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Tunable Active Gyrator Circuit: Operation, Tuning, and Practical Use
This circuit is a tunable active gyrator that behaves, when viewed from its input node, like an adjustable inductor without using a physical coil. It is implemented with an operational amplifier, resistors, and capacitors, allowing the realization of a compact, stable, and continuously tunable inductive element.
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1. Basic operating principle
A gyrator is an active network that transforms the behavior of a capacitor so that it appears electrically as an inductor. From the perspective of the input node, the circuit exhibits the same voltage–current relationship that would be produced by an ideal inductor, even though only resistors and capacitors are physically present.
In this design, the capacitor of ten nanofarads is the element whose behavior is converted into that of an inductance by the action of the operational amplifier.
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2. Function of the operational amplifier
The operational amplifier is used in a high-gain configuration and can be considered nearly ideal for the frequencies involved.
Its main roles are to isolate the capacitor from the load, to enforce the correct relationship between voltage and current required to imitate inductive behavior, and to ensure that the apparent inductance does not vary significantly with changes in load impedance.
The one-hundred-ohm resistor at the output improves stability, isolates the amplifier from reactive loads, and limits current, reducing the risk of unwanted oscillations.
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3. Network that generates the inductive behavior
The upper part of the circuit consists of a series resistor connected to the input node and a capacitor connected to the non-inverting input of the amplifier.
Together with the feedback provided by the amplifier, this network forces the current flowing through the capacitor to be proportional to the rate of change of the input voltage. This is exactly the behavior expected from an inductor, which is why the circuit appears inductive when observed from the input.
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4. Tuning mechanism and inductance control
The lower resistor network, made up of two fixed resistors and a small potentiometer between them, forms an adjustable voltage divider. This divider controls the effective feedback of the gyrator and therefore determines the value of the simulated inductance.
By adjusting the potentiometer, the effective inductance increases or decreases smoothly. As a result, the circuit can be tuned continuously without changing any fixed components.
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5. Resonant behavior and frequency selection
A capacitor connected from the input node to ground forms, together with the simulated inductance, a resonant network.
At a particular frequency, the inductive and capacitive effects balance, producing resonance. By changing the value of the simulated inductance through the tuning network, this resonant frequency shifts accordingly. The circuit therefore functions as a tunable resonator or band-pass filter.
With the component values shown, the resonance occurs in the lower audio range, close to one kilohertz.
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6. How individual components affect the behavior
The small potentiometer provides fine control of the tuning. Increasing its effective resistance increases the simulated inductance and lowers the resonant frequency. Decreasing it has the opposite effect.
The capacitor connected to ground sets the overall frequency range. Larger values move the operating frequency lower, while smaller values shift it higher.
The series resistor in the inductance-generation network scales the base value of the simulated inductance. Changing this resistor is useful when redesigning the circuit for a different frequency range.
The capacitor being gyrated changes the simulated inductance directly and is especially convenient for large, step-by-step changes in frequency range.
The output resistor primarily affects selectivity. Higher values reduce the sharpness of the resonance but improve stability, while lower values increase selectivity at the risk of oscillation.
The values of the resistors in the tuning divider influence both selectivity and noise performance.
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7. Stability and component quality
The choice of operational amplifier does not set the nominal frequency, but it strongly affects accuracy, noise, and stability. The amplifier must have sufficient bandwidth and slew rate to maintain correct inductive behavior over the frequency range of interest.
Capacitor type also matters. Stable dielectric materials such as C0G ceramic or polypropylene produce the most predictable and repeatable results.
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8. Typical design configurations
For general audio filtering, the circuit provides smooth tuning across several octaves and is suitable for tone control, voice filtering, and laboratory demonstrations.
For narrow-band or high-selectivity applications, reducing internal resistances produces a sharper resonance, making the circuit useful for tone detection and instrumentation.
For very low frequencies, increasing the capacitor values allows the simulation of extremely large inductances that would be impractical or impossible to realize with real coils.
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9. Practical design guideline
First select the capacitor that sets the frequency range. Then adjust the simulated inductance using the gyrator network. Use the potentiometer only for fine tuning.
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Summary
This circuit uses an operational amplifier to transform a capacitor into a tunable inductive element. Combined with a second capacitor, it forms a stable, adjustable resonant circuit suitable for active filters, resonators, and low-frequency signal-processing applications where physical inductors are undesirable.
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