Speaker impedance. Tomi Engdahl, Speaker Impedance Page 1 of 6 SPEAKER NOMINAL IMPEDANCE: PRACTICAL CASE: MEASURING SPEAKER NOMINAL IMPEDANCE:

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1 Speaker impedance The fllwing article is based n news articles psted t rec.audi.tech newsgrup by Richard Pierce, Dan Marshall and Jhn Wdgate at 1998 and The article is cmpiled and edited by Tmi Engdahl at The fllwing things have effect n speaker impedance: Vice cil's electrical impedance (resistance, inductance, stray capacitance) Driver's mechanical impedance (stiffness, mass, damping) Driver's acustic radiatin impedance (resistance, reactance) SPEAKER NOMINAL IMPEDANCE: There is a cnventin t the use f the term "nminal impedance", and if the impedance ver the majrity f the bandwidth, specifically cvering the range in spectrum where majrity f the musical spectral pwer ccurs, it's 8 hms. A single number cannt tell all there is t tell abut impedance that varies with frequency. Yu must keep in mind that 'nminal impedance' is nt defined in IEC. Indeed, the electrnics industry was advised when the Trade Descriptins Act was intrduced, that the wrd 'nminal' shuld n lnger be used in specificatins. That is why the IEC cncept f 'rated value' is s useful. There is a very detailed definitin and explanatin f this term in IEC The IEC standard (IEC6068-3) allws any "increase" abve the rated value, but limits the "decrease". The standard des nt allw the impedance t fall belw the 80 % f the nminal value at any frequency, including DC. PRACTICAL CASE: In practice all ludspeakers are a cmprmise, the designer is therefre free t allw the speaker t suck mre pwer frm the amp in rder t ptimise ther parameters. Mst high-quality ludspeakers d dip well belw 80% f their nminal impedance at ne r mre pints in the audi band. Speakers which attempt t present a flat impedance lad using cnjugate techniques have smetimes been described as 'flat and bring', which may r may nt be cnnected t their excessively cmplex crssvers. Speaker design is nn-trivial! Remember that a specificatin is nly f relevance when a prduct is claimed t meet it. A specificatin is nly f value when it lays dwn a minimum standard which is f relevance t the intended purpse f the prduct. A high-quality speaker may reasnably be assumed t be intended t be driven by a high quality amplifier; hence minimum impedance is nt an imprtant criterin in establishing snic perfrmance. MEASURING SPEAKER NOMINAL IMPEDANCE: If yu just want t find ut the nminal impedance f the speaker e.g. ist it 4, 8 r 15 hms then there is a rugh & ready way. Just use yur multimeter t measure the DC resistance f the vice cil i.e. acrss the speaker terminals (with nthing else cnnected) and multiply the answer by 1.3. S if the DC resistance is say 6 hms then the speaker is nminally 8 hm impedance. Mre cmplete analysis with minimal equipments: Tmi Engdahl, Speaker Impedance Page 1 f 6

2 a) Measure the DC resistance acrss the vice cil with the driver discnnected. The hm value yu get is the lwer impedance bund f the driver. Add an hm r tw t this value, and yu shuld be at the nminal (rated) impedance f the driver. b) Cnnect a pt in series with the driver vice cil and then t the amp. c) Cnnect frequency generatr r CD player with suitable test CD in it t the amp input, and start walking up the frequency scale in steps. Fr each step, measure the vltage acrss the vice cil terminals and then acrss the pt. Adjust the pt until bth vltages match. Nw shut dwn the amp. and measure the resistance acrss the pt. This is the driver impedance fr the current drive frequency. This apprach is nt the mst accurate, but it needs minimal set f measuring equipments: multimeter, signal generatr and a ptentimeter f 50 hms 5-10 watts. The clear advantage f this apprach is that the accuracy f the measurement is nt affected by the multimeter frequency respnse (their AC range is designed t shw right values at arund 50 Hz range and at higher frequencies the accuracy can drp nticeably depending n the meter cnstructin, but this des nt affect in this measurement because the abslutely crrect AC vltage values are nt needed). Warning, KEEP DRIVE LEVELS TO SPEAKER VERY LOW. High levels f sustained sine wave can up the driver vice cil. SPEAKER MODEL: The single mst dminant branch f the mdel is the vice cil DC resistance, re. It's ging t be in series with everything else we will lk at (yu mentined "stray capacitance". Yes, there is sme, but its magnitude is abslutely miniscule cmpared t all ther cmpnents s it can be ignred). Next we have the vice cil inductance (we'll call it L vc ). Nw, it, t, is in series with everything else, but it's n simple inductance. S far, we have the tw real electrical cmpnents, and they lk like: In Re Lvc Out Nw, the next majr set f cmpnents are the electrical equivalents f the majr mechanical cmpnents f suspensin cmpliance, cne mass and suspensin lsses. The suspensin cmpliance is mdelled as an inductr, L ces. The cne mass is mdelled as a capacitance, C mes, and the suspensin lsses are mdelled as a resistr, R es. These three are in parallel and frm a damped, parallel resnant branch called the driver mechanical branch. Finally, in series with that is the radiatin impedance. N single lumped-parameter synthesis cmes clse t apprximating this. Als the magnitude f the impedance f this branch is small cmpared t the thers, s fr simulating the ELECTRICAL characteristics, it can be safely eliminated. The driver electrical mdel, then, lks like this: + Re Lvc Lces Cmes Res - Xrs Tmi Engdahl, Speaker Impedance Page f 6

3 Nw, the relative values f these cmpnents depends upn the magnitudes f the physical values times a transfrmatin factr. That transfrmatin factr is the electrmagnetic transductin factr, prprtinal t the Bl prduct (the prduct f the length f the wire l immersed in the magnetic field B), measured in N/A (r T/M, if yu will). S, IF we knw the magnitudes f the physical cmpnents, we can easily calculate their electrical equivalents: R e L vc Dn't calculate it, just measure it with a gd hmmeter! Measure it, but see belw! Lces = Cms Bl Where C ms is the mechanical cmpliance in m/n, and the resulting Inductance is in Henries. L ces Depends upn the suspensin cmpliance: ( ) C mes R es X rs Mms depends upn the cne mass: Cmes = ( Bl) Where Mms is the mechanical cmpliance in kg, and the resulting Capacitance is in farads ( Bl) depends upn the suspensin lsses: Re s = Rms Where R ms is the mechanical lsses in 1/s, and the resulting Resistance is in hms. Depends upn the air, the driver diameter, the baffle dimensins, psitin f the driver n the baffle, etc., but has little effect n the electrical impedance. TYPICAL CHARACTERISTICS: Fr example, a typical 8" wfer with F s =30 Hz, V as =60L, Q ms =.40, Q es =0.4, Q ts =0.36, R e =6.5 hms, might have the fllwing mechanical parameters: 3 Cms = 1.01*10 m N 3 Mms = 7.9 *10 kg Rms =.19 kg s Bl = 8.84 N A Then, the electrical equivalents wuld be: Lces = 78.9mH Cmes = 356uF Re s = 35.7Ω Re = 6.5Ω Tmi Engdahl, Speaker Impedance Page 3 f 6

4 EFFECT OF ENCLOSURE: One can cnstruct a similar branch fr the enclsure, using the lumped parameters f a capacitive equivalent C mep fr the prt mass M mp, and inductive equivalent L ceb fr the enclsure cmpliance C mb a resistive equivalent R eb fr the system lsses R mb and the prt radiatin impedance X rp (which is, again, small). That branch lks like: + Lceb Cmep Rmb - Xrp The cmplete driver + enclsure + electrical mdel lk like: Re Lvc + Lceb Lces Cmes Res Cmep - Xrs Reb Xrp Nw there are sme ther cmplicating elements that wuld make fr a cmplete mechanical and acustical mdel, such as the mutual cupling f the driver and prt, etc., but fr the electrical mdel the abve suffices quite well fr predicting reality. TYPICAL IMPEDANCE CHARACTERISTICS OF SPEAKER ELEMENT AT DIFFERENT FREQUENCIES: Let's lk at the impedance f a very typical driver. It has the fllwing characteristics: At DC, the impedance is cmpletely dminated by the DC resistance f the vice cil. As yu increase in frequency twards the fundamental mechanical resnance, the reflected mtinal impedance begins t dminate and is inductive in nature. Hwever, the ttal phase angle f the impedance RARELY exceeds 45 degrees and thus the resistive and reactive (inductive) parts f the impedance are just abut equal. At fundamental resnance, the impedance is purely resistive, its phase angle is 0, and is determined by the effective series cmbinatin f the vice cil DC resistance and the reflected mechanical lsses f (primarily) the suspensin (R e + R es in standard Thiele/Small ntatin). Abve fundamental resnance, the impedances drps, has a negative phase angle (rarely exceeding 45 degrees) and is, surprise, capacitive in nature. The impedance drps until... In the midrange, it appraches the DC resistance f the vice cil it is SLIGHTLY higher than that DC resistance fr a variety f reasns, typically abut 10-0% (and THIS is the regin that is used by MOST reasnably respnsible manufacturers fr specifying the nminal Tmi Engdahl, Speaker Impedance Page 4 f 6

5 impedance). The impedance at these frequencies is predminantly resistive in nature and is dminated by the DC resistance f the vice cil. Abve this regin, the inductance f the vice cil begins t influence the impedance. Hwever, it NEVER becmes purely inductive, r even remtely clse. First, ver the majrity f the range f peratin, the vice cil resistance still dminates. Secnd, eddy current lsses in the ple piece (see Vaderky, et al) dminate quickly, such that the phase angle f the impedance asympttically appraches abut 45 degrees, and NEVER 90 degrees, which wuld be necessary if yur assertin that the impedance was almst a pure inductance were true. Impedance f a speaker IS NOT ALMOST A PURE INDUCTANCE. It is NOWHERE NEAR a pure inductance. The impedance f a speaker is nly a rugh average f the impedance and that the vice cil dc resistance f mst nrmal cne type dynamic speaker is rughly 75% f its "rated" impedance as the industry rates impedance. Mst 8 hm speakers will measure smewhere arund 6+ hms dc give r take a bit. (When hrn laded, the impedance increases). IMPEDANCE AND EFFIENCY: Let's lk at the fllwing situatin: Take an 8 hm speaker and wind twice the length f wire nt the vice cil. The resistance wuld g up, fr sure, but because there is n mre wire in the gap, the electrmagnetic cupling cefficient, the B l prduct, wuld als g up. And yu wuld have, as a result, a 16 hm speaker with essentially the same efficiency as the 8 hm speaker, all ther things being equal. Or yu culd design a speaker with bth a higher impedance (lnger wire in the vice cil) AND a larger magnet assembly with higher flux density in the gap and get a higher impedance driver with higher electr-acustic efficiency. Or yu culd design a higher impedance driver with a strnger magnet and a lighter cne and get even mre efficiency. The pint is, the rated impedance IS NOT the same as the efficiency, nr is there any direct crrelatin between the tw. Efficiency f a given direct radiatr driver is determined by the fllwing relatinship: N0 = K R where: e B S d L MAS k is a cnstant determined by the prperties f air. B is the magnetic flux density in the gap. l is the length f wire in the magnetic field. R e is the DC resistance. S d is the radiating area f the cne. M as is the effective ttal mving acustical mass f the driver. S, we can see that by dubling the length f the wire that's in the gap (dubling l) will, by itself, increase the efficiency by a factr f 4, but since Re als dubles, it drps it by half, meaning that, all ther things being equal, lengthening the vice cil winding in the gap increases BOTH impedance AND efficiency. Nw, there ARE tradeffs, and everything CAN'T be equal. Lengthening the wire ALSO increases the mass, thugh the vice cil is nly part f a larger mass (it includes the vice cil frmer, the cne, and s n) s there is nt a direct relatin. Als, the gap may need t be widened t accmmdate the greater winding diameter f the vice cil, and that may reduce B. Tmi Engdahl, Speaker Impedance Page 5 f 6

6 Add resistance certainly reduces efficiency all by itself. Yu culd, fr example, just simply slder a resistr in series and, l and behld, the impedance ges up and the efficiency ges dwn. But we already have a case where the efficiency ges up as the impedance ges up. Yu culd wind the vice cil with the same length f finer gauge wire. The result wuld be the impedance ges up, and s des the resistance, but since l remains abut the same, l^, remains the same and the efficiency ges dwn. But wait!, finer wire means less mass, s we can gain sme efficiency back frm that and the finer wire means a smaller thickness t the vice cil, and the designer may be able t clse up the gap and increase B. Or, the designer may just design a TOTALLY difference driver with a different B, a different l, a different cne diameter (changes S d ), a different mving mass and a different resistance and get smething ttally different efficiency wise. The pint being is that a statement like "The higher the impedance, the lwer then efficiency," as a generalizatin has NO basis in physical fact. Tmi Engdahl, Speaker Impedance Page 6 f 6