How a loudspeaker works — the electrodynamic transducer

Overview

The electrodynamic (or moving-coil) loudspeaker is the dominant transducer type in audio reproduction. Its operating principle is straightforward: a current-carrying conductor placed in a magnetic field experiences a force. In a loudspeaker, that conductor is the voice coil; the magnetic field is provided by a permanent magnet; and the force drives a cone that moves air.

The key components are:

• Magnet system — provides a strong, stable magnetic field in a narrow gap
• Voice coil — a coil of wire wound on a former, suspended in the magnetic gap
• Cone — a lightweight diaphragm attached to the voice coil former, which radiates sound
• Spider — a flexible suspension element that centres the voice coil in the gap and provides axial restoring force
• Surround — a compliant ring at the outer edge of the cone that allows axial movement while providing additional restoring force

The motor force

The force applied to the voice coil is given by the Lorentz force law:

F = B × I × l

where B is the magnetic flux density in the gap (teslas), I is the instantaneous current through the coil (amperes), and l is the total length of wire in the magnetic field (metres). The product Bl — often called the force factor or motor strength — is a fundamental parameter in loudspeaker design and appears throughout the Thiele-Small parameter set. Thiele-Small parameters explained covers these in detail.

A higher Bl produces more force for a given current, which improves sensitivity and reduces the effect of mechanical losses. Typical values range from around 4 N/A for a small wideband driver to 15–20 N/A or more for high-sensitivity PA drivers.

The mechanical system

The voice coil and cone form a moving mass (Mms) suspended by a total mechanical compliance (Cms) — the combined compliance of the spider and surround. Together with the mechanical resistance (Rms, representing friction and internal losses in the suspension), these elements form a second-order mechanical resonator. The resonant frequency is:

fs = 1 / (2π × √(Mms × Cms))

This is the driver's free-air resonant frequency — the frequency at which the mechanical system resonates with no enclosure loading. Below fs, cone movement is controlled by the suspension stiffness (stiffness-controlled region). Above fs, it is controlled by the moving mass (mass-controlled region). In the mass-controlled region, cone displacement falls at 12 dB/octave with increasing frequency, but the radiated acoustic power is approximately flat — this is the normal operating region for a woofer or midrange driver.

From mechanical motion to acoustic radiation

The cone acts as a piston, pushing and pulling air to create pressure variations. In the piston band — the frequency range where the cone moves as a rigid body — the radiated acoustic power depends on the cone area (Sd), the velocity of the cone, and the acoustic radiation resistance (which depends on frequency and cone size).

At low frequencies where the wavelength is much larger than the cone, a driver is a very inefficient radiator. The acoustic radiation resistance is low, and most of the mechanical energy goes into oscillating the air rather than compressing it. As frequency rises and the wavelength becomes comparable to the cone diameter, radiation efficiency increases. This relationship between cone size and radiation efficiency is one reason why large woofers are used for bass reproduction.

Cone breakup occurs at higher frequencies when the cone can no longer move as a rigid piston. Different parts of the cone vibrate at different amplitudes and phases, producing resonances visible as peaks in the frequency response. The frequency at which breakup begins depends on the cone material, geometry, and stiffness. Well-designed drivers are crossed over below their breakup region; the breakup modes of a driver used above this frequency produce coloration and elevated distortion.

Back EMF and electrical damping

As the voice coil moves in the magnetic field, it generates a back electromotive force (back EMF) that opposes the applied signal — by Lenz's law, a conductor moving in a magnetic field produces a voltage opposing the motion that caused it. This back EMF appears as an electrical impedance at the driver terminals and is the mechanism by which the amplifier's source impedance damps the mechanical resonance.

A low source impedance (high damping factor amplifier) allows the back EMF to circulate a braking current through the voice coil, damping the resonance. A high source impedance (valve amplifier, current source) allows the resonance to ring more freely. This is the basis of amplifier damping factor as a system parameter — though the voice coil resistance typically dominates over the amplifier output impedance in practice, limiting the practical effect of very high damping factor values.

What limits performance

The key physical trade-offs in electrodynamic transducer design are:

• Sensitivity vs low-frequency extension vs cabinet size — these three are linked by the fundamental Hofmann iron law. Improving any one requires sacrifice in another, for a given driver topology.
• Linear excursion — the Bl product and spider stiffness are only linear over a limited range of voice coil displacement. Beyond this range, distortion rises sharply.
• Thermal power handling — the voice coil can only dissipate a limited amount of heat. Sustained high-power operation causes the coil temperature to rise, increasing resistance and reducing sensitivity.
• Moving mass — more mass extends bass but reduces sensitivity and high-frequency extension.

These constraints explain why no single driver covers the full audio frequency range optimally, and why multiway loudspeaker systems with crossovers are the standard approach for high-performance reproduction.