Model of microspeakers
Traditionally, lumped parameters methods with EMA analogy are commonly exploited to model loudspeakers. Despite the simplicity, the conventional methods are applicable to model the dynamics in low frequency regime especially in the neighborhood of fundamental resonance. However, this may not be sufficient for microspeaker analysis. The lumped parameter model can not predict well the high frequency responses of microspeakers that may play an important role in overall performance such as output level and roll-off frequency. In this work, the diaphragm-coil assembly of microspeaker will be modeled using FEA. The FEA model will be combined with the EMA analogous circuit to establish a fully coupled model for the microspeaker.
EMA analogous circuit of microspeaker
A sample of moving-coil microspeaker with a 16.4 mm diameter and 4.3 mm thickness is shown in Fig. 14. The front and rear view of the microspeaker are shown in Figs. 14 (a) and (b), respectively. The EMA analogous circuit of this microspeaker can be established in Fig. 3. The coupling of the electrical domain and the mechanical domain is modeled by a gyrator, whereas the coupling of the mechanical domain and the acoustical domain is modeled by a transformer [9]. The T-S parameters can be identified via electrical impedance measurement [9] and [10], as summarized in Table 2. The dynamic response of the microspeaker can be simulated on the platform of this model.
Loop equations can be written for the preceding FEA-lumped parameter circuit of the microspeaker as follows [29]:
0
The symbol “ ” denotes parallel connection of circuit. The loop equations can be solved for the current and velocity of the diaphragm for each frequency. From the current and velocity, the electrical impedance and the on-axis SPL responses of the microspeaker can be simulated.
3.1 Simulation and Measurement of Frequency Responses
Simulations and experiments are undertaken in this paper to validate the aforementioned integrated micro-speaker model. The frequency response from 20 Hz to 20 kHz of the micro-speaker is measured using a 2 Vrms sweep sine input.
Figure 15 (a) shows the experimental arrangement for measuring voice-coil impedance (with symbols defined in the figure):
s
Figure 15 (b) shows the experimental arrangement for measuring the on-axis SPL response by using a microphone positioned at 5 cm away from the micro-speaker.
Next, simulation of the diaphragm response was carried out using the integrated FEA-lumped parameter model mentioned above. Figures 16 (a) and (b) compare the voice-coil impedance and the on-axis SPL obtained from the simulation and the experiment, respectively. It can be observed that response predicted by conventional lumped parameter model is in good agreement with the measurement in low frequencies. In high frequencies, the conventional approach fails to capture the response due to the flexural modes of the diaphragm. However, the response simulated by the integrated FEA-lumped parameter model matches the measured response quite well.
3.2 Diaphragm Optimization using the Taguchi method
As mentioned previously, the diaphragm pattern has major impact on the micro-speaker response. To pinpoint the optimal pattern design, the Taguchi method and sensitivity analysis are exploited in this study. The Taguchi method [18] is very useful for experimental design, particularly for problems with finite number of discrete levels of design factors and thus reduction of the number of experiments is highly desired. In the following, the dimensions of diaphragm-voice coil assembly of micro-speakers will be optimized by using the Taguchi method. Table 4 shows the L9(3 )4 orthogonal array to be used in the Taguchi procedure. Here, nine observations and four factors are involved. The factors, each discretized into three levels, include the height of inner arc (H), the height of outer arc (h), the bandwidth of outer arc (d) ,and the thickness of diaphragm (t), as summarized in Table 4.
The following procedure aims to find the optimal parameters for the micro-speaker diaphragm design according to the cost function:
0 1
where f is the lower cutoff frequency of micro-speaker, 0 f is the upper cutoff 1 frequency of micro-speaker, SPL denotes the mean SPL in the piston bandwidth (defined in Fig. 17) and STD denotes the standard deviation of SPL in the piston bandwidth that serves as a flatness measure
( )
2where n is the number of frequency components of SPL in the band and SPL is the i ith SPL in the band. The symbol Δ signifies the difference of the performance parameters between the original design and the Taguchi design, e.g.,
0 0,Taguchi 0,original
f f f
Δ = − , ,w jj =1 ~ 4, is the weight for the performance parameter i.
In order to accommodate more design objectives, we consider using four kinds of weighting schemes, and summarized in Table 5. In scheme 1, the weights for the performance parameters are equal. Larger weights are used to emphasize the lower cutoff frequency and the mean of SPL in evaluating schemes 2 and 3, respectively.
In the weighting scheme 4, however, more emphasis is placed on the lower cutoff frequency, the upper cutoff frequency and the mean of SPL than the standard deviation of SPL.
Figures 18 (a)-(d) show the simulated voice-coil impedance and the SPL response of Run 1 to 9 in the L9(3 )4 orthogonal array. The values of calculated cost function for all weighting schemes are summarized in Table 6. The cost function of Run 7 has attained the highest value among all schemes. In Run 7, the lower cutoff frequency is reduced to 567.3 Hz, the upper resonance frequency is increased to 20 kHz, the SPL of the resonance frequency is increased to 84.8 dB, and the standard deviation is 1.88 dB. The optimal design result indicates that the height of inner arc (H) and the width of the outer arc (d) should be as large as possible, and
the height of outer arc (h) should be as small as possible, which will maximize the cost functions.
3.3 Sensitivity Analysis of Corrugation
Sensitivity analysis of diaphragm corrugation is undertaken to examine the effect of corrugation number on the micro-speaker performance. The analysis is based on the optimal diaphragm dimensions obtained in Run 7 of the preceding Taguchi procedure. The simulated voice-coil impedance and SPL response of Run 7 for different corrugation numbers are shown in Figs. 19 (a)-(b). The values of performance indices and the resulting cost function for different corrugation numbers are summarized in Table 7. It can be observed that corrugation tends to reduce the fundamental resonance frequency, but the relation is not linear. Further, corrugation tends to increase the mean and the standard deviation of the SPL response. In another word, increasing the number of corrugations will decrease the flatness of SPL during the effective frequency range. Nevertheless, the corrugation does not seem to affect the upper cutoff frequency significantly.
The values of cost function in relation to the corrugation number for different weighting schemes are also summarized in Table 7. The values of cost function are derived from the result of Run 7 of the Taguchi method. The results reveal that the optimal corrugation number is 30, in which the cost function is within 0.0493 - 0.0616 for the four weighting schemes.