voltage response is limited by the power supply. Since gyrators use active circuits, 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. A gyrator's transient response is limited by the bandwidth of the active device in the circuit and by the power supply. '''Externalities.''' Simulated inductors do not react to external magnetic fields and permeable materials the same way that real inductors do. They also don't create magnetic fields (and induce currents in external conductors) the same way that real inductors do. This limits their use in applications such as sensors, detectors and transducers. '''Grounding.''' The fact that one side of the simulated inductor is grounded restricts the possible applications (real inductors are floating). This limitation may preclude its use in some low-pass and notch filters.<ref>{{Cite journal |last=Carter |first=Bruce |title=An audio circuit collection, Part 3 |date=July 2001 |id=SLYT134 |url=http://focus.tij.co.jp/jp/lit/an/slyt134/slyt134.pdf |journal=Analog Applications Journal |publisher=Texas Instruments }}. Carter page 1 states, "The fact that one side of the inductor is grounded precludes its use in low-pass and notch filters, leaving high-pass and band-pass filters as the only possible applications."</ref> However the gyrator can be used in a floating configuration with another gyrator so long as the floating "grounds" are tied together. This allows for a floating gyrator, but the inductance simulated across the input terminals of the gyrator pair must be cut in half for each gyrator to ensure that the desired inductance is met (the impedance of inductors in series adds together). This is not typically done as it requires even more components than in a standard configuration and the resulting inductance is a result of two simulated inductors, each with half of the desired inductance. ==== 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 example, [[RLC circuit|RLC]] bandpass filter characteristics can be realized with capacitors, resistors and operational amplifiers without using inductors. Thus [[graphic equalizer]]s can be achieved with capacitors, resistors and operational amplifiers without using inductors because of the invention of the gyrator. Gyrator circuits are extensively used in telephony devices that connect to a [[Plain old telephone service|POTS]] system. This has allowed telephones to be much smaller, as the gyrator circuit carries the [[Direct current|DC]] part of the line loop current, allowing the transformer carrying the AC voice signal to be much smaller due to the elimination of DC current through it.<ref> Joe Randolph. [http://www.randolph-telecom.com/articles/AN-5,%20Transformer-based%20phone%20line%20interfaces%20_DAA,%20FXO_.pdf AN-5: "Transformer-based phone line interfaces (DAA, FXO)"]. </ref> Gyrators are used in most DAAs ([[data access arrangement]]s).<ref> [http://www.daycounter.com/Circuits/Gyrator/Gyrator.phtml "Gyrator - DC Holding Circuit"] </ref> Circuitry in telephone exchanges has also been affected with gyrators being used in [[line card]]s. Gyrators are also widely used in [[hi-fi]] for graphic equalizers, [[parametric equalization|parametric equalizers]], discrete [[Bandstop filter|bandstop]] and bandpass filters such as [[Rumble measurement|rumble filters]]), and [[Pilot signal|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 commonly use real inductors as they are quite small at these frequencies and integrated circuits to build an active gyrator are either expensive or non-existent. However, passive gyrators are possible. * Power conversion, where a coil is used as energy storage.
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