IMPLEMENTING THE MODEL

The equivalent circuit model was implemented using MATLAB to plot the pre abso

ode generate the results can be

und in Appendix J.

(5.27)

Multiplying this by a factor of the diaphragm area gives the specific acou o

dicted rption versus frequency of the driver. Figure 5.15 shows the predicted and

measured absorption on the same axes. The c used to

fo 50 100 150 200 250 300 350 400 0 0.2 0.4 0.6

Using a Loudspeaker as an Absorber

1 0.8 A b s o rp ti o n C o e ffi c ie n t

Results from Impedance Tube Equivalent Circuit Prediction

Frequency, Hz

ood correlation between measurement and prediction is shown in terms of absorption ver predict a roader Q-factor of absorption than measurements show. This is due the limitations of the lumped element modelling technique and results in difficulty in accurately predicting the surface impedance of the system for all frequencies. Looking at the real

Figure 5.15 Comparison of equivalent circuit model with impedance tube measurements

5.4.1 Discussion G

magnitude and resonant frequency. The equivalent circuit model does howe b

part of the impedance (shown in Figure 5.16) for b elled cases reveals that there is a dramatic increase in the real part of the measured surface impedance at higher frequencies which is not present in the predicted data.

oth the measured and the mod

50 100 150 200 250 300 350 400 450

0 500

Real Part of the Surface Impedance of a Loudspeaker used as an Absorber

3000 2500 1000 1500 2000 S ur fac e I m pedanc e Measured Predicted Frequency, Hz

Figure 5.16 Real part of surface impedance from both predicted and measured data

Accurate prediction of the losses in the system are shown at low frequency but the accuracy decreases as the frequency increases, this explains why the predicted Q-factor of the resonant curve is broader than the measured value. With the real part of the measured impedance tending sharply away from characteristic impedance the system reaches maximum absorption over only a narrow bandwidth which is contrasted with the prediction where the real component of the impedance remains roughly equal to characteristic impedance for the entire frequency range. The inaccuracy in the

aphragm that annot be modelled using the lumped element method as it only predicts the

ce of systems. The first three modes of a circular plate can be given prediction model is the result of secondary resonances of the driver di

c

fundamental resonan as Figure 5.17 [38].

f01 f02

-

+

-

+

f11

Figure 5.17 First three vibrational modes of a circular plate

The second modal frequency given by f11 is a resonant mode but will not generate any absorption as there is cancellation on the diaphragm i.e. the diaphragm is ‘pushing’ and ‘pulling’ the same amount of air, consequently there is no resultant transmission of energy and hence no absorption. It would therefore be expected that the imaginary part of the surface impedance would exhibit a secondary point of zero crossin at this modal frequency but which would show insignificant absorption, looking at Figure 5.18 this

becomes clear. The can at this modal frequency causes the real part of the

surface impedance to increase preventing efficient transmission, resulting in minimum absorption as shown by Figure 5.18:

g cellation 50 100 150 200 250 300 350 400 450 0 0.5 1 Absorption Coefficient α 50 100 150 200 250 300 350 400 450 0 1000 2000 3000 Real Impedance R e a l(z ), M K S ra y l 50 100 150 200 250 300 350 400 450 -4000 -2000 0 2000 Im a g (z ), M K Frequency, Hz

Absorption and Surface Impedance of a Loudspeaker Used as an Absorber

Imaginary Impedance (a) (b) (c) S r a y l

Figure 5.1 lti-plot of absorption and surface imped showing the first two resonant modes of the

loudspeaker

The blue lines on the Figure 5.18 show where the imaginary part of the surface impedance goes to zero, illustrating the first two resonances of the diaphragm. It can be seen f the figure that at the second of these modes (corresponding to Figure 5.17b) there is negligible absorption as the real part of the surface impedance has reached a aximum and much larger than characteristic. Thus the inability of the model to predict

5.5 Conclusion

Using a loudspeaker as a membrane absorber has been shown to produce high absorption coefficients at low frequency. The system behaves as a membrane absorber and could prove to be useful for practical studio applications by using redundant loudspeakers to absorb unwanted modal components within a room.

The loudspeaker absorber system has been modelled using electroacoustic theory and a lumped element model. The prediction of acoustic absorption matched up well with the measured values obtained from impedance tube tests. It was noted that the lumped element model does not allow for the prediction of the system’s higher order resonances, causing inaccuracy in the prediction of the surface impedance at higher frequencies, resulting in the model predicting broader Q-factors than the measured data shows. The model does however predict accurately the frequency and magnitude of resonance and can be used as a first approximation of the absorber’s behaviour especially with a changing electronic load impedance as shown in chapter 6.

8 Mu ance

rom m

secondary and tertiary resonances of the driver means that the final predicted absorption curve exhibits increased Q-factors when compared to the measured data. As a result there will be inaccuracies in the predictions made by the model but the behavioural characteristics of the fundamental mode in terms of frequency and magnitude of absorption will be accurate. Thus the model can be used to obtain predictions of further

scenarios as modelled in chapter 6. It is further shown in chapter 6 odel

accurately predicts the trends in changing resonant characteristics introduced by additional electronic loads connected to the terminals of the driver as shown in

that the m

Figure 6.4 and Figure 6.11.

ection of work outlines how a passive electronic load on the driver can be sed to reduce the resonant frequency and Q-factor of the loudspeaker absorber system. The next s

u

The equivalent circuit model presented in this chapter will be extended to model such changes in the motor impedance of the loudspeaker.

6.

CHANGING THE RESONANT