INPUT CURRENT REQUIREMENTS OF HIGH-QUALITYLOUDSPEAKER
SYSTEMS
By
Ilpo Martikainen
Genelec
IisalmiFinland

PREPRINT NO 1987 (D7)and Ari Varla

Oy

andMatti Otala
Technical ResearchOulu
FinlandCentreof Finland

Presented at

1983March
15-18
the73rd Convention
Eindhoven, The Netherlands_[_l_Thispreprint has been reproduced from the author's advance
manuscript, without editing, corrections or consideration bythe Review Board.The AES takes no responsibility for thecontents.
Additional preprints may be obtained by sending request
and remittance to the Audio Engineering Society, 60 East
42nd Street,New York,New York10165USA.
All rights reserved. Reproductionof this preprint, or any
portion thereof, is not permitted without directpermission
from the Journal of the Audio Engineering Society.

AN AUDIO ENGINEERINGSOCIETY PREPRINTINPUT CURRENT REQUIREMENTS
HIGH-QUALITYLOUDSPEAKEROFSYSTEMS

Ilpo Martikainen and Ari Varla
Genelec Oy, Iisalmi_ FinlandandTechnicalMatti Otala
Research Centre
OUIU, Finlandof Fin'land_Al)stra('t: Based on a.nanalysis oi i:heequivalent circuit oi:ainuti'iway
lm_dspeal(er,the possil)i'lityoF large drive
ctlrrents 'is predicted For a (:lass oF non--sinusoidal bandand ampl'itude...'limited
signals_ The current [)till<isnp as
coherent sum of two paYts; charying of the driver
reactances, and simul_taneous current drain by severai
drivers,
The input current of three commercial loudspeaker systems
was measured using a signal derived From on the analysis.
The results show that a loudspeaker may draw currents three
to six times larger than those calculable from the rated
speaker impedance. This indicates that certain general'ly
accepted power amplifier design criteria should be reconsidered.

1.

INTRODUCTION
Audio power amplifiers are normally designed to deliver full power'into a "rated" loado In international standards (1,2), this load
is invariably specified as a pure resistor, normally 8 ohms invalue. In more modern draft standards (3), a parallel capacitor
is sometimes specified for checking the amplifier stability under'
various signal conditions_
Loudspeakers have a "rated" impedance, normally 8 ohms. This
impedance is measured using swept sinusoidal tones, and international standards (4) prescribe that the actual impedance may not
be less than a given minimum, usually 80 % of the rated value, inany part of the rated frequency range of the loudspeaker.
For an amplifier designer familiar with international standards(1-5), it would then be obvious that 'thepeak output current
required to drive a loadspeaker is simply the peak output voltageof the amplifier, divided by the rated impedance of theloudspeaker. In the case of a I00 watt amplifier this would leadto a peak output current of, say, 5 amperes to an 8 ohm
loudspeaker.

- 2 -The purpose of Lhis paper is to show that the required output
current capability is considerably 'larger, typically by a factorof 3 to 6o Thus, the required peak output current for the above
100 W amplifier may be in excess of 30 A in the case of normal
musical signals and typical commercial loudspeakers. In the caseof a 250 W amplifier with a 4 ohm rating, the worst-case peakcurrent capal)ility required could he close to 100 A.
The paper is based on previous work on distortion in theamplifier-loudspeaker
interface (6_.9), and on measurements ofloudspeaker hehaviour under non_sinusoidal excitation {I0),x. !:._QU9
s_:?_Er!r__ujvA_ _L:_N'[..C.
U?,l T
I'he dynami(' 1oudspeakerprov ides a compl ex 1oad to the amp/i fief.
)he total comp'llance of the cone suspens'Jonand the loudspeaker
cah'Jrlet,
dnd the cone mass, Form a damped l_lecharlicalresonance,
typically in i;tlefrequency range of 30-80 }lz For the woofer and at
correspondingly higher Frequencies for the midrange and thetweeter, Other mechanical resonances are created by the differentmoving /)artsof Lhe cone, excited by the voice coil, but notnecessarily rigidly coupled to 'it,Ali I:hesemechanical resonances
hehave like tuned circuits corinected to _:he voice roil resistanceand inductance. The cross-.over,filters also exhibit comp'!ex
reac/:ivebehavior, especially around the cro_s--overi:requencios_
Energy is stored in all these reactanees, especially at theresonances. Since a reactance cannot dissipate energy, and theinl;ernaldissipation in the loudspeaker is relatively low at tiles(}resonances, the stored enerqy will create oscillatory behaviour intile circuit. Fig. i shows a strongly simplified eqnivalent circuitof a loudspeaker, taking into accounL only major effects
discussed.

3.

LOUDSPEAKER CURRENT
Let us analyze an amplifier working into two different loads. A
pure resistance R is used when measuring the rated
characteristics o_ the amplifier° A loudspeaker, here represented
by the grossly simplified equivalent circuil; of Irig_ 1, is thetrue load. To f'acilitate the analysis, the loudspeaker is assLJmed
to have a linear resistance R and Fiegenerator effects. It isstressed that this circuit is far from perfect, but the purpose of
the analysis is to illustrate the basic mechanism only, not to
calculate it to a high degree of accuracy. It will hecome evident
that all these approximations do not affect the general outcome of
the analysis.
Following the analysis presented in detail in Refo (6), the input
voltage to the loudspeaker equivalent circuit is taken to be astep function from-_1 to +1. The impedance of the loudspeakercircuit isZ L = R(s2LC + sL/R + 1) / (s2LC + J)

,I1)

3 -

which in time domain yields the current

flowing into the circuit

2 exp(- mti{t) : [1 -.-_-_---) sin _t] vl/R,

(2)

where= (1/LC - 1/4R2C2)½ is the resonant frequency of the loudspeakercone, terminals short-circuited,
Q = mRC is the quality factor at the resonance, andv1 = step function amplitude.
Dividing Eq.(2) by the current flowing into an equivalent "rated
load resistor" Rr , we obtain the ratioI{t) : ii t) s_p_eake[_i(t) rated load- Rr [1 -2exp(- mt ) sin_t]
RQ2Q(3)Eq. (3) represents damped oscillation at the cone resonant
frequency. There are negative minima and positive maxima at
T : 1-_(arctan2Q+ n_),(4)

where n is an integer.
The maxima and minima assume the values
I(T): _Rr [1R4
(1+ 4Q2)½

exp(- arctan2Q + n_ )]. (5)20Some typical waveforms of Eq. 3 are plotted in Fig. 2 under theassumption that R,/R : 1. The values of the first minima andmaxima from Eq. (_) are plotted in Fig. 3 as functions of Q. The
amplitude of the oscillation increases with decreasing Q, thereason for this apparently strange behaviour being that a low-Q
resonant circuit absorbs more energy from the broad signal
spectrum,Three important things can be seen from this analysis* In response to a positive-going step voltage, the loudspeakercurrent swings after a while to a negative value, the amplitudeof which depends on the Q of the resonance.
* If a negative-going step voltage is introduced during thenegative undershoot of the loudspeaker current, the peaknegative current will reach a large value as shown in Fig. 5.
* In this simple model, the magnitude of the current is inversely
proportional to the voice coil re3istance.

-4-4.

MULTIWAY SYSTEMSIn a multiway loudspeaker system, the drivers are connected
parallel via cross-over networks. Fig. 6 shows the initial
current response of the Yamaha NS 1000 M speaker to a stepfunction. The first negative-going notch is the midrange driverresponse, whereas the second comes from the woofer. Also thetweeter exhibits similar behaviour, but it cannot be seen inFig. 6 because of its short duration.
It is then evident that a class of signals exists, which will
excite several of the drivers simultaneously so that therespective currents superimpose. A typical example of such asignal is a sequence of alternate step functions with varying
timing. This type of signal resembles the composition of normal
musical signals, for example percussion instruments. It is to be
noted that no requirements are being made with regard to therisetime of the step functions, as it suffices that the spectral
components are contained within the normal audio band. The only
requirement is the timing of the steps and impulses.
This situation is illustrated in Figs. 6 through 8. They depict
measured low-level current responses for three commercial
loudspeakers:- I.
inn Sara, an English two-way high fidelity speaker,- Yamaha NS 1000 M, a Japanese semiprofessional three-way monitor
speaker, and- Genelec 1051 A, a Finnish high fidelity three-way speaker.
The measurements were done using the Hewlett-Packard HP 3582A
FFT Spectrum Analyzer and a custom-made signal generator. The
input waveform was a binary sequence of -1/+1 transitions, soarranged that first a relatively long 3 to 6 ms positive pulse
excites the woofer into its negative-going current peak, at which
moment a rapid sequence of pulses excites the midrange into its
corresponding current peak. By virtue of the parallel structure oF
the multiway loudspeaker concept, these currents add up, causing
high momentary current peaks.
These currents should be compared to the "rated current" flowing
into an 8 ohm resistor for the same input voltage, as shown inFigs. 6 - 8 with dashed lines. Table I shows the actual relative
peak currents for the loudspeakers tested.
TABLE I

8 ohm
resistor
1LinnSara

YamahaNS 1000M

Genelec
1051A

5,3

3,63,7

It should be noted that only the woofer and the midrange responses
were fully excited in these experiments. It is conceivable thathigher peak currents could result, if the signal would have been
designed so as to fully excite the tweeter aswell. Further
increase in current could be realized if the level of themeasurement signal would be sufficiently large as to excite drivernonlinearities or cause cross-over inductor saturation.
As can be seen from Figs, 6-8 and Table 1, the worst-casemomentary current drain of a nominally 8 ohm loudspeaker may be up
to six times larger than anticipated. The signals Chat excite thiskind of behaviour can be considered as fully possible, legitimate
musical passages. They may not be frequent, but if an amplifier is
not allowed to enter the region of voltage clipping, it should not
be allowed to current-clip, either.

5.

CONCLUSIONSIt has been shown that
* Under conditions where the loudspeaker is excited with certain
amplitude- and band-limited signals, the oub_nt cnrrent demandedfrom an amplifier may grossly exceed the rated output current.
It follows that
* A new way of characterizing amplifier otltputis needed. Insteadof power specification to a Fictitious resistive load, a more
appropriate way could be to specify peak output voltage and peakoutput current.
* Amplifier distortion should also be specified at the elevatedcL_rrentlevels, since this may he a legitimate operating region.
* Methodology should be developed to observe loudspeaker linearity
at high momentary current levels.
It can be speculated that
* Many oF the present commercial amplifier designs may exhibit
current-related nonlinearities and/or current limiting in thecase of normal music and ordinary commercial loudspeakers. Thismay be one of the reasons for the reported tonal differences
between various power amplifiers of otherwise comparable
specifications, as this effect will not be revealed inconventional amplifier testing.
* Some loudspeakers may exhibit various forms oF response aberrations if an amplifier is capable of supplying the larger
current levels in question.
Many of the presently used power amplifier protection circuits
operate upon sensing the output current, and may have been
designed under false premises of operating just a little above
the rated output current.

-6.

6--

ACKNOWLEDGEMENT
This paper is based on theoretical work of one of the authors (MO)and on measurements and experimental verification by the others(IM and AV). The author_ wish to express their gratitude to J.
Lammasniemi of the Technical Research Centre of Finland for his
early work on this subject_7o

REFERENCES(1)

International Electrotechnical Commission, Publication 268-3,
SpeciFying and measuring the characteristics of sound system
equi i_lrle
FIt.

(2)

Electronic Industries Association, EIA Standard RS-_4gO,Standard
test methods for measurement of audio amplifiers.

(3)International Electrotechnical [;ommission, Draft-Revision
Publication 268-3, Sound system equipment°(4)International Electrotechnical Commission, Publication 581-7,
liigh fidelity audio equipment and systems. _inimum requirements.

(5)International Electrotechnical Commission, Draft-Revision ofPublications 268_3, 268-5 and 268-15. Document 29B(Secretariat)20g.

(6)

Otala, M., and Lan_asniemi, J., Intermodulation distortion inthe amplifier-loudspeaker
interface. 5gth Convention of the AES,/tamburg, O, 1978. Preprint 1336, 19 p°

I7)

Lammasniemi, Jo, and Otala, M., Power amplifier design
parameters and intermodulation distortion in the amplifier_loudspeaker interface. 65th Convention of the AES, London, UK,1980. Preprint 1608, 15 p.

(8)

Otala, M., and Lammasniemi, J., Intermodulation distortion at
the amplifier-loNdspeaker interface. Wireless world, Part I,
November 1980, pp. 45-47, Part 2, December 1980, pp. 42-44,(9)Cordell, R., Open-loop output impedance and interface
intermodulation distortion in audio power amplifiers. 64th
Convention of the AES, New York, L/SA,1979. Preprint 1537, 15 p_(10)Martikainen, I., and Varla, A., About loudspeaker system
impedance with transient drive. 71st convention of the AES,
Montreux, CFI,1982. Preprint 1884, 16 p.

Fof

-7-RF'---'l·.iC0Fig. 1. A strongly simplified loudspeaker equivalent circuit. L and C
are the cone dynamic mass and the suspension compliance, respectively,and R is the voice coil resistance.

Amplitude/-RESISTOR+_,o--/3o__.__'_10-1,o_. o

123_. _& _t[;d]Fig. 2. Typical current waveforms from Eq.(3) as functions ofnormalized time, with the resonance quality factor Q as parameter.
The loudspeaker-generatedoscillation is large, especially for lowvalues of Q. The corresponding waveform for resistive load is shownwith a solid line.

-8-Amplitude
firstmaxI;3+1,O ....

o-1,00',1013

103'0Fig. 3. The values of the first minimum and the first maximum of theloudspeaker current from Eq.(3), as function of the resonance quality
factor Q.

Current-2/_---3Fig. 4. Current waveform in the equivalent circuit of Fig. 1, when apositive-going step and a negative-going step have a worst-casetiming. The solid line indicates the loudspeaker current, while thedotted line shows the current in an equivalent resistor R.

- 9-06Fig. 5. Current waveform of the Yamaha NS 1000 M loudspeaker for astep function excitation. Dotted line shows the current in anequivalent resistor R. The first current notch is generated by themidrange, while the second ori!_inatesfrom the woofer.

036 ms]Fig. 6. Current waveforms into an 8 ohm resistor (dotted line) andinto a Linn Sara loudspeaker (solid line). Signal waveform is selectedto excite both the woofer and the tweeter simultaneously. Peakcurrent is 5,3 times larger than the current into the 8 ohm resistor.

- 10+0Fig. 7. Current waveforms into an 8 ohm resistor (dotted line) andinto a Yamaha NS 1000 M loudspeaker (solid line). Signal waveform isselected to excite both the woofer and the midrange simultanously.
Peak current is 3,6 times larger than the current into the 8 ohmresistor.

....jJ]:

Fig. 8. Current waveforms into an 8 ohm resistor (dotted line) andinto a Genelec 1051A loudspeaker (solid line). Signal waveform isselected to excite both the woofer and the midrange simultaneously.
Peak current is 3,7 times larger than the current into the 8 ohm
resistor.