RFUnderstanding Resonant Circuits: Series, Parallel, and Applications
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A resonant circuit is an electric circuit composed of inductor (L) and capacitor (C) components where the inductive reactance and capacitive reactance are equal.
If the L and C components are connected in series, it’s known as a series resonant circuit. When they’re connected in parallel, it’s called a parallel resonant circuit. Both types are illustrated in the diagram below.
At the resonant frequency, the reactances of the inductor and capacitor effectively cancel each other out, resulting in a purely resistive impedance.
Series Resonant Circuit
In this configuration, the inductor (L) and capacitor (C) are connected in series, with a load resistor (R) connected in parallel to the combination.
The resonant frequency of a series resonant circuit is calculated as follows:
f = 1 / (2 * π * √(L * C))
At the resonant frequency, the impedance of the series circuit reaches its minimum. This allows the maximum current to flow through the circuit.
Series resonant circuits are commonly used in radio frequency (RF) applications, such as frequency filtering and tuning.
Resonant circuit types
Parallel Resonant Circuit
In a parallel resonant circuit, the inductor (L) and capacitor (C) are connected in parallel with each other, and the load resistor is connected in series with this combination.
The same formula used for series resonant frequency calculation is typically applied to parallel resonant circuits.
At the resonant frequency, the impedance of the circuit is at its maximum. This results in a high voltage across the load resistor.
Parallel resonant circuits find common use in audio applications, such as filtering frequencies in audio signal processing.
Other Types of Resonant Circuits
Besides the series and parallel configurations, there are other types of resonant circuits, including bandpass resonant circuits, bandstop resonant circuits, and tuned transformers.
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Bandpass Circuit: A combination of series and parallel resonant circuits, designed to pass a narrow range of frequencies. It’s utilized in communication systems and audio signal processing.
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Bandstop Circuit: Designed to attenuate or reject a specific frequency band, while allowing other frequencies to pass through.
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Tuned Transformer: A resonant circuit that uses a transformer with tuned primary and secondary windings.
Equivalent Circuits of Resonant Circuits
Equivalent circuits of resonant circuits
The figure above depicts equivalent circuits of resonant circuits shown previously.
Difference Between Series and Parallel Resonance
The following table summarizes the key differences between series and parallel resonance circuits:
| Specifications | Series resonance | Parallel resonance |
|---|---|---|
| Configuration | Components are connected in series. | Components are connected in parallel. |
| Impedance at resonance | Minimum | Maximum |
| Current at resonance | Maximum | Minimum |
| Effective impedance | R | L/CR |
| Resonant frequency | 1/(2*π√(LC)) | { 1/(2*π) } * { (1/LC) - (R²/L²) }^0.5 |
| Magnifying parameter | Voltage | Current |
| Other name | Acceptor circuit | Rejector circuit |
| Power factor value | Unity | Unity |
| Bandwidth | Narrow | Wide |
| Quality Factor (Q) | High | Low |
| Applications | Used in tuning circuits, filters and amplifiers. | Used in impedance matching circuits, inductor/capacitor selection |
Conclusion
Resonance is a fundamental concept in diverse applications, including radio frequency (RF) circuits, audio signal processing, filters, transformers, and antennas. By understanding and controlling resonance in electronic circuits, engineers can design and optimize devices for specific frequency related tasks, ultimately enhancing overall performance.
