Thiele-Small Parameters Reference
Thiele-Small (T/S) parameters are a set of measurements that describe the electrical and mechanical properties of a loudspeaker driver. They're essential for predicting how a driver will perform in different enclosure designs.
Electrical Parameters
Re (DC Resistance)
Definition: Voice coil DC resistance measured in ohms.
Typical values: 3-7Ω (4Ω nominal), 5-12Ω (8Ω nominal)
This is the resistance of the voice coil wire. It's always lower than the nominal impedance. Re affects efficiency and how much electrical energy is converted to heat vs motion.
Le (Voice Coil Inductance)
Definition: Voice coil inductance measured in millihenries (mH).
Typical values: 0.2-2 mH for woofers, higher for larger drivers
Inductance causes impedance to rise at higher frequencies. This reduces high-frequency output and affects crossover design. Not critical for subwoofer-only enclosures.
Znom (Nominal Impedance)
Definition: Rated impedance, typically 4Ω or 8Ω.
Typical values: 2Ω, 4Ω, 8Ω, 16Ω
This is the impedance you'd see on the driver's label. The actual impedance varies with frequency and is always higher than Re. Affects amplifier power delivery.
Mechanical Parameters
Mms (Moving Mass)
Definition: Total moving mass including cone, voice coil, former, and air load. Measured in grams (g) or kilograms (kg).
Typical values: 20-200g for woofers, more for subwoofers
Heavier mass means lower resonant frequency but reduced efficiency. Lighter mass means better efficiency but higher resonant frequency.
Cms (Mechanical Compliance)
Definition: Suspension compliance, measured in meters per newton (m/N) or millimeters per newton (mm/N).
Typical values: 0.2-2 mm/N
How easily the suspension moves. Higher compliance (softer suspension) means lower resonant frequency. Lower compliance means stiffer suspension and higher Fs.
Rms (Mechanical Resistance)
Definition: Mechanical damping from suspension losses, measured in kg/s or N·s/m.
Typical values: 0.5-5 kg/s
Represents energy lost to heat in the suspension. Affects Qms. Lower values mean less damping. This parameter is rarely critical for design decisions.
Electro-Mechanical Coupling
Bl (Force Factor)
Definition: Product of magnetic field strength and voice coil length, measured in tesla-meters (T·m).
Typical values: 5-25 T·m depending on size and design
Describes how effectively electrical current is converted to mechanical force. Higher Bl means more efficient motor. Critical for efficiency and control.
Resonance and Q Factors
Fs (Resonant Frequency)
Definition: Free-air resonance frequency where mechanical impedance is minimum. Measured in Hz.
Typical values: 20-60 Hz for subwoofers, higher for midrange
Fundamental frequency where the driver naturally resonates. Lower Fs means deeper bass potential. Determined by Mms and Cms: Fs = 1/(2π√(Mms·Cms)).
Qms (Mechanical Q)
Definition: Quality factor representing mechanical damping losses.
Typical values: 2-10
How much the suspension damps motion. Higher Qms means less mechanical damping (less energy lost to suspension heat). Usually high enough to not be the limiting factor.
Qes (Electrical Q)
Definition: Quality factor representing electrical damping from the motor.
Typical values: 0.2-1.0
How much the magnetic motor damps motion through back-EMF. Lower Qes means stronger motor control. More important than Qms for driver behavior. Related to Bl, Re, and Mms.
Qts (Total Q)
Definition: Combined mechanical and electrical Q factor.
Typical values: 0.2-0.8
The most important Q factor for enclosure design. Calculated as: Qts = (Qms · Qes)/(Qms + Qes). Since Qms is usually much larger than Qes, Qts ≈ Qes.
Design implications:
- Low Qts (0.2-0.4): Best for vented enclosures, well-damped
- Medium Qts (0.4-0.6): Works in both sealed and vented
- High Qts (0.6-0.8): Best for sealed enclosures, less damped
Physical Dimensions
Sd (Effective Piston Area)
Definition: Effective radiating area of the cone, measured in square meters (m²) or square centimeters (cm²).
Typical values: 200-500 cm² for 10-12" woofers
The actual area that moves air. Larger Sd means more air displacement and higher output. Used to calculate Vd and SPL.
Dd (Effective Diameter)
Definition: Effective diameter of the radiating area, measured in meters or millimeters.
Typical values: Slightly less than nominal size (10", 12", etc.)
Calculated from Sd. Not the same as the mounting diameter or overall diameter. Used for reference and calculating Sd.
Xmax (Maximum Linear Excursion)
Definition: Maximum one-way linear excursion before significant distortion, measured in millimeters (mm).
Typical values: 3-20mm for woofers, more for high-excursion designs
How far the cone can move in one direction before the voice coil leaves the magnetic gap or suspension becomes nonlinear. Critical for determining maximum clean output.
Derived Parameters
Vas (Equivalent Compliance Volume)
Definition: Volume of air with the same compliance as the driver's suspension, measured in liters or cubic meters.
Typical values: 10-200 liters for typical woofers
Indicates how "stiff" the suspension is. Larger Vas means softer suspension. Roughly indicates the minimum box size needed. Calculated from Cms, Sd, and air properties.
Vd (Volume Displacement)
Definition: Maximum volume displaced by the driver, measured in liters or cubic centimeters.
Typical values: 100-500 cm³ for typical woofers
Calculated as Vd = Sd × Xmax. Indicates maximum air volume the driver can move. Larger Vd generally means higher maximum output.
Power Handling
Pe (Rated Power)
Definition: Thermal power handling rating, measured in watts (W).
Typical values: 100-1000W for subwoofers
Maximum continuous power the voice coil can handle before overheating. Usually based on AES standard (noise signal, 2 hours). Peak power is often higher but not useful for design.
In practice, mechanical limits (Xmax) often limit usable power before thermal limits, especially at low frequencies.
Relationships and Trade-offs
Efficiency vs Extension
Higher efficiency (louder with less power) typically comes with higher Fs and less deep-bass capability. Lower Fs (deeper bass) usually means lower efficiency.
Qts and Enclosure Type
Low Qts drivers need larger sealed boxes for flat response but work well in smaller vented boxes. High Qts drivers work well in small sealed boxes but are poor choices for vented alignments.
Xmax and Output
Along with Sd, Xmax determines maximum linear output. Vd = Sd × Xmax is a useful single-number indicator of potential output capability.
How Parameters Are Measured
Manufacturers measure T/S parameters using various methods:
- Added mass method: Measures resonance change when adding known mass
- Current/voltage method: Uses electrical measurements at resonance
- Laser measurement: Direct measurement of cone motion for Cms and Xmax
Parameters can shift with break-in (suspension loosens) and temperature (voice coil resistance changes). Published values are typically at room temperature after break-in.