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A gyrator is a very interesting device. It is a two-port device similar to a transformer, but instead of a voltage on one side creating a voltage on the other side and the same for currents, it criss-crosses the voltages and currents. This means that a voltage on one side makes a current on the other, and vice versa. In order to satisfy conservation of energy, the gyrator is a non-reciprocal device. One volt on side side will create some current on the other side, but one volt on the other side will create the opposite current (same magnitude, opposite direction) on the first side. The ratio of voltage and current is measured as the impedance. In this circuit, the impedance of the gyrator is 50Ω. This means that 1V on one side will create 20mA on the other side, and 20mA on one side will create 1V on the other side. The impedance here is equal to the product of the resistors’ resistance (1mΩ here) and the amplifiers’ gain (50,000 here). Clearly, this is highly dependent on the open-circuit gain of the OP-amp, so this is not suitable outside the simulator unless a differential amplifier with a large and fixed open-circuit gain can be made IRL. Furthermore, since this is an active emulation of a gyrator, some of the possible uses for a gyrator are not possible. These primarily include things that take advantage of the gyrator to save energy because a true gyrator is a passive device and does not consume any energy. According to wikipedia, a passive gyrator is theoretically possible but requires at least one component with a negative value and is therefore not realizable in real life.
The gyrator has some very interesting properties and can be used to make circuits that are simply not possible to construct with other passive components. One fascinating property is the ability to transform any impedance on one end to it’s dual on the other end. This is similar to the behavior of a transformer, where the transformer transforms the impedance according to the equation (r^2) * Z where Z is the impedance and r is the ratio (in other words it simply scales the impedance, so an 8Ω speaker on one end looks like an 800Ω load on the other end with a transformer ratio of 10). However, the gyrator transforms it according to (r^2)/Z which gives it some very interesting properties. For example, a capacitor is made into an inductor and vice versa. An open circuit is made into a short circuit and vice-versa. In the case of the capacitor-inductor relation, one must take into account the impedance of the gyrator. Since the impedance here is 50Ω the 1μF capacitor is transformed into a 2.5mH inductor. If the impedance were 1Ω or 10Ω, it would produce a 1μH or 100μH inductor respectively.
Some unique circuits that the gyrator can make are the isolator and circulator. The isolator allows a generator to perceive a fixed load regardless of what’s actually connected to the other end. Unfortunately, this is only interesting in the case of all-passive components but is trivial when active components are allowed, so this gyrator is of little use here. The circulator on the other hand is far more interesting. It has 3 ports (or more, but I’ll take the example of 3). A signal flowing into the first will be directed to the second. But the critical part here is that a signal sent to the second port will be directed not to the first port but to the third port. The same then happens with signals from the third port going to the first again, completing the circulation. This allows some very interesting things such as a single antenna to be used for both reception and transmission at the same time on the same frequency. You connect the antenna to port two, connect the transmitter to port one, and connect the receiver to port three. Assuming the antenna transmits perfectly without reflecting any of the signal this will allow you to listen to what other people are transmitting on a given frequency while you yourself transmit on that same frequency from the very same antenna. Of course, as is standard in radio, the received signal is far, far weaker than the transmitted signal (like ten orders of magnitude) so it is highly unrealistic that such isolation can actually be achieved between the transmitter and receiver, especially when any real antenna will always reflect a little bit of signal back no matter how well-tuned or how narrow-band the transmission. Of course, tuning as well as possible and narrowing the transmission bandwidth as far as possible (which means using continuous wave/morse code) will produce minimal reflection from the antenna, but then at that point you’ll probably be limited by the quality of the circulator.
The gyrator can also be used to simulate the interface between a standard electrical circuit and the magnetic circuit of a transformer. This allows for the accurate simulation of many transformer configuration. Please see https://en.m.wikipedia.org/wiki/Gyrator–capacitor_model for more information.
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