Exploring the Resonant Frequency of an RLC Circuit

February 12, 2021

Key Takeaways

• Understand what a resonant frequency is.

• Learn how a resonant frequency affects series and parallel RLC circuits.

• Determine what happens at the resonant frequency of an RLC circuit.

There are moments where the logical part of yourself is heavily burdened by unfounded fears. Imagine getting stuck in traffic on a bridge that spans miles across the ocean. As your car inches to the middle of the bridge, you suddenly feel the vehicle start to sway with the bridge. For a fleeting moment, you are terrified that an earthquake struck or the bridge is on the verge of collapse. This may not be an experience everyone has had, but it does happen to me on occasion.

If you are an engineer, your logical mind might consider a theory that revolves around resonant frequencies, which states that a bridge could vibrate when it’s subjected to an oscillating force that matches its resonant frequency.

The scenario above offers a visceral insight into our topic of what happens at the resonant frequency of an RLC circuit. Let’s explore this topic further.

What Does Resonant Frequency Mean?

A resonant frequency is defined as the natural frequency of a system where it oscillates at the greatest amplitude. A system is said to be in resonance when an external force applied shares the same frequency as its natural frequency.

In daily life, you’ll come across mechanisms that resonate at their resonant frequency, which results in greater amplitude. Besides bridges, swings, string instruments, and RLC circuits are also known to exhibit extraordinary behavior at their resonant frequencies.

For example, if a swing is pushed at its resonant frequency, it results in the swing reaching greater heights than it would otherwise. The strings of a musical instrument interact with each other in a similar way. In electronics, you’ll come across resonant frequencies, particularly in RLC circuits.

Resonant Frequency in a Series RLC Circuit Series RLC circuit resonant frequency.

The series RLC circuit depicted above is commonly used in various PCB applications. Both inductor and capacitor display dynamic properties in reactance across a different range of frequencies.

At a specific frequency, the inductive reactance and the capacitive reactance will be of equal magnitude but in opposite phase. They are represented by the equation:

XL = XC

As both capacitive and inductive reactance cancel each other out, the circuit’s impedance will be purely resistive. When this phenomenon occurs, the circuit is said to be oscillating at its resonant frequency. The resonant frequency of the series RLC circuit is expressed as

fr = 1/2π√(LC)

At its resonant frequency, the total impedance of a series RLC circuit is at its minimum. It also means that the current will peak at the resonant frequency as both inductor and capacitor appear as a short circuit. Frequency response of a series RLC circuit.

A series RLC circuit, which achieves maximum power transfer at resonance, is commonly used as a bandpass filter for radio, TV, or as a noise filter.

Resonant Frequency in a Parallel RLC Circuit Diagram of a parallel RLC circuit.

A parallel RLC circuit will also exhibit peak behaviors at its resonant frequency, however, there will be big differences compared to a series RLC circuit.

The resonant frequency of a parallel RLC circuit is also expressed by:

fr = 1/2π√(LC)

But, that’s where the similarities end. At resonance, both capacitive and inductive reactance will be equal to each other.  The inductor and capacitor will also be conducting more current at the resonant frequency.

Current flowing across both components is 180° out of phase, which results in a mutually canceling current. Therefore, the segment of inductor and capacitor in parallel will appear as an open circuit.

When the frequency response of the parallel RLC circuit is plotted on a chart, you’ll find that the current decreases to a minimum at the resonant frequency. This is the opposite of the response of a series RLC circuit. The frequency response of a parallel RLC circuit.

The parallel RLC circuit is also dubbed an anti-resonance circuit. It’s used as a rejector circuit to suppress current at a specific frequency from passing through.

Whether you’re designing a series or parallel RLC circuit, you’ll need a good PCB design and analysis software. Allegro, by Cadence, has a robust selection of schematic, PCB, and simulation tools that will be instrumental in designing resonance circuits and other types of PCB designs.

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