In VAHIM, the residual sound pressure inside the middle ear cavity is used to compensate for the low frequency degradation of the acceleration-type MEMS sensor, and to improve its overall sensitivity in the 0.1 to 10 kHz frequency range. Sound entering the ear canal is attenuated by less than 3 dB by the eardrum [
15] and its vibration is not significantly changed by the loading of less than 25 mg at the umbo [
18]. Therefore, in the middle ear, if an acceleration sensor with a sensitivity of −50 dBV and an additional acoustic sensor with a sensitivity of −40 dBV are placed, but the total weight is unchanged, a microphone sensitivity of at least −40 dBV can be achieved in a low frequency range. Therefore, we have developed a hybrid sensor with an acoustic sensor in place of a dummy mass to compensate for the high-pass response of the conventional capacitive acceleration MEMS-type implantable acoustic sensor. As shown in
Figure 2a, the dummy mass (
Figure 1b) is replaced by an ECM of a similar mass in the proposed sensor. An upper electrode is located beneath the substrate containing the vibration beam, and is separated by a gap distance (30 μm from the electret disc surface, which contacts the lower electrode position to the bottom plate. The output signal of the hybrid sensor is the sum of the acoustic signal from the ECM and the acceleration signal influenced by the mass of the ECM. However, in this case, this sensor provides two separate outputs without summing so that each sensor can be monitored individually.
3.1. Frequency Characteristics of the Capacitive Acceleration Sensor
The hybrid acoustic sensor combines the output of two sensors: the ECM, which has a flat frequency characteristic in the whole band; and the capacitive acceleration sensor, which has a low gain in a low frequency band, but a high gain in a high frequency band, with an upper cutoff frequency. When the hybrid acoustic sensor vibrates according to the motion of the umbo, the displacement of the ECM mass and the upper electrode mechanism connected to it is shown as a low-pass filter (LPF) characteristic
GM(
f) (
Figure 3a). In this configuration, there is one resonance frequency peak at
fecm, the position and height of which are determined by the ECM mass, the stiffness of the vibration beam, and the energy loss factor. In this second order LPF system, by selecting the damping coefficient of the vibration beam of the hybrid sensor, resonance-peak overshoot can be minimized [
19].
The major difference between the proposed sensor and previous designs shown in
Figure 1b is that the dummy mass is replaced with the ECM mass. The vibration characteristics of the ECM mass coupled with the vibration beam can be described as a second order LPF that has a spring with elastic modulus k, mass M, and loss coefficient r. When a vibrator drives the hybrid sensor with constant sinusoidal displacement at the umbo and if the vibrator frequency is lower than the LPF cutoff frequency
f1, the vibration amplitude of the ECM mass is almost the same or higher than that of the vibrator. At frequencies exceeding the
fn, the displacement of the ECM mass is decreased to almost zero due to the increase in the inertia effect of the ECM mass with increasing frequency. Therefore, at frequencies higher than
f2, which is low-cutoff frequency of the capacitive acceleration sensor
GCAS(
f), the displacement amplitude of the umbo vibration corresponds to the gap distance of the plane capacitor. Thus, the frequency response of capacitive acceleration sensor
GCAS(
f), which has a relative output response to the displacement change of the gap due to the vibration between frequencies from 0 Hz to the upper cutoff frequency
f2 can be given as:
and this response is shown in
Figure 3b. The absolute value is taken on the right side of this equation because the displacement of the upper electrode changes from the original position to both the upper and lower side at the time of resonance. The
f2 of the acceleration sensor is formed by coupling of the umbo and the small mass m, which is the sum of the bottom plate of the hybrid sensor, the upper and lower connecting pins, and the lower electrode. This m is a much smaller mass than the ECM mass M, but the loading effect increases as the driving frequency increases. Therefore, as the frequency increases above the
f2, the effect on the gap distance variation of the plane capacitance due to umbo displacement weakens rapidly.
Finally, the overall response of the hybrid vibro-acoustic sensor
GHVA(
f) is plotted in
Figure 3c.
GHVA(
f) is the combination of the responses in
Figure 3b: solid line characteristics and dotted line characteristics, which represent the ECM gain with a uniform response in the desired frequency domain (0.1~10 kHz). In this case, the maximum response of the ECM is assumed to be 30% greater than that of the capacitive acceleration sensor. In
Figure 3b, the gain of
GMC(
f) is very small below the
f1. In other words, the low frequency gain is very small except for the distortion caused by the resonance peak in this band. However, as shown in the graph of the total gain
GMCE(
f) in
Figure 3c, the low frequency gain below
f1L shows more than 57% of the maximum gain between
f1L and
f2H. This also demonstrates that the greater the ECM gain, the more the low-frequency gain of the
GMCE(
f) improved compared to
GMC(
f). In
Figure 3b,c, the upper cutoff frequency is indicated, and the dotted ECM characteristic generally has a higher upper cutoff frequency than the acceleration sensor. The resonance peak of the upper electrode displacement
GM(
f) may include distortion of the gain characteristic in the vicinity of 1.5 kHz (
Figure 3c). This distortion problem can be solved by designing the springs and attenuation factor to ensure critical damping.
In this hybrid sensor, the actual output of the capacitive acceleration sensor part depends on the amount of Δ
C, which is the capacitance change between the two electrodes. Additionally, Δ
C is proportional to
y, the vibrational gap displacement of the umbo:
where
ε is the dielectric constant of the inner medium of the plain capacitor,
S is the opposing area of the electrode plane, and
Y0 is the gap interval [
10].
To convert ΔC into a signal voltage, we connected the upper electrode to the gate of the low noise field effect transistor (FET) integrated circuit (IC) of the capacitive acceleration sensor preamplifier.
3.2. Vibration Beam Plate Design
The low cut-off frequency
f1 of the gain characteristic curve of the acceleration sensor (
Figure 3b) depends on where the resonance frequency
fn of the vibration beam is set. In this paper, we arbitrarily set
fn at 1.5 kHz only for the purpose of confirming the effect of the ECM instead of the dummy mass of the acceleration sensor. In general, the vibration beam is determined by parameters such as the thickness, width, length, and number of the beams shown in
Figure 4. By varying the parameters of the vibration beam, resonance points can be generated in the desired frequency band. The stiffness
k and resonant frequency
ωn of the vibrating beam are given by Equations (3) and (4), respectively [
20].
where
k is the stiffness coefficient of the vibrating beam,
n is the number of beams,
E is the modulus of elasticity of the beam,
I is the moment of inertia of the cross-section of the beam,
W is the width of the beam,
m is the mass of the ECM, and
T is the thickness of the beam.
A circular four-beam vibration plate that responds to acceleration and is of a sufficiently low mass is shown in
Figure 4. For this reason, materials lighter than metals and more flexible than silicone are advantageous. Thus, we designed a four-beam vibration plate of flexible thin polyimide, which acts as a vibrating beam with a mounted PCB with a low noise amplifier IC chip for a capacitive acceleration microphone.
To design the frequency characteristics of the beam plate located immediately below the ECM, the mass applied to the beam plate, the beam structure, and the elasticity need to be considered simultaneously. Therefore, the characteristics of the vibrating beam were analyzed using FEA software (COMSOL Multiphysics 5.0; COMSOL Inc., Stockholm, Sweden) to obtain values more precisely than the first order approximations yielded by the simpler formula. For the FEA, the structure of the hybrid vibro-acoustic sensor was analyzed by dividing it into meshes (
Figure 5a), and subjected to three-dimensional vibration displacement analysis (
Figure 5b). The mesh of the sensor model consisted of 233,105 domain elements, 22,532 boundary elements, and 1992 edge elements using a defined “free tetrahedral”.
To perform the analysis, the angle
θ of the beam was changed from 30° to 60°. The width
W of the beam was fixed to 350 µm and the beam thickness
T was set to 200 µm for the planned PCB production. As shown in
Figure 5c, resonance occurs at 1.5 kHz when
W = 350 µm, T = 200 µm, and angle = 50°. As the length of the beam decreases, attaching the connecting pins to the beam plate becomes more problematic. Therefore, the structure of the vibration beam was set to a 350 µm width, 200 µm thickness, and 50° angle based on the error range of the manufacturing process. To provide a signal input/output function on one side of the four-beam elastic bodies, 10 µm thick gold lines are printed. However, because these lines are markedly thinner than the polyimide, their effect on the migration of the resonance peak is insignificant.
3.3. Fabrication of the Hybrid Vibro-Acoustic Sensor
Based on the results of the FEA, the vibration beam plate printed circuit board (PCB) was fabricated using polyimide material (
Figure 6a,b; blueprint and actual product, respectively). The PCB had a 3 mm diameter and four round vibration beams were present on the edge of the vibration plate. Bonding electrodes are disposed at the center of the vibration plate so that a low-noise amplifier IC chip (LMV1032UR-25, Texas Instruments, Dallas, TX, USA) for signal amplification can be fixed in an area with a 2 mm inner diameter. This hybrid sensor uses the ECM (OBG-311L42-C33, BSE Co., Ltd., HongKong) as a mass at the center of the vibration plate to respond to the acceleration of the umbo vibration. Furthermore, a plane capacitor is formed between the circular electrode on the underside of the vibration plate and the circular electrode on top of the bottom plate. The ECM of the uppermost layer and the vibration beam plate beneath it are electrically connected so that the output signal arrives at the bottom plate. The printed circuit board (PCB) patterns are designed to connect the signal and power lines of the ECM, and the top and bottom of the vibration plate and the bottom plate.
The vibration and bottom plates are electrically connected via four conductive miniature connecting pins standing vertically on the bottom plate. The four output terminals on the bottom plate are configured to pull out one ECM output signal, one capacitive acceleration sensor output signal, two power lines for driving the ECM, and the integrated circuit (IC) for the capacitive acceleration sensor.
The VAHIM components and the final assembly are shown in
Figure 7. The VAHIM is cylindrical, with an outer diameter of 3.1 mm and height of 2.8 mm. Immediately below the ECM is a 0.1 mm thick plastic insulation plate, and the power and signal lines of the ECM are connected through the holes in the insulation plate to the PCB pattern above the vibration beam plate. The bottom surface of the vibrating beam substrate is provided with an IC chip as a preamp and a plate electrode for detecting any change in capacitance. An electret disc is attached to the upper surface of the bottom plate to increase the sensitivity of the acceleration sensor according to the capacitance change, without using an external battery. The four vibrating beams at the edges of the vibrating beam plate are connected to the four connecting pins. Since the gap between the electrodes in the acceleration sensor is controlled by the length of the connecting pins, some laser trim processing is required.