# What is Resonant Frequency?

March 10, 2021

What you’ve seen in cartoons is not necessarily from the wild imaginations of writers—some scenes are actually rooted in science. As a child, I thought the scene of a terrible singer hitting a high note and breaking a piece of glass was hilarious, only to find out that the phenomenon is possible in real life because of something called resonant frequency.

What is resonant frequency and what does it do? While lousy singing skills are unlikely to shatter glass, producing sound that equals the resonant frequency of the glass will. At least, that’s what I recall from my high school physics class. As time went on, I also discovered that resonant frequency isn’t only about shattering glass, but also an important principle in how some electronics work.

## What Is Resonant Frequency?

Resonant frequency is the natural frequency where a medium vibrates at the highest amplitude

Why would a glass shatter when it’s exposed to sound? Sound is an acoustic wave that causes molecules to vibrate. When projected from a source, the vibration traverses through the air onto the physical structure of the glass. If the acoustic frequency of the sound matches the natural frequency of the glass, the latter starts to vibrate at a larger amplitude, potentially disintegrating its structure.

In other words, the glass could possibly break when it’s vibrating at its resonant frequency. The resonant frequency can also be defined as the natural frequency of an object where it tends to vibrate at a higher amplitude. For example, you could feel a bridge “shake” if the collective oscillation force from vehicles caused it to vibrate at its frequency.

The term resonant frequency is also commonly encountered in electronics design, although it’s less dramatic than shattered glass or a violently-shaking bridge.

## Resonant Frequency In Electronics Circuits

Resonant frequency in electronics is expressed when a circuit exhibits a maximum oscillatory response at a specific frequency. This is observed for a circuit that consists of an inductor and capacitor.

To better understand what resonant frequency is and the role it plays in electronics, let’s take a look at a series RLC circuit that’s driven by an AC source. It is known that the value of capacitive and inductive reactance changes accordingly to the frequency. Capacitive reactance is defined by the equation Xc = 1/ (2ℼfC), while inductive reactance is given by the equation XL = 2ℼfL.

The relationship of inductive and capacitive reactance across frequencies

When plotted on a chart, the decreasing capacitive reactance will cross paths with the increasing inductive reactance at a specific frequency. The frequency where both parameters overlap is known as the resonant frequency of an RLC circuit. Therefore, the resonant frequency can be derived by expressing the equal value of both capacitive and inductive reactance as follows:

1. XL = XC
2. 2ℼfL =  1/ (2ℼfC)
3. fr = 1/ (2ℼ √LC)

In a series RLC circuit, the impedance is at its minimum when it’s driven at the resonant frequency. The circuit’s impedance is expressed by the following equation:

Z = R + XL - XC

At resonance, XL equals XC, meaning they cancel each other out. This leaves the impedance of the circuit to be purely resistive. As a result, the current that flows through the series RLC circuit is at its peak when it’s operating at its resonant frequency.

In a parallel RLC circuit, the formula for calculating the resonant frequency remains the same. However, you’ll find the current is suppressed to the minimum, as the circuit’s impedance is at its maximum. This happens as the LC of the circuit appears as an open circuit when connected in parallel.

## Applications of Resonant Circuits

RF receivers let through signals that oscillate at the circuit’s resonant frequency

The concept of driving a circuit in its resonant frequency is found in various applications. In an oscillator, a parallel LC is used as a tank-circuit, which is driven in its resonant frequency. The result is a continuous series of steady, oscillating clock pulses that drive components like microcontrollers and communication ICs.

Resonant circuits are also seen in RF applications. They become the basics of a tuner, amplifying signals that correspond with its resonant frequency and rejecting those that are out of its bandwidth.

When designing resonant circuits, it helps to work with advanced PCB design software. Allegro has all the layout and simulation tools needed to ensure that a circuit works accordingly at the desired resonant frequency. You can also use InspectAR to accurately assess and improve PCBs using augmented reality and intuitive interaction. Inspecting, debugging, reworking, and assembling PCBs has never been faster or easier.

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts

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