Gyrator: Definition from Answers.com
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Gyrator
Sci-Tech Dictionary:
gyrator
(′jī′rād·ər)
(electromagnetism) A waveguide component that uses a ferrite section to give zero
phase shift for one direction of propagation and 180° phase shift for the other
direction; in other words, it causes a reversal of signal polarity for one direction of
propagation but not for the other direction. Also known as microwave gyrator.
English▼
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Sci-Tech Encyclopedia:
Gyrator
A linear, passive, two-port electric circuit element whose transmission properties are
such that it is effectively a half wavelength longer for one direction of transmission than
for the other direction of transmission. Thus a gyrator is a device that causes a reversal
of signal polarity for one direction of propagation but not for the other. (A two-port
element has apair of input terminals and a pair of output terminals.) This device is
novel, since it violates the theorem of reciprocity. See also Reciprocity principle.
Until the early 1950s, all known linear passive electrical networks obeyed the theorem
of reciprocity. However, several different types of nonreciprocal networks are now
widely applied, principally at microwave frequencies. These devices are used to control
the direction of signal flow and to protect or isolate components from undesired signals.
One common application of a three-port nonreciprocal network, called a circulator, is to
permit connection of a transmitter and a receiver to the same antenna. This is
accomplished with minimum interference and virtually no power loss of either
transmitted or received signal. See also Continuous-wave radar.
Perhaps the first passive nonreciprocal system was an optical one proposed by Lord
Rayleigh,making use of the rotation of the plane of polarization of light when it passed
through a transparent material in the presence of a magnetic field. This phenomenon is
called Faraday rotation.
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The microwave analogy of Lord Rayleigh's device was proposed by C. L. Hogan. The
nonreciprocal medium used is fer-rite. In such a material, infinitesimal magnetic dipole
moments which arise from the electronic structure of the material act gyroscopically
when a steady magneticfield is applied. They precess about the applied field direction in
a counterclockwise sense, thus permitting strong coupling to the component of a
microwave-frequency magnetic field which is circularly polarized in the same sense. The
component with the opposite sense of polarizationis weakly coupled. Thus energy
exchange between the magnetic dipoles and the microwave field is polarizationsensitive. See also Ferrimagnetism; Ferrite.
Wikipedia:
Gyrator
A gyrator is a passive, linear, lossless, two-port electrical network element proposed in
1948 by Tellegen as a hypothetical fifth linear element after the resistor, capacitor,
inductor and ideal transformer[1]. Unlike the four conventional elements, the gyrator is
non-reciprocal. Gyrators permit network realizations of two-(or-more)-port devices
which cannot realized with the just the conventional four elements. In particular,
[2]
gyrators make possible network realizations of isolators and circulators . Gyrators do
not however change the range of one-port devices that can be realized. Although the
gyrator was conceived as a fifth linear element, its adoption makes both the ideal
transformer and either the capacitor or inductor redundant. Thus the number of
necessary linear elements is in fact reduced to three.
Tellegen's
proposed
symbol
for his
gyrator
Tellegen invented a circuit symbol for the gyrator and suggested a number of ways in
which a practical gyrator might be built.
An important property of a gyrator is that it inverts the current-voltage characteristic of
an electrical component or network. In the case of linear elements, the impedance is
also inverted. In other words, a gyrator can make a capacitive circuit behave
inductively, a series LC circuit behave like a parallel LC circuit, and so on. It is primarily
used in active filter design and miniaturization.
Contents [hide]
• 1 Behaviour
• 2 Implementation: a simulated inductor
◦ 2.1 Operation
◦ 2.2 Comparison with actual inductors
◦ 2.3 Applications
• 3 See also
• 4 References
• 5 External links
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Behaviour
Gyrator
schematic
labelled
An ideal gyrator is a linear two port device which couples the current on one port to the
voltage on the other and vice versa. The instantaneous currents and instantaneous
voltages are related by
v2 = Ri1
v1 = − Ri2
where
is the gyration resistance of the gyrator.
The gyration resistance (or equivalently its reciprocal the gyration conductance) has an
[3]
associated direction indicated by an arrow on the schematic diagram . By convention,
the given gyration resistance or conductance relates the voltage on the port at the head
of the arrow to the current at its tail. The voltage at the tail of the arrow is related to
the current at its head by minus the stated resistance. Reversing the arrow is
equivalent to negating the gyration resistance, or to reversing the polarity of either
port.
Although a gyrator is characterized by its resistance value, it is a lossless component.
From the governing equations, the instantaneous power into the gyrator is identically
zero.
A gyrator is an entirely non-reciprocal device, and hence is represented by
antisymmetric impedance and admittance matrices:
If the gyration resistance is chosen to be equal to the characteristic impedance of the
two ports (or to their geometric mean if these are not the same), then the scattering
matrix for the gyrator is
which is likewise antisymmetric. This leads to an alternative definition of a gyrator: a
device which transmits a signal unchanged in the forward (arrow) direction, but
reverses the polarity of the signal travelling in the backward direction (or equivalently,
[4]
180° phase-shifts the backward travelling signal ).
As with a quarter wave transformer, if one of port of the gyrator is terminated with a
linear load, then the other port presents an impedance inversely proportional to that of
the load,
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A generalization of the gyrator is conceivable, in which the forward and backward
gyration conductances have different magnitudes, so that the admittance matrix is
[5]
However this no longer represents a passive device
.
Implementation: a simulated inductor
An example of a gyrator
simulating inductance,
with an approximate
equivalent circuit below.
The two Zin have similar
values in typical
applications.
The gyrator network can be used to transform a load capacitance into an inductance.
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. An 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.
Operation
The circuit works by inverting and multiplying the effect of the capacitor in an RC
differentiating circuit where the voltage across the resistor 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 RL. The desired effect is an
impedance of the form of an ideal inductor L with a series resistance RL:
From the diagram, the input impedance of the op-amp circuit is:
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With RLRC = 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 adequately large that the dominant term is; so, the RC circuit does not
impact the input:
.
This is the same as a resistance RL in series with an inductance L = RLRC. There is a
practical limit on the minimum value that RL can take, determined by the current
output capability of the op amp.
Comparison with actual inductors
Simulated elements only imitate actual elements as in fact they are dynamic voltage
sources. They cannot replace them in all the possible applications as they do not
possess all their unique properties. So, the simulated inductor only mimics some
properties of the real inductor.
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 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 synthetic inductor realized with a
gyrator and a capacitor may, for certain applications, be closer to an "ideal inductor"
than any 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 of an LC filter can be
either lower or higher than that of an actual LC filter – 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 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.
Grounding. The fact that one side of the simulated inductor is grounded restricts the
possible applications (real inductors are floating). This limitation precludes its use in low
-pass and notch filters, leaving high-pass and band-pass filters as the only possible
applications.[6]
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
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bandpass filter characteristics can be realized with capacitors, resistors and operational
amplifiers without using inductors. Thus graphic equalizers 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 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 elimination of DC current through it. Circuitry in
telephone exchanges has also been affected with gyrators being used in line cards.
Gyrators are also widely used in hi-fi for 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.
See also
• Negative impedance converter (which can be used to implement a negative inductor
with a capacitor)
• Sallen–Key topology
References
1. ^ B. D. H. Tellegen (April 1948). "The gyrator, a new electric network element".
Philips Res. Rep. 3: 81–101.
http://techpreservation.dyndns.org/beitman/abpr/newfiles/The%20Gyrator.pdf.
Retrieved 2010:03:20.
2. ^ K. M. Adams, E. F. A. Deprettere and J. O. Voorman (1975). Ladislaus Marton.
ed. "The gyrator in electronic systems". Advances in Electronics and Electron
Physics (Academic Press, Inc.) 37: 79–180.
3. ^ Chua, Leon (unknown), EECS-100 Op Amp Gyrator Circuit Synthesis and
Applications, Univ. of Calif. at Berkeley,
http://inst.eecs.berkeley.edu/~ee100/fa04/lab/lab10/EE100_Gyrator_Guide.pdf,
retrieved May 3, 2010
4. ^ The IEEE Standard Dictionary of Electrical and Electronics terms (6th ed.). IEEE.
1996 [1941]. ISBN 1-55937-833-6.
5. ^ Theodore Deliyannis, Yichuang Sun, J. Kel Fidler, Continuous-time active filter
design, pp.81-82, CRC Press, 1999 ISBN 0849325730.
6. ^ An audio circuit collection, Part 3
External links
•
•
•
•
•
•
•
Good description of this form of the simulated inductor — Elliot Sound Products
Another description, with the same circuit
LC filter design using equal value R gyrator, an alternative design
An alternative circuit
Webarchive backup: Another alternative circuit
Discussion of the gyrator in general and a macro for Micro-Cap V
Java simulation of this circuit
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• Single transistor gyrator for telephony applications
• SPICE Analysis of gyrator for telephony applications
• Negative floating inductor with only 2 Op-amps Article here
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