Qualitative descriptions Thiele/Small parameters

cross-section of dynamic cone loudspeaker. image not scale.



fs
also called fs, resonance frequency measured in hertz (hz). frequency @ combination of energy stored in moving mass , suspension compliance maximum, , results in maximum cone velocity. more compliant suspension or larger moving mass cause lower resonance frequency, , vice versa. less efficient produce output @ frequencies below fs, , input signals below fs can cause large excursions, mechanically endangering driver. woofers typically have fs in range of 13–60 hz. midranges have fs in range of 60–500 hz , tweeters between 500 hz , 4 khz. typical factory tolerance fs spec ±15%.


qts
a unitless measurement, characterizing combined electric , mechanical damping of driver. in electronics, q inverse of damping ratio. value of qts proportional energy stored, divided energy dissipated, , defined @ resonance (fs). drivers have qts values between 0.2 , 0.5, there valid (if unusual) reasons have value outside range.


qms
a unitless measurement, characterizing mechanical damping of driver, is, losses in suspension (surround , spider.) varies between 0.5 , 10, typical value around 3. high qms indicates lower mechanical losses, , low qms indicates higher losses. main effect of qms on impedance of driver, high qms drivers displaying higher impedance peak. 1 predictor low qms metallic voice coil former. these act eddy-current brakes , increase damping, reducing qms. must designed electrical break in cylinder (so no conducting loop). speaker manufacturers have placed shorted turns @ top , bottom of voice coil prevent leaving gap, sharp noise created device when driver overdriven alarming , perceived problem owners. high qms drivers built nonconductive formers made paper or various plastics.


qes
a unitless measurement, describing electrical damping of loudspeaker. coil of wire moves through magnetic field, generates current opposes motion of coil. so-called back-emf (proportional bl * velocity) decreases total current through coil near resonance frequency, reducing cone movement , increasing impedance. in drivers, qes dominant factor in voice coil damping. qes depends on amplifier output impedance. formula above assumes 0 output impedance. when amplifier nonzero output impedance used, output impedance should added re calculations involving qes.


bl
measured in tesla-metres (t·m). technically b×l or b×l sin(θ) (a vector cross product), standard geometry of circular coil in annular voice coil gap gives sin(θ)=1. b×l known force factor because force on coil imposed magnet b×l multiplied current through coil. higher b×l value, larger force generated given current flowing through voice coil. b×l has strong effect on qes.


vas
measured in litres (l) or cubic metres, inverse measure of stiffness of suspension driver mounted in free air. represents volume of air has same stiffness driver s suspension when acted on piston of same area (sd) cone. larger values mean lower stiffness, , require larger enclosures. vas varies square of diameter. typical factory tolerance vas spec ±20–30%.


mms
measured in grams (g) or kilograms (kg), mass of cone, coil , other moving parts of driver, including acoustic load imposed air in contact driver cone. mmd cone/coil mass without acoustic load, , 2 should not confused. simulation software calculates mms when mmd entered. mmd can closely controlled manufacturer.


rms
units not given parameter, in mechanical ohms . rms measurement of losses, or damping, in driver s suspension , moving system. main factor in determining qms. rms influenced suspension topology, materials, , voice coil former (bobbin) material.


cms
measured in metres per newton (m/n). describes compliance (ie, inverse of stiffness) of suspension. more compliant suspension system is, lower stiffness, higher vas be. cms proportional vas , has same tolerance ranges.


re
measured in ohms (Ω), dc resistance (dcr) of voice coil, best measured cone blocked, or prevented moving or vibrating because otherwise pickup of ambient sounds can cause measurement unreliable. re should not confused rated driver impedance, re can tightly controlled manufacturer, while rated impedance values approximate @ best. american eia standard rs-299a specifies re (or dcr) should @ least 80% of rated driver impedance, 8-ohm rated driver should have dc resistance of @ least 6.4 ohms, , 4-ohm unit should measure 3.2 ohms minimum. standard voluntary, , many 8 ohm drivers have resistances of ~5.5 ohms, , proportionally lower lower rated impedances.


le
measured in millihenries (mh), inductance of voice coil. coil lossy inductor, in part due losses in pole piece, apparent inductance changes frequency. large le values limit high frequency output of driver , cause response changes near cutoff. simple modeling software neglects le, , not include consequences. inductance varies excursion because voice coil moves relative polepiece, acts sliding inductor core, increasing inductance on inward stroke , decreasing on outward stroke in typical overhung coil arrangements. inductance modulation important source of nonlinearity (distortion) in loudspeakers. including copper cap on pole piece, or copper shorting ring on it, can reduce increase in impedance seen @ higher frequencies in typical drivers, , reduce nonlinearity due inductance modulation.


sd
measured in square metres (m²). effective projected area of cone or diaphragm. difficult measure , depends largely on shape , properties of surround. accepted cone body diameter plus 1 third 1 half width of annulus (surround). drivers wide roll surrounds can have less sd conventional types same frame diameter.


xmax
specified in millimeters (mm). in simplest form, subtract height of voice coil winding height of magnetic gap, take absolute value , divide 2. technique suggested jbl s mark gander in 1981 aes paper, indicator of loudspeaker motor s linear range. although determined, neglects magnetic , mechanical non-linearities , asymmetry, substantial drivers. subsequently, combined mechanical/acoustical measure suggested, in driver progressively driven high levels @ low frequencies, xmax determined measuring excursion @ level 10% thd measured in output. method better represents actual driver performance, more difficult , time-consuming determine.


pe
specified in watts. 2 power ratings given, rms rating , music (or peak , or system ) rating, peak given ~2 times rms rating. loudspeakers have complex behavior, , single number unsatisfactory. there 2 aspects of power handling, thermal , mechanical. thermal capacity related coil temperature , point adhesives , coil insulation melt or change shape. mechanical limit comes play @ low frequencies, excursions largest, , involves mechanical failure of component. speaker can handle 200 watts thermally @ 200hz, may damaged few watts @ low frequency, 10hz. power handling specifications generated destructively, long term industry standard noise signals (iec 268, example) filter out low frequencies , test thermal capability of driver. actual mechanical power handling depends on enclosure in driver installed.


vd
specified in litres (l). volume displaced cone, equal cone area (sd) multiplied xmax. particular value may achieved in of several ways. instance, having small cone large xmax, or large cone small xmax. comparing vd values give indication of maximum output of driver @ low frequencies. high xmax, small cone diameter drivers inefficient, since of voice coil winding outside magnetic gap @ 1 time , therefore contribute little or nothing cone motion. likewise, large cone diameter, small xmax drivers more efficient not need, , may not have, long voice coils.


η0 - reference efficiency
specified in percent (%). comparing drivers calculated reference efficiency more useful using sensitivity since manufacturer sensitivity figures optimistic.


sensitivity
the sound pressure, in db, produced speaker in response specified stimulus. specified @ input of 1 watt or 2.83 volts (2.83 volts = 1 watt 8 ohm load) @ distance of 1 metre.