Editing Thiele/Small parameters (section)

==Qualitative descriptions==
[[Image:Speaker-cross-section.svg|thumb|right|450px|Cross-section of a dynamic cone loudspeaker. ''Image not to scale.'']]

; <math>f_{\rm s}</math>
: Resonance frequency of driver, measured in [[hertz]] (Hz). The frequency at which the combination of the energy stored in the moving mass and suspension compliance is maximum, and results in maximum cone velocity. A more compliant suspension or a larger moving mass will cause a lower resonance frequency, and vice versa. Usually it is less efficient to produce output at frequencies below <math>f_{\rm s}</math>, and input signals significantly below <math>f_{\rm s}</math> can cause large excursions, mechanically endangering the driver.  Woofers typically have an <math>f_{\rm s}</math> in the range of 13–60&nbsp;Hz. Midranges usually have an <math>f_{\rm s}</math> in the range of 60–500&nbsp;Hz and tweeters between 500&nbsp;Hz and 4&nbsp;kHz. A typical factory tolerance for the value of <math>f_{\rm s}</math> is ±15%.

; <math>Q_{\rm ts}</math>
: A unitless measurement, characterizing the combined electric and mechanical damping of the driver. In electronics, <math>Q</math> is the inverse of the damping ratio. The value of <math>Q_{\rm ts}</math> is proportional to the energy stored, divided by the energy dissipated, and is defined at resonance (<math>f_{\rm s}</math>). Most drivers have <math>Q_{\rm ts}</math> values between 0.2 and 0.5, but there are valid (if unusual) reasons to have a value outside this range.

; <math>Q_{\rm ms}</math>
: A unitless measurement, characterizing the mechanical damping of the driver, that is, the losses in the suspension (surround and spider). It varies roughly between 0.5 and 10, with a typical value around 3. High <math>Q_{\rm ms}</math> indicates lower mechanical losses, and low <math>Q_{\rm ms}</math> indicates higher losses. The main effect of <math>Q_{\rm ms}</math> is on the impedance of the driver, with high <math>Q_{\rm ms}</math> drivers displaying a higher impedance peak. One predictor for low <math>Q_{\rm ms}</math> is a metallic voice-coil former. These act as [[eddy-current]] brakes and increase damping, reducing <math>Q_{\rm ms}</math>. They must be designed with an electrical break in the cylinder (so no conducting loop). Some speaker manufacturers have placed shorted turns at the top and bottom of the voice coil to prevent it leaving the gap, but the sharp noise created by this device when the driver is overdriven is alarming and was perceived as a problem by owners. High <math>Q_{\rm ms}</math> drivers are often built with nonconductive formers made from paper or various plastics.

; <math>Q_{\rm es}</math>
: A unitless measurement, describing the electrical damping of the loudspeaker.  As the coil of wire moves through the magnetic field, it generates a current which opposes the motion of the coil. This so-called "Back-EMF" (proportional to <math>Bl</math> × velocity) decreases the total current through the coil near the resonance frequency, reducing cone movement and increasing impedance. In most drivers, <math>Q_{\rm es}</math> is the dominant factor in the voice coil damping. <math>Q_{\rm es}</math> depends on amplifier output impedance.  The formula above assumes zero output impedance.  When an amplifier with nonzero output impedance is used, its output impedance should be added to <math>R_{\rm e}</math> for calculations involving <math>Q_{\rm es}</math>.

; <math>Bl</math>
: Measured in [[tesla (unit)|tesla]]-metres (T·m). Technically this is <math>B \times l</math> or <math>B \times l sin(\theta)</math> (a [[vector cross product]]), but the standard geometry of a circular coil in an annular voice-coil gap gives <math>sin(\theta)=1</math>. <math>B \times l</math> is also known as the 'force factor' because the force on the coil imposed by the magnet is <math>B \times l</math> multiplied by the current through the coil. The higher the <math>B \times l</math> product, the larger the force that is generated by a given current flowing through the voice coil. <math>B \times l</math> has a very strong effect on <math>Q_{\rm es}</math>.

; <math>V_{\rm as}</math>
: Measured in [[litre]]s (L) or cubic metres, it is an inverse measure of the 'stiffness' of the suspension with the driver mounted in free air. It represents the volume of air that has the same stiffness as the driver's suspension when acted on by a piston of the same area (<math>S_{\rm d}</math>) as the cone. Larger values mean lower stiffness, and generally require larger enclosures. <math>V_{\rm as}</math> varies with the square of the diameter. A typical factory measurement tolerance for <math>V_{\rm as}</math> is ±20–30%.

; <math>M_{\rm ms}</math>
: Measured in [[gram]]s (g) or kilograms (kg), this is the mass of the cone, coil, voice-coil former and other moving parts of a driver, including the acoustic load imposed by the air in contact with the driver cone. <math>M_{\rm md}</math> is the cone/coil mass without the acoustic load, and the two should not be confused. Some simulation software calculates <math>M_{\rm ms}</math> when <math>M_{\rm md}</math> is entered. <math>M_{\rm md}</math> can be very closely controlled by the manufacturer.

; <math>R_{\rm ms}</math>
: Units are not usually given for this parameter, but it is in mechanical 'ohms'. <math>R_{\rm ms}</math> is a measurement of the losses, or damping, in a driver's suspension and moving system. It is the main factor in determining <math>Q_{\rm ms}</math>. <math>R_{\rm ms}</math> is influenced by suspension topology, materials, and by the voice-coil former ([[bobbin]]) material.

; <math>C_{\rm ms}</math>
: Measured in metre per newton (m/N). Describes the compliance (i.e., the inverse of stiffness) of the suspension. The more compliant a suspension system is, the lower its stiffness, so the higher the <math>V_{\rm as}</math> will be. <math>C_{\rm ms}</math> is proportional to <math>V_{\rm as}</math> and thus has the same tolerance ranges.

; <math>R_{\rm e}</math>
: Measured in [[ohm]]s (Ω), this is the DC resistance (DCR) of the voice coil, best measured with the cone blocked, or prevented from moving or vibrating because otherwise the pickup of ambient sounds can cause the measurement to be unreliable. <math>R_{\rm e}</math> should not be confused with the rated driver impedance, <math>R_{\rm e}</math> can be tightly controlled by the manufacturer, while rated impedance values are often approximate at best. American [[Electrical Industries Association|EIA]] standard RS-299A specifies that <math>R_{\rm e}</math> (or DCR) should be at least 80% of the rated driver impedance, so an 8-ohm rated driver should have a DC resistance of at least 6.4&nbsp;ohms, and a 4-ohm unit should measure 3.2&nbsp;ohms minimum. This standard is voluntary, and many 8-ohm drivers have resistances of ≈5.5&nbsp;ohms, and proportionally lower for lower rated impedances.

; <math>L_{\rm e}</math>
: Measured in henries (H), this is the [[inductance]] of the voice coil. The voice coil is a lossy inductor, in part due to losses in the pole piece, so the apparent inductance changes with frequency.<ref name="Wright1990"/><ref name="Leach2002"/><ref name="KlippelVCImpedance"/> Large <math>L_{\rm e}</math> values limit the high-frequency output of the driver and cause response changes near cutoff. Simple modeling software often neglects <math>L_{\rm e}</math>, and so does not include its consequences. Inductance varies with excursion because the voice coil moves relative to the pole piece, acting like a sliding inductor core, increasing inductance on the inward stroke and decreasing it on the outward stroke in typical overhung voice coil arrangements. This inductance modulation is an important source of nonlinearity (distortion) in loudspeakers. Including a copper cap on the pole piece, or a copper shorting ring on it, can reduce the increase in impedance seen at higher frequencies in typical drivers, and also reduce the nonlinearity due to inductance modulation.

; <math>S_{\rm d}</math>
: Measured in square metres (m<sup>2</sup>). The effective projected area of the cone or diaphragm. It is difficult to measure and depends largely on the shape and properties of the surround. Generally accepted as the cone body diameter plus one third to one half the width of the annulus (surround). Drivers with wide roll surrounds can have significantly less <math>S_{\rm d}</math> than conventional types with the same frame diameter.

; <math>X_{\rm max}</math>
: Specified in millimetres (mm). In the simplest form, subtract the height of the voice-coil winding from the height of the magnetic gap, take the absolute value and divide by 2. This technique was suggested by [[JBL (company)|JBL]]'s Mark Gander in a 1981 [[Audio Engineering Society|AES]] paper,<ref name="Gander1981"/> as an indicator of a loudspeaker motor's linear range. Although easily determined, it neglects magnetic and mechanical non-linearities and asymmetry, which are substantial for some drivers. Subsequently, a combined mechanical/acoustical measure was suggested, in which a driver is progressively driven to high levels at low frequencies, with <math>X_{\rm max}</math> determined by measuring excursion at a level where 10% [[Total harmonic distortion|THD]] is measured in the output. This method better represents actual driver performance, but is more difficult and time-consuming to determine.

; <math>P_{\rm e}</math>
: Specified in watts.  Frequently two power ratings are given, an "RMS" rating and a "music" (or "peak", or "system") rating, usually peak is given as ≈2&nbsp;times the RMS rating. Loudspeakers have complex behavior, and a single number is really unsatisfactory. There are two aspects of power handling: thermal and mechanical.  The thermal capacity is related to coil temperature and the point where adhesives and coil insulation melt or change shape. The mechanical limit comes into play at low frequencies, where excursions are largest, and involves mechanical failure of some component. A speaker that can handle 200 watts thermally at 200&nbsp;Hz, may sometimes be damaged by only a few watts at some very low frequency, like 10&nbsp;Hz. Power handling specifications are usually generated destructively, by long-term industry standard noise signals (IEC&nbsp;268, for example) that filter out low frequencies and test only the thermal capability of the driver. Actual mechanical power handling depends greatly on the enclosure in which the driver is installed.

; <math>V_{\rm d}</math>
: Specified in litres (L). The volume displaced by the cone, equal to the cone area (<math>S_{\rm d}</math>) multiplied by <math>X_{\rm max}</math>. A particular value may be achieved in any of several ways. For instance, by having a small cone with a large <math>X_{\rm max}</math>, or a large cone with a small <math>X_{\rm max} </math>. Comparing <math>V_{\rm d}</math> values will give an indication of the maximum output of a driver at low frequencies. High <math>X_{\rm max}</math>, small cone diameter drivers are likely to be inefficient, since much of the voice-coil winding will be outside the magnetic gap at any one time and will therefore contribute little or nothing to cone motion. Likewise, large cone diameter, small <math>X_{\rm max}</math> drivers are likely to be more efficient as they will not need, and so may not have, long voice coils.

; <math>\eta_0</math>
: Reference efficiency, specified in percent (%). Comparing drivers by their calculated reference efficiency is often more useful than using 'sensitivity' since manufacturer sensitivity figures are too often optimistic.

; ''Sensitivity''
: The sound pressure, in dB, produced by a speaker in response to a specified stimulus. Usually this is specified at an input of 1&nbsp;watt or 2.83&nbsp;volts (2.83&nbsp;volts = 1&nbsp;watt into an 8-ohm load) at a distance of one metre.