How does a loudspeaker work?
From electrical signal to mechanical motion and acoustic power
A loudspeaker is an electromechanical transducer. It turns voltage and current into force, force into motion, and motion into an acoustic field. The elegance - and difficulty - lies in the coupling between its electrical, mechanical and acoustic domains.
1. Lorentz force in the motor
A current-carrying voice coil in the magnetic gap experiences force approximately proportional to current:
Symbols: F is force on the voice coil in newtons, B magnetic flux density in teslas, l effective conductor length in the field and I current in amperes. The product Bl is the driver force factor, measured in N/A.
The force factor Bl combines magnetic flux density and active conductor length. In an ideal small-signal model, current maps linearly to force. At large excursion, Bl becomes position-dependent and one source of distortion.
2. Back electromotive force
Motion of the coil in the magnetic field generates a back EMF:
Symbols: e is motion-induced back EMF in volts, Bl force factor and v voice-coil velocity in metres per second. The expression gives magnitude; by Lenz’s law the induced voltage opposes the change that creates it.
This couples mechanical motion back into the electrical impedance. The complete small-signal input impedance can be represented as:
Zmech(s) = Rms + sMms + 1sCms
Symbols: Ze is electrical input impedance, Re voice-coil DC resistance, Le inductance, s complex frequency and Zmech mechanical impedance. Rms, Mms and Cms represent mechanical loss, moving mass and compliance. The reflected term shows how cone mechanics load the electrical input.
Near mechanical resonance the motional term strongly alters terminal impedance, producing the familiar resonance peak.
3. Cone, surround, spider and voice coil
The moving assembly combines diaphragm mass, voice coil former, coil, surround and spider. The suspension provides restoring stiffness and damping while maintaining alignment. Their mass, compliance and losses determine resonance and transient behaviour together with the motor and enclosure.
4. Resonance and Thiele-Small parameters
Parameters such as fₛ, Qₑₛ, Qₘₛ, Qₜₛ, Vₐₛ, Mₘₛ, Cₘₛ, Rₑ, Bl and Sd describe the driver’s small-signal behaviour. The quality factors satisfy:
Symbols: Qts is total, Qes electrical and Qms mechanical quality factor. Adding their reciprocals expresses how electrical and mechanical losses combine to determine total damping.
They are modelling parameters, not a ranking system. Good enclosure design matches driver parameters to the required alignment.
5. Sealed enclosure
A sealed box adds an air spring behind the cone, raising system resonance and changing Q. At low frequency the classic sealed alignment behaves approximately as a second-order high-pass system, with about 12 dB/octave asymptotic roll-off below resonance. It provides excellent control but demands increasing excursion as frequency falls.
6. Bass reflex
A vented enclosure uses a Helmholtz resonance so the port contributes strongly around the tuning frequency fb. Near tuning, cone excursion can be reduced while acoustic output remains high. Below tuning, however, the acoustic system becomes approximately fourth-order and rolls off rapidly - about 24 dB/octave asymptotically - while cone excursion can rise sharply. A suitable high-pass filter is therefore a critical protection tool.
7. Directivity - why does a large diaphragm beam at high frequency?
A radiator becomes increasingly directional as its dimensions become comparable with wavelength. The dimensionless parameter ka is useful:
Symbols: here k is acoustic wavenumber, λ wavelength, ω angular frequency, c sound speed, a the radius of a circle with the same area as diaphragm area Sd, and ka their dimensionless product. Larger ka generally means stronger directivity; this k is not spring stiffness.
For ka≪1 the source is broadly omnidirectional; by ka≈1-2 directivity narrows significantly. This is why crossover design must consider not only on-axis magnitude but also the off-axis behaviour of adjacent drivers.
8. Compression driver and horn
Compression drivers use a small diaphragm coupled through a phase plug into a narrow throat and then a horn or waveguide. The phase plug equalises path lengths from different diaphragm regions so they reach the throat with limited destructive interference. Ideally the path-length spread is much smaller than half a wavelength at the highest operating frequency.
9. Distortion
Loudspeaker distortion includes harmonic, intermodulation and modulation components. Large excursion changes Bl(x), suspension stiffness Kms(x) and inductance Lₑ(x); Doppler-like modulation and airflow nonlinearities can also contribute. Distortion therefore depends on frequency, level and displacement, not only on a single THD number.
10. Piston range and cone breakup
At low enough frequency the diaphragm can approximate a rigid piston. As frequency rises, bending modes develop and different regions no longer move in phase. These breakup modes can create sharp response peaks, directivity irregularities and stored energy. Material choice and cone geometry are used to control where and how breakup occurs.
11. Xmax, Xmech and real excursion
Xmax is usually a defined linear-excursion metric based on motor/suspension geometry or an accepted distortion criterion. Xmech is a mechanical damage or travel limit and is not a recommended operating point. Datasheet definitions vary, so comparison requires reading the manufacturer’s method.
12. Bl(x), Kms(x) and Le(x)
Modern large-signal analysis, including Klippel-style measurements, examines how motor force factor, suspension stiffness and inductance vary with displacement. Asymmetry in these curves predicts even-order distortion, DC offset tendencies and compression. They reveal information that small-signal T/S parameters cannot.
13. Horns and waveguides
A waveguide controls radiation impedance and directivity; a horn can also provide acoustic loading and efficiency gain. Geometry determines coverage, high-frequency pattern control, mouth behaviour and internal reflections. “Horn” therefore describes an acoustic transformer/directivity device, not merely a shape.
14. Coaxial and point-source constructions
Placing HF and LF acoustic centres close together can improve spatial coherence and directivity consistency, especially off axis. Coaxial systems still require careful control of horn loading, cone geometry, diffraction and crossover phase; “point source” is an approximation, not a guarantee of perfect behaviour.
15. Why diaphragm diameter does not equal “bass”
Low-frequency capability is determined by displacement volume Sd·Xmax, resonance, enclosure alignment, motor strength, thermal capability and target SPL. A large cone with little excursion or poor motor control may produce less useful deep bass than a smaller high-excursion design. Diameter is only one parameter.
Sources and professional background
- Thiele, A. N. and Small, R. H. - classical low-frequency loudspeaker alignment papers
- IEC 60268-5 and AES loudspeaker measurement standards
- Klippel - large-signal loudspeaker measurement and modelling literature
- Electroacoustic transducer and waveguide design texts
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