artificial ear is shown in Fig. 13. In Fig. 3 (a), the coupling of the electrical and the mechanical domains is modeled by a gyrator, whereas the coupling of the mechanical and the acoustical domains is modeled by a transformer. The T-S parameters of the microspeaker identified via an electrical impedance measurement are summarized in Table 1. A distinct feature of the el
ne oacoustic modeling of earphone 3.1.1 EMA analogous circuit of earphone
In this section, a lumped parameter model based on EMA analogy is established for the earphone. The cross-section of a Bluetooth earphone connected to a type 2
ectroacoustic modeling of the earphone as compared with the other free-field loudspeaker systems is the ear canal impedance.
To gain an appreciation of the main difference of these two environment, the ear canal is approximated as a cavity with acoustic compliance
C
A. Simplifying the circuit in the acoustical domain leads to the pressure response at the ear canal2 1
compliance of the suspension,
M
AD is the acoustic mass of the diaphragm,( )
2resistance,
R
MS is the mechanical resistance of the suspension, andS is the
D . It follows that the pressure response has a second-order lowpass characteristic, which is quite different from a direct radiator typically having a second-order highpass cheffective area of the diaphragm
aracteristic. Note that, since the
combined acoustic compliance C’ is effectively decreased due to the ear canal impedance, the system quality factor Q will be increased. Thus, it is crucial in AT
designing earphones to “shape” the resonant peak at ωs for an acceptable Q value.
Apart from the approximation above, a more detailed circuit model of the acoustical system is illustrated in Fig. 14 (a). The acoustical system primarily consists of tree parts: a cavity (
AT
C
AF) and a duct in front of the speaker, the artificial ear, and a cavity ( C ) with a leakage hole behind the speaker.eaker can be modeled as an acoustic resistance [9]
AB
The duct in front of the sp
R cascaded with a transmission line which can be simulated with a T-circuit with
STparameters
Z
STA andZ
STB. The T- circuit with parameters is given byThe analogous circuit of the type-2 artificial ear us 1 ear simulator [26]
is shown in Fig. 14 (a). Instead of an acoustic mass, the duct embedded in the artificial ear is modeled with a transmission line T-circuit. The artificial ear can be modeled as a transmission line T-circuit in series with the circuit of an IEC 711 simulator [26], as shown in Fig. 14(b). The parameters of the transmission line T-circuit have been defined in Eqs. (63) - (65), where
ing IEC 71
A AEA
Z
=Z
,Z
B =Z
AEB ,a
=a
AE andL
=L
AE.The leakage hole impedance is given in the acoustical domain as [9]
The leakage hole has radiation of air loading. The acoustic element parameters in Ref. 9 are summarized in Table 2.
n platform for the earphone.
3.1.2
calculated according to the formulas given This analogous circuit serves as the simulatio
Verification of the lumped parameter model
The volume velocity
U
AE flowing throughC in the artificial ear can be
A8 obtained from solving the analogous circuit in Fig.2. FromU
AE, the pressurep
CA8 at the elementC can be calculated by
A8The ear canal and the eardrum are simulated by the transmission line T-circuit shown in Fig. 14 (b). Assume the eardrum here is rigid. Hence, the eardrum impedance
Z
ED → ∞ , which renders theZ
ED in the ear canal circuit in Fig. 14 (b) an open circuit. Therefore, the sound pressure at the tympani positionp
ED is given bydenote the impedance elements of the duct represented by the transmission line T ircuit, as defined in Eqs. (2)-(4), and
Z
ECA=Z
A,Z
ECB =Z
B.the leng the duct and
L
EC =L
th ofa
EC = is the radius of the duct.a
Expe were undertak to validate the aforementioned earp ne sim
model. The dimensions of the earphone enclosure are shown in Table 2. It can be nse
(denoted as original simulation) is in good agreement with the measurement (denoted as original experiment) up to approximately 16 kHz.
3.2 Optimization of the enclosure design of earphone
riments en ho ulation
observed from Fig. 15 that SPL respo predicted by lumped parameter model
The SPL response of the earphone shown in Fig. 15 apparently did not meet the requirement in 3GPP2 C.S0056-0 [13]. The peak at 1 kHz exceeded the frequency
response mask. This calls for optimization of the enclosure design, where Simulated annealing (SA) is exploited in this study.
SA is a generic probabilistic meta-algorithm for the global optimization problem, namely, locating a good approximation to the global optim of a given function in a large s
um
earch space. SA's major advantage over other methods is the ability to avoid becom
changes (bad solutions) that increase it. The acceptance of the bad solutions is determined by the probability
ing trapped at local minima. The algorithm employs a random search which, in the initial stage, not only accepts changes that decrease cost function Q but also
( )
is a random number generated uniformly in the interval (0,1).
ization, we and the
final temperature is gi
T
ke Δ is the increase in Q and T is a control parameter, which by analogy is
Q
wn as the system “temperature” irrespective of the cost function involved.In the earphone optim choose the initial temperature
( )
0,1ion will be rejected if it fails to comply with the the f onse mask. fu ptimization is chosen to be SPL curve passing the central region of the mask. The parameter n is the frequency index within the band 20–4500 Hz. The design variables and the associated constraints are given in the following inequalities:
4 3
With the SA procedure, the optimized enclosure parameters are compared with the original non-optimized ones in Table 3. Note that the front port radius has the largest
educed to 13.33% of its original
size. igi
simulation and experiment, as shown in Fig. 15. As opposed to the original non-optimized design, the optimized design effectively lowers the resonance peak to
3GPP2. This improvement also comes at the price of steepe
since the p
design change to make. The port radius has to be r
The SPL responses of the optimal and or nal designs are compared in
be within the frequency response mask of
r roll-off above 3 kHz. Nevertheless, this should not be a problem resent study is aiming at only the speech application in which the upper cutoff frequency at 3 kHz is deemed sufficient.