How Microphones Work

What are Microphones?

Microphones are devices that convert sound into electrical signals through a process called transduction. Transduction is the conversion of one form of energy into another. Microphones convert the mechanical energy (vibrations) into electrical energy (an electrical signal). This electrical signal is then fed into an analog-to-digital converter (ADC) that converts the signal into a list of numbers that can be used by the computer. This conversion process is called sampling. Some microphones have built-in ADCs, while others use the ADC built into the computer's sound card.

The sampling process is extremely important to understanding how audio is represented in a computer. In Module 1, which is sometimes referred to as a lollipop chart, you can see both the analog signal and the sampled digital signal. The individual samples from the digital signal are the values that are stored in a .wav file in a computer.

Module 1

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Discrete samples recorded from a continuous sound wave.

Types of Microphones

There are two common types of microphones: dynamic microphones and condenser microphones. Each one uses a slightly different method to capture sound.

• Dynamic microphones contain a diaphragm (also known as a membrane) that vibrates as sound waves hit it. The diaphragm is attached to a coil that is wrapped around a magnet. As the sound causes the diaphragm to vibrate, it moves the coil back and forth over the magnet, which generates an electric signal because of electromagnetic induction.

Module 2

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A diagram of a dynamic microphone.

• Condenser microphones also contain a diaphragm that vibrates as sound waves hit it. As the sound causes the diaphragm to vibrate, it travels closer or farther away from a charged plate at the back of the microphone housing. The diaphragm and backplate form a capacitor, and the varying distance between the plates generates an electrical signal.

Module 3

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A diagram of a condenser microphone.

Condenser microphones tend to capture sound more accurately than dynamic microphones. However, because the electrical signal is so weak, it must go through an amplifier built into the microphone before it is fed to the digital-to-audio converter. This means that condenser microphones require an external power source, commonly known as phantom power (since there is a "phantom circuit" formed inside the microphone).

Most consumer electronics, including laptops, phones, and headsets, use condenser microphones. However, because the microphones need to be extremely small, they are typically special variations of condenser microphones.

Polar Patterns

When recording audio, it is often the case that you would like to pick up sounds only from some directions while filtering out sounds from other directions. The most common way of doing this is to include multiple sensors within one microphone housing, and then post-process the recorded audio to amplify sounds coming from the desired directions. For example, this USB microphone includes three condensers microphones internally.

The area around a microphone where sound is effectively captured is called its polar pattern. This is a reference to the fact that the areas traced out in the patterns come from functions that operate on polar coordinates ($r$ as a function of $\theta$), as opposed to Cartesian coordinates ($y$ as a function of $x$).

There are three basic types of polar patterns.

• The omnidirectional pattern captures sound equally from all directions. This is great for capturing ambient sound or when the sound source moves around.

• The cardioid (heart-shaped) pattern captures sound mostly from the front and rejects sound from the back. This is great for isolating a sound source, like a speaker, from background noise.

• The bidirectional (figure-8) pattern captures sound from the front and back but not the sides. This is often used in studio setups for capturing two sound sources, like two singers standing on opposite sides of the microphone.

Module 4

Figure 8

The figure 8 polar pattern.

Omnidirectional

The omnidirectional polar pattern.

Cardioid

The cardioid polar pattern.

Code

The code used to produce the example.

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There are also several variations of these patterns, such as the supercardioid, hypercardioid, and lobar patterns, but for recording setups you ultimately just try everything and use what works best.

Most consumer electronics (including the MacBook Pro, the iPhone, and the Bose QC45 headphones) include multiple microphones to isolate sound from specific regions in space. Depending on how the microphones are arranged, they may not pick up sound in strictly "polar" regions.

Derivation of the Polar Patterns

There are two types of condenser microphones: pressure-sensitive and pressure-gradient.

• Pressure-sensitive microphones position the diaphragm in front of a chamber with air trapped inside. If the chamber experiences vibrations from any angle, then the air pressure inside increases, which pushes against the diaphragm. Therefore, pressure-sensitive microphones have an omnidirectional polar pattern. Assuming no attenuation, the intensity of the sound can be represented with the following equation.

$$\text{Intensity} = 1$$

• Pressure-gradient microphones are open at both sides of the diaphragm. The diaphragm only moves if sounds are produced on-axis. If a sound is off-axis, only the perpendicual component of the sound wave will cause the diaphragm to move. Therefore, pressure-gradient microphones have a figure 8 polar pattern. Assuming no attenuation, the intensity of the sound can be represented with the following equation.

$$\text{Intensity} = \cos(\theta)$$

The cardioid pattern can be formed by adding together the signals from a pressure-gradient and a pressure-sensitive microphone.

$$\text{Intensity} = 1 + \cos(\theta)$$

An alternative way to view polar patterns is to use a heatmap, where "hotter" areas represent places where sound is more easily picked up by the microphone. Module 5 shows the heatmaps for each of the polar patterns from a simulated setup of two microphones (one pressure-sensitive and one pressure-gradient). The heatmaps take into consideration the attenuation of sound, which means the intensity decreases quadratically as the distance from the center increases.

Module 5

Figure 8

The figure 8 polar pattern using one pressure-sensitive and one pressure-gradient microphone.

Omnidirectional

The omnidirectional polar pattern using one pressure-sensitive and one pressure-gradient microphone.

Cardioid

The cardioid polar pattern using one pressure-sensitive and one pressure-gradient microphone.

Code

The code used to produce the examples.

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