8 Toward Developing Arrays of Active Artificial Hair Cells 77 Table 8.1 Schematic of the AHC array with its fundamental frequencies Gains AHC1 AHC2 AHC3 AHC4 α1 (s) 3.59 ×10−4 2.27 ×10−4 1.79 ×10−4 1.60 ×10−4 α3 (s 3/V2) 1×10−11 5×10−11 8×10−11 5×10−11 Gains AHC5 AHC6 AHC7 AHC8 α1 (s) 9.27 ×10−5 7.18 ×10−5 5.68 ×10−5 5.08 ×10−5 α3 (s 3/V2) 6×10−11 5×10−11 1×10−9 5×10−9 5 4 3 2 1 Sensed Piezo Voltage - volt (V) Sensed Piezo Voltage - volt (V) 0 –1 –2 –3 –4 –5 0 2 4 6 a b Time (s) 8 10 12 0 1 2 3 4 Base Acceleration - a (m/s2) 5 6 7 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 volt = 0.584a1.0 volt = 0.815a0.38 Uncontrolled Controlled Uncontrolled Controlled Fig. 8.2 (a) Time-domain response of the active and passive AHC for a 7 m/s2 chirp input acceleration; (b) input-output plot 8.3 AHC Array Simulation Results This section evaluates the response of a single AHC to complex inputs as a starting point prior to studying the behavior of the array. The AHC used in this study is the second beam of the array shown in Fig. 8.1. Therefore, it is expected that this AHC affects the input signals that contain a frequency component near 500 Hz. Two types of signals are used in this study: a chirp signal and a periodic input. The chirp signal is applied to the AHC between 250 Hz and 2184.5 Hz and its amplitude is changed from 0.025 m/s2 to7m/s2. The time response of the AHC in response to the highest examined input level is shown in Fig. 8.2a. As displayed in Fig. 8.2a, the maximum response of the uncontrolled AHC is compressed in the active AHC’s output. This maximum response corresponds to the input frequencies near the fundamental frequency of the AHC. The relationship between the input and output of the system is studied using the plot illustrated in Fig. 8.2b. The input-output plot shows nearly one-third power-law relationship between the base acceleration and the voltage. This shows that the AHC can mimic the mammalian cochlea’s behavior when excited by a complex stimulus. It is important to note that as the response spectra of the AHC are time-variant, the values for the sensed piezoelectric voltage are calculated using the short-time Fourier transform (STFT). In the second step, a multi-tone sine signal is used as the input and the response of the AHC was computed. The results for this part of the study are shown in Figs. 8.3b, 8.4b, and 8.5b in the next section. As the single AHC showed desired behavior in response to complex stimuli, a similar study is performed on an array of AHCs in the next section with the periodic input. 8.4 AHC Array Simulation Results In this section, the behavior of the AHC array for various input levels is studied. A signal in the form of, ¨z(t) = A sin(2π ×200t) +sin(2π ×500t) +sin(2π ×1000t) +sin(2π ×3000t) +sin(2π ×5000t) +sin(2π ×8000t) +
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