PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Measurement of the Acoustic Impedance of Multi Resonant Systems– A prior Step to determine Parasitic Resonances in Magnetic
Circuits of Loudspeakers
Cesar CASTRO; Jorge MORENO
Acoustic Laboratory, Physics Department, Pontificia Universidad Católica del Perú, PerúABSTRACTThis paper is focused on the measurement of the acoustic impedance of multi-coupled resonators using animpedance tube; results of measurements of different arrangements are shown in this work. It is well known
that parasitic resonances can have negative effects on the frequency response of transducers, in order toanalyze the effectiveness of the technique, geometries similar to the ones used in magnetic circuits ofloudspeakers are also tested. The results are discussed in the conclusions.
Keywords: Loudspeaker, Acoustic Impedance, Resonance

1. INTRODUCTION
It is well known that the cavities and slits in the magnetic circuits of a loudspeaker have influencein the frequency response, very often the cavities and slits in the magnetic circuits are linked forming
resonators.
During the design process it is desirable to know the parasitic resonances (1) due to the existence ofslits and cavities present in the magnetic circuit, one way of knowing these resonances is by measuringthem.
In this paper, results of measurement done with an impedance tube in manifold resonators arepresented. In (2) the measurement of two coupled Helmholtz r esonators was analyzed.
This paper has three parts: in the first one, the measurement of the acoustic impedance of athreefold Helmholtz resonator system is presented, in the second part, the acoustic impedance of aresonator similar to the one found in the magnetic circuit of a low frequency driver is shown. In the lastpart, the measurement of the acoustic impedance of a model of the cavities of the magnetic circuit of a
mid-range unit is presented.
To validate these measurements, the resonances of the threefold Helmholtz resonator were also
calculated using an electrical model and simulated in a finite element analysis software, in both cases
the results were very similar to those measured in the tube. The other two models of cavities mentioned
above were also simulated using the same software and the results were compared wit h themeasurements in the impedance tube, obtaining satisfactory results.

2. THREEFOLD HELMHOLTZ RESONATOR CASE
In order to verify the possibility of measuring multi resonator systems using an impedance tube, athreefold Helmholtz resonator was built and measured.
Figure 1 and Table 1 show respectively the schemes and dimensions of the resonators. Figure 2
shows the result of the measurement perform on the threefold Helmholtz resonator in the impedancetube. Resonances at 244Hz, 420Hz and 864Hz were found.
Figure 3 (a) shows the equivalent electric circuit of the threefold Helmholtz resonator system,
elements were calculated using the well-known formulas presented in (3). Figure 3 (b) shows themobility frequency response obtained from the circuit shown in Figure 3 (a), resonances at 242Hz,
442Hz and 867Hz were found, this values are similar to the ones measured in the impedance tube.
Additionally, a calculation of the average pressure in volume of this system was measured using afinite element analysis software, here it’s possible to see that the system resonates at 242Hz, 425Hz
and 840Hz, this validates one more time the result of the measurement performed in the impedance
tube. Figure 4 shows the results of the simulation.

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Figure 1 – Scheme of the threefold resonator system
Table 1 – Dimensions of the threefold resonator system
Dimension, mm

Dimension, mm

Dimension, mm

H112.00

H225.76

H334.96h139.60

h231.53h3

64.10

D1101.20

D254.50

D354.50d121.00

d220.50d317.80

Figure 2 – Measurement of the acoustic impedance of the threefold resonator system using an impedancetube(a)(b)

Figure 3 – (a) Lumped parameter equivalent circuit of the threefold resonator, (b) Mobility simulation of theequivalent circuit7318

Average pressure in volume (Pa)Frequency (Hz)Figure 4 – Average pressure in volume of the threefold resonator system simulated in a finite element
analysis software

3. MEASUREMENT OF A PRINTED MAGNETIC CIRCUIT MODEL OF A LOWFREQUENCY DRIVER
In order to simplify the manufacturing process, a model of a magnetic circuit of a low-frequency
speaker was made on a three-dimensional printer. Although the resonances of this model do notinterfere with the bandwidth of a bass speaker, it is very useful to make a measurement to verify that itis possible to measure this type of shape in an impedance tube. The dimensions of the model are shownin Figure 5 and Table 2.
Figure 6 shows the result of the measurement of the acoustic impedance obtained in the impedance
tube, in this result is possible to see that at 1104Hz the system has a resonance due to its internal
volume. The central volume was not measured because its resonance frequency lies outside of theoperating range of the impedance tube.
A simulation of this model was also performed in a finite element analysis software, Figure 7 shows
the result of the average pressure in volume. It is possible to see that there is a resonance at 1080Hz, avalue very close to that measured with the impedance tube.

Figure 5 – Scheme of the printed model of a low frequency driver
Table 2 – Dimensions of the printed model of a low frequency driver
Dimension, mm
H127.66h1

7.53

D110.10d1

1.24

Dimension, mm
h237.46

d2

25.00

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Figure 6 – Measurement of the acoustic impedance of the printed model of a low frequency driver using animpedance tube

Average pressure in volume (Pa)Central resonator not consideredFrequency (Hz)Figure 7 – Average pressure in volume of the printed model of a low frequency driver simulated in a finite
element analysis software

4. MEASUREMENT OF A PRINTED MAGNETIC CIRCUIT MODEL OF A
MID-RANGE FREQUENCY DRIVER
A three-dimensional model of the cavities similar to the one found in a magnetic circuit of a
mid-range speaker was also tested. Unlike the previous model, all the resonances of this cavities fallwithin the working range of the impedance tube. The dimensions of this second model are shown in
Figure 8 and Table 3.
This model was measured twice, the first measurement without filling material and the second one
with filling material in the central resonator only; the comparison of both results can be seen in Figure
9. It is evident that the resonance at 430Hz has been damped due to the absorbent material. The otherresonance is presented at 1260Hz.
A simulation was carried out in a finite element analysis software to verify that both resonanceswere correctly measured in the impedance tube. The result of this simulation is shown in Figure 10,
where it is possible to observe peaks at 443Hz and 1236Hz, these values are very close to the ones
measured in the impedance tube.

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Figure 8 – Scheme of the printed model of a mid-range driver
Table 3 – Dimensions of the printed model of a mid – range driver
Dimension, mm

Dimension, mm

H1

15.00

H234.50h1

5.00

h225.00

D110.5

D235.44

d10.70d2

9.00

Measured Acoustical Impedance (Ohm)Measurementswith andmaterial
Measurement withandwithout
withoutfilling
fillingmaterial
100000000

Without filling materialWith filling material

10000000

1000000

1000002507501250

1750

HzFigure 9 – Comparison of the measurements of the acoustic impedance of the printed model of a mid-range
driver using an impedance tube with and without filling material in the central resonator

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Average pressure in volume (Pa)Frequency (Hz)Figure 10 – Average pressure in volume of the model of a mid-range driver simulated in a finite element
analysis software

5. MEASUREMENT SETUP
The setup is shown in Figure 11. The signals obtained from the microphones go to the B&K
front-end module which is connected by an Ethernet cable to the computer, the acquired data isanalyzed and processed in the PULSE TM software of B&K. The impedance tube is custom made and it
was built following the formulas presented in (4).

Figure 11 – Measurement setup

6. CONCLUSIONS
It is possible to measure the acoustic impedance of multi resonant systems using an impedance
tube.
It is possible to measure the acoustic impedance of models with cavities similar to those that can befound in magnetic circuits of loudspeakers; therefore, it is feasible to say that it is viable to measure theacoustic impedance of magnetic circuits of drivers using an impedance tube.
It is possible to measure the effect of filling material in a resonator using an impedance tube; hence,
a comparison of different absorbent materials can be done. Furthermore, it is possible to make anoptimization of the effect of these materials in loudspeakers.

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ACKNOWLEDGEMENT
We want to thank Richard Rivera for his help with the measurements.

REFERENCES
1. Shozo Kinoshita, Bart Locanthi. The influence of parasitic resonances on compression driver
loudspeaker performance. AES prepint No 1422 (M-2) 61st Convention November 1st 1978.
2. Jorge Moreno, Richard Rivera, Celso Llimpe. Measurement of the contribution to the acoustical
impedance of a loudspeaker due the internal cavities in magnetic circuit using an impedance tube. Proc
ICA 22th; 5-9 September 2016; Buenos Aires, Argentina 2016. p. 261
3. Beranek, L.L. Acoustics. Mc Graw Hill, USA; 1954.
4. International Organization for Standardization. ISO 10534-2:1998. Acoustics - Determination of soundabsorption coefficient and impedance in impedance tubes - Part 2: Transfer - function method. Geneva
1998.

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