ABOUT LOUDSPEAKER SYSTEMIMPEDANCEWITH
TRANSIENT
DRIVE

1886

(D-3)

Ilpo Martikainen,
Ari Varla
GenelecOy, Satamakatu
7SF - 74100
Iisalmi/ Finland

Presentedat
the 71stConvention
1982March2-5Montreux_[_lThisprepdnt has been reproducedfrom the author'sadvance
manuscript, without editing, corrections or considerationby
the Review Board. TheAES takes no responsibilityfor thecontents.
Additional preprints may be obtained by sending request
and remittance to the Audio Engineering Society, 60 East
42nd Street, New York,New York 10165 USA
All rights reserved.Reproduction of this preprint, or any
portion thereof, is not permitted without direct permission
from the Journalof the Audio EngineeringSociety.

AN AUDIO ENGINEERINGSOCIETY PREPRINTABOUT LOUDSPEAKER

SYSTEM

IMPEDANCEWITH

TRANSIENT

DRIVE

Ilpo Martikainen
Ari Varla
Genelec Oy
Satamakatu
7SF-74100
IisalmiFinland

ABSTRACTThis experimental work deals with the loudspeaker-amplifierinterface.
The
instantaneous
input
voItage/current relationships ofloudspeakers are measured with low-passfilteredsquarewave atdifferent levels. These preliminary measurement
results allow us toassumethat power amplifiers intended to drive loudspeakers
shouldbe designed to supply several times
the current
which couldbeexpected directly from the system nominal impedance.

1. INTRODUCTION
The problems
of many amplifiers to supply full power at iow frequencies to loudspeaker loads led us to investigate, howdoes
theloudspeaker
look from the side of an amplifier, what is the peakcurrent absorbed and how these are related to the system's
nominalimpedance.
A series of measurements was performed first with real
program signals, with strQng LF content ( like setting
phonographstylusonto groove,
synthesizersetc.) and later with filteredsquare waves.
During the work it was found that the systembehaviour
itself is independent of frequency.

Theamplifier,being
basicallya voltage source, does not know,whether the current is flowing to a resistanceor a reactance,
therefore
we definethe measurement result, instantaneous
input
voltage divided by instantaneous
current,
as an Apparent
Load( Zs__ ), expressed in ohms. The ratio, nominal impedance ( Znom ,manufacturer's
spec.) divided by the apparent load gives
an indicationof the current increase factor when driving this particularsystem ,as compared to driving a purely resistive , "nominal" load.
2. MEASUR_I_ENTS
First
input
resistance
Rye , impedance magnitude3Zland
impedance
phase _ measurements were carried out to all systems. Then, with afiltered square wave (1st order low-pass at 20 kNz) having constant
amplitude, a frequency was found where load current had a maximum.
Zal was measured
at this frequency at different
levels .The
measurement setup is shown in Fig. 1.

-2-

Generator_

AmplifierUUT

2-ch FFT Spectrum I

0.1

Scope

Peakhold
DVM

Fig,1.
3,MEASURING

Measuring

setup

RESULTS

Measuredsystems and theirin Tablepresented

1.
Impedancein Figs. 2...19.

NO

fundamental

characteristics

plots

Zal

and

Type

are

at different

Nominalimpedance(Mfg.spec.)
ohms

Rvc

ohms

listedlevels are

Zal(minimum)ohms

1

Wooferin a closedbox

8

6.2

4.8

2

Wooferin a ventedbox

8

6,2

4,7

3

Closed-box
2-waysystem

8

7.5

3.4

4

Closed-box 2-way system witha dual voicecoil woofer

4

4.0

2.2

Closed-box 3-way system with
B3 low-frequency
response

8

7.1

2.8

6

Vented-box
3-waysystem

6

7.2

3.0

7

Full-range

4...15

0.6

1,8

Table

1. The characteristics

5electrostatic

systemof the measured

speakersystems

-3-

3.1. Woofer

in a closed box

The
impedance
magnitude
and phase are shown in Fig.2 and the Zal
valuesin Fig.3. Z om/Zal is aroand 1.6, ( Rvc/Zal :1.3) and peakcurrent occurs at 8_Hz.
Zal rises with increasing signal level.
3.2. Woofer

in a vented box

The impedance magnitude an_ phase are shown in Fig.4 andtheZalvaluesin Fig.5.
Znom/Zal _1.7 ,( Rvc/Zal = 1.3 ), peak current
frequency is 26 Hz. Heat generated during measurement affects
thevaluesat higher
levels,therefore
test time was less than one
second.
3.3

2-way closed-box

systemThe impedance and Zal data are presented in Figs.
6, 7 and 8. Twopeak current
frequencies
areobserved,
92 Hz and1.32 kHz.
Znom/Zal
3.4= 2.4,( Bvc/Zal _2.2

2-way closed-box).

_ystem with a dual voice coil in the woofer

The impedance and Zal values are shown in Figs.
9 and 10. The impedance plot is quite flat throughout the frequency range,therefore
only LF part is presented.
Znom/Zal = 1.5 with low level, but
increases
to 1.8 at higher level, in_icating some form of nonlinearity. Peak current occurs at 64 Hz.
3.5

Three-way
response

closed-box

systemwith

B3 low-frequency

The impedance and Zal characteristics are shown in Figs. 11, 12 and13. Rye is measured inside the system, after the series capacitor.
Z nora /Z a_'_is around 2 ' 6 ' ( R_o/Z=__ 2.3 ) bat higher level causes a....
drop in ZalandZ n om/Zal rises
to 2.9.
Current
maximum is at 76 Hz
with a smaller
peak around2.5 kHz.
3.6

Three-wayvented-box

The
impedance
and
16. The manufacturer
7.16
ohms, obviously

systemZal behaviour
are presented
in Figs.
14,
has rated
the system
to 6 ohms although
due to the 4.9 ohm
impedance
minimum

15 andRye isaround120
Hz.
Znom/Za!
is 2.0,(Rve/Zal_2.3)
and at higher
level
some
step-typenonlinearity
takes
place.
Zal risesfrom 3.13 ohms to
3.85 ohms in 0.2 seconds
and increases
teenslowlydue toheating.
Peak current
is observed
at 80 Hz and an almost
similarpeak at 4.4
kHz.
3.7

Full-range

electrostatic

speakersystemThe
impedance
and Za! characteristics
are presented
in Figs
17, 18and 19. At 1.6 kHz, wherelZl=
13 ohms,IZI/
Zal = 4,9 and at
20 kHztheratio
is 1,13.
Peak current
frequency
is 20 kBz but the peakvalue
is fairly
flat
over
the entire
frequency
range.
This speakersystemis commonly
regarded
as a difficult
load,
but mainly
becauseof amplifier
instability
it has caused.

-4-

4. DISCUSSION
In the impedance plots also phase response is shown.
The peak current
frequency
appears
to be near to the frequency (frequencies)
where the capacitive reactancehas a maximum.
To refreshthebasics, a simplified electrical equivalent circuit of a loudspeaker( at resonance) is shown in Fig.20.

7

Fig.20.

A simplified

electricalequivalent[R

circuitofa speaker

Above resonance the capacitance mainly defines the circuitcurrent
andassuming
the parallel impedances to be high comparea to Rye,the capacitor voltage approaches Vo. Channing the source voltage to-Vo causes an instantaneous current of 2Vo/Rvc through thecircuit.
Lookedfrom the electricalside a multiway system with passive
crossover means basically a group of parallel-coupledequivalentsof Fig.20,
isolated
with filters.
Howevert it is unimportant,whetherthecapacitive
reactance
originatesfrom mechanical( driver ) or from purely electrical ( filter ) side, see forexamplesystem No 5 at 2 kHz in Fig.12.,and thus current ratios
greater than 2 are possible with appropriate excitation.
( Although
the filters
isolatethe driverfundamental
resonance from theamplifier, they exhibit capacitive reactance themselveS.
It is thus
easy to see that high current peaks are not a speciality of woofers
only, the peak energy is naturally frequency dependent.

In terms of required amplifier current the systems can be divided
into two groups.
Types_ and 2 where the driver is directly
connected to amplifier (active low-level crossovers) havegreatest
Zal values and are thus easier to drive. This is also true for type
4 ( Znom/Zal about 1.5 ) due to its low reactive content. The othersystems with passive crossovers
form an other group requiring significantly
more linear current
fromthe amplifier.
A simplenumerical
examplewill clarify:
a 200 W into 8 ohms amplifier
provides56.6 V peak output voltage.
When driving 8 ohms
resistance, 7.1 A peak output current is required.
The same signal
to system No 1 causes 11.1A peak output current andwhen driving
system No 5, 20.5 A peak output current is necessary.
It should be
noted,
however, that the test signal used now may not be the worst
possible, and certainly there are
speakersystemswith greater
Znom/Zal than the ones measured

so far.

-5-With the speakers tested the Zal value varies between 55 % ( system
5 ) and 86 % ( system 7) of the impedance magnitude minimum which,in turn, should be at least 83 % of the nominal impedance aceording
to IEC. It should be noted however, that very few speakers in themarketfulfilthis IEC requirement.To be on the safe side, let us
take the impedance minimum as 70 % of the nominal
impedanceasspecifiedby the manufacturer and the Zal value 40 % of that, so
the design load should be not more than 28 % of the rated load. In
pure numbers, an amplifier for 8 ohms "nominal" load should be able
to deliver full output voltage swing down to 2.2 ohms.
We would
like to emphasize
again,
that these figures are based on thepresent measurement data, there may be loudspeaker systems and test
signals which exhibit Zalvalues outside the range
presented
now
and will so change the rule of thumb outlined above.
5. CONCLUSIONS
Seven
loudspeakersystems
representing
different
designweremeasured in terms of theirinstantaneous
input
voltage/current
characteristics.
At certain frequencies they absorb significantly
more, in some cases with passive crossover
filters
severaltimes
morecurrent
than what could
be expectedfrom the specified,"nominal" impedance.
Obviously amplifiers dimensioned for nominal
resistive
loads
cannotdeliver full output power to loudspeakers
and thus a different power amplifier design approach is necessary.

6. ACKNOWLEDGMENT

The authors
during thiswish to thank Dr.Matti
work.

Otala

for

valuable

discussions

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wooferina vented

box.

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-5_ o+_oFig.9.

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2-way

system

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dual

voice

coil

woofer.

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I,"!.....
: "l..._',.,,t..:.'1.kHz_Fig,15_

MD/HE impedance

plot,

of

three-wayvented-box

system,+Sb o

Fig.17. LF/MF impedanceplot offull-range

electrostatic

system.

zl
2_

50
°

40

oo

30

-500

2O

ID

Fig.18. MF/HF impedanceplot offull-range

electrostatic

system.

o

0q

_._

_

_?

t_

o

O

o

I

I

_

:J.

x,

¢1

I

I

_N

I

t

I

_

_>

o

--

·

o

_

_

co

c3

oo

N OZ
co

k2.
_._

_3

_.,q

_o_._

u_

N

_-q .

°oo co
g
_

¢8,_

Za%

Zal

ohm

ohm

Zal
R
vc

ohm

7

7 _

7

6

6

6

5

5

5

4

4

R
vc

Rvc
4

{: _Nz2|l'::'_):'!t:_:lO

20

3 _-_,.I

2

2

I

1

I,,ll_llll,lllt,
lll--10

20

30_

0

Illllilll,l.--_-.-+.-.,-_--i,t_]O
20

30V
,r

Vpeak
Fig.10. ZAL value for closed-box
2-way system with a dual
voice coil woofer. Nominal
impedance is 4 ohms.

'
pe

Vpeak
Fig.13. ZAL value for closed-box
3-way system with B3
LF response. Nominal
impedance is 8 ohms.

Fig.16. ZAL value for vented-box
3-waysystem. Nominal
impedance Is 6 ohms.