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How a loudspeaker works

The moving-coil, or electrodynamic, loudspeaker is the most common type used in home audio, cars, portable products, studios, and professional sound systems.

It is an electromagnetic transducer: it converts electrical energy into mechanical motion and then into sound.

From current to force

The voice coil is a length of wire positioned in the magnetic gap of the motor structure. When current flows through the coil, it interacts with the magnetic field and produces a force.

\[ F = B\ell i \]

Where:

  • \(F\) is force in Newtons
  • \(B\) is magnetic flux density in Teslas
  • \(\ell\) is the effective wire length in the magnetic field in meters
  • \(i\) is current in Amperes

The product \(B\ell\), usually written Bl, is called the force factor.

Reversing the current reverses the force, so an alternating audio signal moves the coil forward and backward.

From force to motion

The voice coil is attached to a diaphragm, usually a cone or dome. The moving assembly has three important properties:

  • Mass, \(M_{MS}\) [g], which resists acceleration
  • Compliance, \(C_{MS}\) [m/N], which describes the flexibility of the suspension
  • Mechanical resistance, \(R_{MS}\) [N·s/m], which represents damping and losses

Together, the moving mass and suspension form a resonant system. The free-air resonance is called \(f_S\) [Hz].

Near resonance, relatively small forces can produce larger motion. The amount and width of this resonance depend on mechanical and electrical damping.

From motion to sound

As the diaphragm moves, it accelerates nearby air molecules. Those disturbances propagate away as sound waves.

At low frequencies, all parts of the cone move together as a rigid body. At higher frequencies, waves travel through the diaphragm and different regions may move with different amplitudes and phases. This behavior is called breakup.

Breakup can create peaks, dips, distortion, and changes in directivity.

Back electromotive force

The conversion also works in reverse. When the coil moves through the magnetic field, it generates a voltage called back EMF:

\[ e = B\ell u \]

Where \(u\) is coil velocity [m/s].

This back EMF contributes to the changing electrical impedance measured at the driver terminals. It is one reason a loudspeaker cannot be treated as a simple resistor.

Why the impedance has a peak

Impedance curve

At the driver’s free-air resonance, mechanical motion and back EMF are high. This usually appears as a prominent peak in the impedance curve.

At very low frequencies, the impedance approaches the voice coil’s DC resistance. At high frequencies, impedance generally rises as voice-coil inductance becomes more important.