An Active 2-D Silicon Cochlea

30 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 2, NO. 1, MARCH 2008 An Active 2-D Silicon Cochlea Tara Julia Hamilton, Senior Member, IEEE, Craig Jin, Member, IEEE, André van Schaik, Senior Member, IEEE, and Jonathan Tapson, Member, IEEE Abstract—In this paper, we present an analog integrated circuit design for an active 2-D cochlea and measurement results from a fabricated chip. The design includes a quality factor control loop that incorporates some of the nonlinear behavior exhibited in the real cochlea. This control loop varies the gain and the frequency selectivity of each cochlear resonator based on the amplitude of the input signal. Index Terms—Log-domain features, neuromnorphic engineering, silicon cochlea. Fig. 1. Effects of the nonlinear behavior of the cochlea on Basilar Membrane Velocity (Adapted from [1, p. 97]). I. INTRODUCTION T HE cochlea is a fascinating transduction organ that illustrates the ingenious way in which engineering problems are solved in nature. It has a frequency range of three decades and a dynamic range of approximately 120 dB [1]—allowing us to hear from the slightest whisper to the roar of a 747 flying overhead. For over 20 years, the cochlea has been the object of neuromorphic engineering research. There have been many previous silicon cochlea designs and for a wide variety of reasons—from the study of nonlinear effects present in the real cochlea to the examination of the debilitating effects of noise and mismatch—there remains substantial work to do before we have results that compare with the performance of the biological cochlea. In this paper, we present a silicon cochlea model with a local, instantaneous control loop that models the instantaneous action of the biological outer hair cells (OHCs). Importantly, we focus only on the instantaneous action of the OHCs and not on the slower feedback control exerted by the auditory brainstem via efferent fibres. The primary contribution of this paper is a demonstration that the silicon cochlea model with -control effectively simulates the dynamical response of biological cochlear resonances. For the rest of this introduction, we briefly review silicon cochleae and also the nonlinear feedback control effected by biological OHCs that is the focus of the current paper. The first silicon cochlea was described by Lyon and Mead [2]. This silicon cochlea uses a cascade of one hundred second-order low pass filters to model the wave propagation and frequency analysis associated with the basilar membrane (BM). The quality factor ( ) of the filters could be externally controlled but were not automatically set by the chip. This original cochlea design was Manuscript received February 28, 2008; revised March 3, 2008. This paper was recommended by Associate Editor R. Sarpeshkar. T. J. Hamilton, C. Jin, and A. van Schaik are with the School of Electrical and Information Engineering, The University of Sydney, Sydney 2006, Australia. (e-mail: [email protected]). J. Tapson is with the School of Electrical Engineering, The University of Cape Town, Rondebosch 7701, South Africa. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TBCAS.2008.921602 followed by improvements in circuit design [3]–[5] and subsequent modelling improvements with the introduction of a 2-D silicon cochlea that models wave propagation horizontally along the BM and vertically in the fluid around it [6]–[8]. The last of these [8] was the first 2-D model to incorporate the cochlea’s nonlinear effects (shown in Fig. 1). Fig. 1 illustrates the nonlinear effects of the biological OHCs. The OHCs adjust the gain and frequency selectivity of the BM based on the intensity of the input. The left-hand side of Fig. 1 illustrates the fine tuning capabilities of the active cochlea in the frequency domain, while the right-hand side illustrates large signal compression, i.e., higher gain at lower input intensities when compared with higher input intensities. While this figure provides only a schematic illustration, it accurately describes the fundamental signal processing characteristics that are contributed by the OHCs [1]. Frequency selectivity suppresses noise outside the frequency band of interest, and this, along with an increase in gain greatly improves the resonator’s performance at low signal levels. We achieve this in our resonator circuit using automatic -control (AQC). This is different from the more common concept of automatic gain control (AGC) which increases only the gain without sharpening the frequency selectivity. It should be noted, however, that the term AGC was used in [28] to represent what we refer to as AQC in this paper. II. SILICON COCHLEA MODEL An analog circuit model of the fluid dynamics within the cochlea may be achieved using a resistive network to simulate the cochlear fluid and with a number of resonator circuits to simulate the BM. The resonator circuits are attached to the resistive network and have an exponentially decreasing resonant frequency that is similar to the decreasing frequency from base to apex in the real BM [9]. A simplified circuit diagram of the model is shown in Fig. 2. This model may be described as 2-D since it models wave propagation horizontally along the BM and vertically in the fluid around it. A simplified Laplace equation 1932-4545/$25.00 © 2008 IEEE HAMILTON et al.: ACTIVE 2-D SILICON COCHLEA 31 Given the negative relationship between voltage and current, the super-capacitor is also referred to as a frequency dependent negative resistance (FDNR). Following from Fig. 2 the relationship between voltage, , and current, , and hence input inpedance, , at the th BM resonator is given by (4) Fig. 2. Simplified 2-D cochlea model. describing the fluid motion within the cochlea can be written as follows: The sensing cells in the cochlea, the inner hair cells, transduce the BM velocity into a neural signal. BM velocity is thus taken as the output for each resonator. Since the current represents the acceleration of the BM, it must be integrated to obtain a representation of BM velocity. Integrating (4) we get (5) (1) where is the pressure difference across the scala is the pressure difference across the scala media, tympani, is the width of the BM, is the acceleration of the BM, is the mass of the BM, is the is the stiffness of the BM. The viscosity of the BM, and circuit model is similarly described by a Laplace equation (2) that is mathematically equivalent (1) The response of the circuit model described above to a given input signal closely matches the response of a passive biological cochlea (Fig. 1) in which the OHCs have been inhibited [7], [9]. In this work, we have extended the aforementioned circuit model by adding an AQC circuit to the resonator circuit. The AQC circuit is used to represent the action of the OHCs. Here we no longer consider viscosity constant but rather dependent on BM velocity. It can be seen that (5) is proportional to the typical bandpass filter response given in (6), where is the time constant of the filter and is the quality factor (6) (2) where is the voltage analog of is the voltage analog of is the equivalent is the electrical curelectrical impedance of the BM, is the conductance of the BM, rent density, is the capacitance of the BM, and is the super-capacitance of the BM. To simplify this model the width , mass , and viscosity , of the BM are assumed to be constant for the entire length of the BM. Thus, we can see that in this model the analog for pressure is voltage, the analog for BM acceleration is current, the analog for BM mass is the inverse of conductance, the analog for BM viscosity is the inverse of capacitance and the analog for BM stiffness is the inverse of super-capacitance. This model represents the passive 2-D cochlea and further details can be found in [17] and [18]. , capacThe resonators in Fig. 2 comprise a conductance , and super-capacitor . Here the “ ” is equivalent itor to a section dx of the BM after spatial quantization. While the conductance and capacitor are common electrical elements, the super-capacitor is less well known. It has an electrical characteracross its terminals is proportional istic in which the voltage, to the double integral of the current, , which flows through it. In the frequency domain this relationship is given by (3) Comparing (5) and (6) we see that capacitance, , and hence the inverse of viscosity, , is proportional to . By varying in response to BM velocity we are varying viscosity [see (7)]. Increasing leads to undamping while decreasing leads to positive damping of the system (7) There have been a number of cochlea models which have incorporated the action of the OHCs as a feedback system although there is still much debate on the details of this system (for example, [23]–[26], [8], and [27]). Nearly all of these models, however, agree that it is an undamping term that is controlled by the feedback (often referred to as active damping). Our implementation of the 2-D cochlea model is shown in Fig. 3. It operates in the current domain utilizing both pseudovoltage [9] and log-domain circuits. With this mode of operation current becomes an analog for BM acceleration and voltage becomes an analog for pressure as required by (1) and (2). As described earlier, low signal levels in the biological cochlea result in an increase in gain as well as a sharpening in the tuning of the cochlear filters (see Fig. 1). To model this nonlinear effect, we have implemented an AQC loop [22] which controls both the gain and frequency selectivity of the BM resonators (BMRs). The AQC loop represents a “high-level” approach to our active cochlea design. Clearly we do not yet have comparable resources available to us in analog IC design 32 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 2, NO. 1, MARCH 2008 Fig. 5. Decision circuit operation. TABLE I DECISION CIRCUIT MODES Fig. 3. Current domain 2-D cochlea model. Fig. 6. Pseudo-conductor. Fig. 4. Automatic Q-control loop. that biology has to deal with mismatch and noise. For instance, there are over 3000 inner hair cells in the human cochlea and about ten spiral ganglion neurons connected to each of these [1]. This is several orders of magnitude greater than what we can currently achieve in an analog integrated circuit. A top-level circuit schematic of the AQC is shown in Fig. 4. The control loop consists of the BMR, a simple peak detector [10], a decision module, a ramp generator, and a wide-linearrange (WLR) transconductance amplifier [11]. In the integrated circuit implementation, the control loop can be externally disabled allowing the -value to be set manually. The output signal of each resonator is equivalent to BM velocity which is equivain Fig. 2. lent to the voltage across the capacitor The peak detector continuously measures the peak level of the output signal from the BMR. The peak current forms an input to the decision module which employs two current comparators—one comparator is used to set the ceiling level for the signal amplitude and the other sets the threshold level. In other words, the decision module sets the target signal amplitude between the threshold and ceiling level as shown in Fig. 5. The decision module employs hysteresis to prevent oscillations. The state logic describing the operation of the decision module is shown in Table I. The -value of the BMR is controlled by the output current from the WLR transconductance amplifier. The magnitude of , from this current is controlled by the output voltage, the ramp generator. Larger voltages generate larger currents and hence a larger -value. The bias current of the WLR transconductance amplifier is set to give the maximum -value when is equal to the supply voltage . III. CIRCUITS A. Resistive Network The resistive network was created using pMOS transistors operating as pseudo-conductances. The principle of pseudo-voltage and pseudo-conductance is described relative to Fig. 6. The current though the depicted transistor when operating in the subthreshold regime is given by (8) where is the specific current, is the slope factor, is , and are the terminal voltages the threshold voltage, in most cases), and referred to the local substrate ( is the thermal voltage where is Boltzmann’s constant, is temperature and is the charge of a single electron. We may define a pseudo-voltage as (9) where is an arbitrary positive scaling constant. Combining (8) and (9) we obtain the following relationship: (10) HAMILTON et al.: ACTIVE 2-D SILICON COCHLEA 33 Fig. 8. Schematic of the current controlled current source from Fig. 7 implemented as a multiplier cell. Fig. 7. Schematic of the second-order bandpass filter. Here it is seen that using pseudo-voltages yields a relationship between current and voltage in the form of Ohm’s law, with the pseudo-conductance given by (11) As shown in (11), the pseudo-conductance (horizontal) and (vertical) in the resistive network may be controlled by of the transistors in the network. varying the gate voltage, the centre frequency. Errors in bias current due to noise or mismatch between different AQC circuits result in a reduction in as each WLR amplifier cannot be individually tuned. The current controlled current source shown in the first tau cell in Fig. 7 can be implemented using the log-domain multiplier circuit shown in Fig. 8. In Fig. 8 transistors M7, M8, M9, and M4 create a translinear loop [14] such that (14) and, hence B. Basilar Membrane Resonators (BMRs) The BMR was implemented using a log-domain and secondorder bandpass filter, with an embedded AQC loop that sets the -value. The bandpass filter was implemented using two tau cell log-domain filters [12]. Fig. 7 shows the circuit schematic for the bandpass filter. The transfer function for this filter is given by (12) where is the time constant that determines the resonant fre, where quency. The time constant is given by is the capacitance, the thermal voltage and the bias current. By using the tau cell for the bandpass filter design, the resonant frequency and -control can be configured in a variety of ways [13]. The objective of AQC is to maximize for low signal levels and have little to no for high signal levels. The tau cell bandpass filter is configured to have a -value which is governed by the following equation: (13) where when the input signal level is low and when the input signal level is high. When using the AQC loop, the maximum -value is obtained by setting the bias current of the WLR amplifier to be approximately . This bias current can be set to its optimum value by turning off the automatic -control loop and varying the bias current until the output amplitude of the resonator is at its maximum when stimulating at (15) The above circuit can be simplified and improved given a number of considerations. First consider that the voltages and in Fig. 8 are actually identical to the voltages and in Fig. 7, respectively. Transistors M11, M12, M13, and M14, in Fig. 8 are necessary to mirror the output current of the mulbecause the voltage node cannot be directly tiplier (see Fig. 7). This last point connected to the voltage node and is made clear by consideration of both the voltages which will be close to the voltage in normal operation. Thus, transistor M8 would not be guaranteed to stay in saturation, as is needed for correct operation of the translinear loop, and its source voltage is . Consider if its drain voltage is further that the transfer function specified in (9) is obtained with the assumption that is the dominant capacitance in the circuit and much larger, for instance, than the gate capacitance seen at voltages and . Given this assumption, the voltages and in Fig. 7 are level shifted by an identical amount from the voltages at and , since both M3 and M6 have a constant bias current flowing through them. Furthermore, from Fig. 8 it is clear that the multiplier has a differential structure and as and such will be insensitive to a common DC level shift on as long as there is sufficient voltage headroom for transistor M10 to operate. This voltage headroom can be ensured by setto an appropriate level. The point of the ting the voltage above considerations is that the voltages and in Fig. 8 can now be connected to the voltages and instead, which allows the output voltage node to be connected directly to the voltage node as well. This means that the current mirrors M11-M12 and M13-M14 are no longer necessary and can be removed, simplifying the circuit and improving matching. 34 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 2, NO. 1, MARCH 2008 Fig. 9. Simplified schematic of the multiplier cell shown in Fig. 8. Fig. 10. Schematic of the peak detector circuit. The final implementation of the multiplier circuit which provides a current controlled current source is shown in Fig. 9. It can be seen that transistor M8 has its drain connected to and its gate connected to . The voltage swing on these nodes is small for this type of log-domain filter so that saturation of M8 is guaranteed. C. Automatic Fig. 11. (a) Block diagram of the decision circuit. (b) Current comparator. -Contol Circuits Fig. 10 shows the peak detector circuit for the AQC. This circuit was adapted from [10]. It rectifies the input current, , using the capacitor to hold the charge. A peak in the input current results in a peak voltage held across the capacitor. A is included so that the circuit can small leakage current track changes in the input. The decision circuit [Fig. 11(a)] comprises two current comparators [Fig. 11(b)] and digital logic that implements the operation described in Fig. 5. The digital logic adjusts the current , so that the threshold level is comparator reference current, set between Threshold1 and Threshold2 (see Fig. 5). The output is mirrored and fed into the current from the peak detector current comparators as is the reference current . The curis sourced into voltage node , while the reference rent provides a current sink [see Fig. 11(b)]. Thus, current increases when exceeds . Assuming that the transistor flows into voltage node M3 is turned on, a copy of and subsequently back into voltage node via transistor M1, forming a positive feedback loop. Hence, the increase in is reinforced and the output voltage goes low. The voltage decreases when is greater than . In this case the is reinforced through the action of transistors decrease in goes high. In summary, the M2 and M4 and the voltage decision circuit responds quickly to changes in , and the digital logic results in hysteresis, so that the decision circuit is . not sensitive to small fluctuations in The circuit diagram for the ramp generator is shown in and , Fig. 12. Based on the voltage control signals, Fig. 12. Schematic of the ramp generator circuit. the capacitor, , is either charged, discharged or held constant. , increases As the capacitor is charged the output voltage, decreases linearly when the capacitor is dislinearly. rises and falls is determined charged. The rate at which by voltages and , respectively. The WLR transconductance amplifier shown in Fig. 13 is described in detail in [11]. It utilizes techniques such as bump linearization and well inputs to increase its linearity over a wide voltage range. In the AQC loop, the WLR transconductance amplifier is used as a voltage controlled current source. As the , increases, the output current increases and vice input, versa. Although the current from the WLR transconductance amplifier is bidirectional, the voltage is always in normal operation and hence the circuit greater than always sources current. D. Terminator Circuit The resistive network is terminated (see Terminator in Fig. 3) using a circuit that models the biological helicotrema to pre- HAMILTON et al.: ACTIVE 2-D SILICON COCHLEA 35 Fig. 15. Input generator circuit. Fig. 13. WLR transconductance amplifier. this current to a pseudo-voltage by passing it through a transistor operated as a pseudo-conductance. This yields the input generator circuit shown in Fig. 15. In Fig. 15, is a current representation of the input voltage, , plus a DC bias current, can be written in terms of and as follows: the current , and voltages (19) is the thermal voltage. This equation can then be where , as follows: rewritten using the pseudo-voltage, Fig. 14. Terminator circuit for the BMR network. (20) vent low-frequency signal reflections. Low frequency signals that otherwise have not been given a low impedance path via a BMR circuit could create standing waves in the resistive network. The circuit diagram for the terminator is shown in Fig. 14. It is a first-order tau cell designed to model a conductor and capacitor in series. However, due to a layout error in the fabricated chip, it has the following characteristic: (16) The value of A is determined from a biasing circuit described in subsection H. From Fig. 14, we see that the transistor implementing is saturated, i.e., , so that . From this it follows that (17) and, hence, from (13) we have (18) The layout error does not greatly influence the operation of the silicon cochlea apart from some low frequency reflections in the resistive network. This error will, of course, be fixed in future versions of the silicon cochlea. E. Input Generator Pressure is represented by pseudo-voltage in the resistive network modelling the cochlear fluid. Since sound input from a microphone or sound card represents sound pressure as a voltage, we need to convert this voltage to a pseudo-voltage (see Input Generator in Fig. 3). We do this by converting the voltage linearly to a current using a WLR amplifier and then converting where is some positive scaling constant. From this equation is a pseudo-voltage representation of the current we see that and is, hence, linearly related to . F. The Impedance Matching Circuit The impedance matching circuit is necessary to ensure that the impedance of the BMRs in the model is maintained when using the resonator circuits with AQC. The input current to each , (as shown in Fig. 3) must satisfy the following resonator, equation to ensure that (4) holds: (21) The circuit required to implement this is shown in Fig. 16. In Fig. 16, , and are all currents from the resonator and are obtained by multipli(shown in Fig. 7) and, is a cation using the translinear multiplier circuit of Fig. 17. single transistor used as a pseudo-conductance which converts into the current [9] and provides a dc offset to the resonator circuit. G. Output Circuit , is fed off chip via a The output current of the BMR, simple output circuit comprising a WLR amplifier and a simple is a refbuffer. The circuit is shown in Fig. 18. In Fig. 18, removes the DC offset from the output erence voltage and current, . Thus, the relationship between and is (22) where is the transconductance of the WLR amplifier. 36 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 2, NO. 1, MARCH 2008 Fig. 16. Impedance matching circuit. Fig. 17. Translinear multiplier circuit. Fig. 20. Active 2-D silicon cochlea chip. Fig. 18. Output circuit. Fig. 21. Creation of I Fig. 19. Biasing circuit for a single resonator. H. Resonator Biasing Circuit The bias current for each resonator, , and the bias current , are setting the maximum value for the quality factor, distributed exponentially. In this way, the resonant frequencies of the BMRs are also distributed exponentially. This is achieved by first applying a voltage difference across a resistive line that is realized using high resistance polysilicon and then linearly tapping a voltage off the line and feeding it into the base of three compatible lateral bipolar junction transistors (CLBTs) [16]. The CLBTs convert the linear voltage change on the resistive line into an exponential change in the bias currents. and Fig. 19 shows the bias circuitry for a single BMR. are the biasing voltages for the MOSFETs incorporated and I using V . in the CLBT. The cascode is included to increase the output , is used to vary the impedance of the CLBT. The voltage, value of the bias current for setting the maximum value of the quality factor. line in and line out are the ends of the short section of resistive line for the single resonator. For the first resonator line in connects to a pad and for the terminator line out connects to a pad. IV. ACTIVE SILICON COCHLEA CHIP The silicon cochlea was fabricated in the AMI 0.5- m process. The integrated circuit included an on-chip bias current generator [15] to improve current matching as well as allow easy bias current tuning. A photomicrograph of the chip is shown in Fig. 20. There are 83 active BMRs on a single chip. The layout for the resonator minimizes the width of the cell and hence the number of rows of resonators required to fit the entire silicon cochlea on a single die. Fig. 20 shows that three rows are used with only two bends, i.e., direction reversals, in the chain of BMRs. Previous silicon cochleae have shown HAMILTON et al.: ACTIVE 2-D SILICON COCHLEA (a) 37 (b) Fig. 22. Frequency response of BMRs with (a) no AQC and (b) AQC enabled. that each bend increases mismatch. All of the capacitors shown in the previous circuit schematics were implemented as MOS capacitors as their performance in this process was comparable with the poly–poly capacitors. The chip allows access to the output of each active BMR via a scanner consisting of a shift register and transmission gates to select which BMR will be observed. In addition to providing access to the output, the scanner allows access to several control voltages in the automatic -control loop. The AQC mechanism can be switched on and off as can the BM resistive network. Thus, each resonator can be tested and tuned individually. The ceiling and threshold levels in the decision circuit [ , in Fig. 11(a)] can be manually set via a single control and . The relationship between and the voltage, ceiling and threshold levels is shown in Fig. 21. In Fig. 21 “M” is the multiplier of the transistor. Various other currents used in the active BMR can be manually set. V. RESULTS The operation of the silicon cochlea had to be tested using extremely high bias currents because the on-chip bias generator had too much gain resulting in instability of the generated bias currents. The instability is normally controlled with the addition of a capacitor, however, an oversight meant that the node to which the capacitor must be connected was not brought out to a pin. As some of the bias currents on the chip were not brought out to pads, we were unable to switch off the bias generator. We were, however, able to obtain a stable bias generator output by reducing an external resistor, but this meant that the generated bias currents were at least 40 times larger (according to simulation) than they were originally designed to be. A summary of the performance characteristics of the chip is given in Table II. Note that the power consumption figure includes necessary off-chip bias circuits. These circuits have a power consumption of 39.6 mW. Thus, the net power consumption of the chip is 16.72 mW. This would be reduced by a further factor of 40 with normal bias currents to approximately 418 W. Also note that 7 mV RMS corresponds to the noise at the output. As our gain changes (due to AQC) we have not referred this value back to the input. TABLE II CHIP PERFORMANCE CHARACTERISTICS A. Operation of the Individual Active BM Resonators We first configured the chip to test the individual BMRs. This was achieved by bypassing the resistive network and inputting a test signal into an individual resonator via a multiplexer and scanner. The voltage across the resistive line used to bias the resonators was set to give a frequency range of approximately 750–4200 Hz and the AQC was initially disabled. Fig. 22(a) shows the frequency response of 21 resonators approximately equally spaced out of the 83 resonators in the network. The gain decreases some 5 dB towards the lower frequency resonators, which means that the output of some of the resonators is almost twice the output of others. This is an undesirable effect in a silicon cochlea. Fig. 22(b) shows the frequency response of the same 21 resonators with the same resistive line settings but now with the AQC turned on. When we compare Fig. 22(a) and (b) we see that the inclusion of AQC has little effect in improving matching. In order to have a properly functioning silicon cochlea, it is important that we can control the resonant frequencies of the BMRs precisely. To test this, we biased all of the resonators to have the same resonant frequency by setting the ends of the resistive line to the same voltage. Fig. 23 shows the frequency response of the 21 BMRs in this case. We see in this plot that there is some variation in the resonant frequency of the BMRs. Statistical analysis shows the average resonant frequency to be 4133 Hz with a standard deviation of 550 Hz. We set the frequency range of the resonators from 200 Hz to 6.6 kHz and plotted the resonator number versus the corresponding resonant frequency in Fig. 24. From this we can see 38 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 2, NO. 1, MARCH 2008 Fig. 23. Frequency response of BMRs with identical tuning. Fig. 24. Resonator number versus corresponding resonant frequency. Fig. 25. Frequency response of a BMR with varying Q. that the best frequencies deviate somewhat from being logarithmically distributed but not enough to impact upon the operation of the cochlea. Consider now changes in the quality factor. With the AQC disabled, the quality factor in a single resonator was varied from low to high. The frequency response of this resonator is shown in Fig. 25. Here we see that we can achieve gains of 20 dB with very little change in the resonant frequency because the time Fig. 26. Frequency response of a BMR with varying ceiling. constant and -value are independently determined in the tau cell configuration used in the bandpass filter. In other configurations a change in the -value necessitates a change in the time constant [13]. The legend in Fig. 25 indicates the value of a control voltage used to set the -value on chip. We see that small changes in voltage can result in large changes in -value due to the nonlinear function shown in (13). This can be a problem as any drift in the power supply voltage can result in large changes in the value. Therefore, we used a voltage regulator to maintain the power supply voltage. In this case was held at 5.227 V. The effect of the ceiling and threshold levels of the decision circuit on the operation of the AQC is shown in Fig. 26. In this V corresponds to a high ceiling level and figure, V corresponds to a low ceiling level. In Fig. 26, the V has several bumps at low curve corresponding to frequencies and is rounded at its peak; these nonidealities arise because the output was close to limit cycling at this point and as a result had an increased number of distortion products. While the frequency response curves illustrate the gain and frequency selectivity of the BMRs, they do not show the extent of the distortion in the output signal. Fig. 27 shows the fast Fourier transforms (FFTs) for two curves. These were measured using a 2.6-kHz sine wave of amplitude 100 mV as input into the resonator with resonant frequency set at approximately 2.6 kHz. The output was sampled at 500 kHz using a Tektronix digital Oscilloscope (TDS 3014) and MATLAB software was used to obtain the FFTs. Fig. 27(a) shows the FFT when V. Here we see the second harmonic at 5.2 kHz, however, the third harmonic, at 7.8 kHz, is barely visible. The total harmonic distortion (THD) for this curve was calculated to be 2.5%. V. In this plot both Fig. 27(b) shows the FFT when the second and third harmonic are clearly visible and the THD was calculated to be 10%. It is reasonable that a larger -value results in more harmonic distortion, especially since the control loop attempts to hold the -value at the edge of limit-cycling. Using to appropriately set the ceiling of a single BMR, we explore the nonlinear compressive effects of the AQC. Figs. 28 and 29 show the nonlinear compressive effects of a single BMR with AQC enabled. For these measurements, the frequency of the input signal is held constant, at or near to the HAMILTON et al.: ACTIVE 2-D SILICON COCHLEA Fig. 27. FFTs for the output of the BMR when (a) V 39 = 4:0 V and (b) V Fig. 28. Nonlinear compressive effects of a single BMR. = 3:0 V. Fig. 30. Transient response of a BMR with AQC and low Q. Fig. 31. Transient response of a BMR with AQC and high Q. Fig. 29. Frequency response of a single resonator varying the input amplitude. resonant frequency of the BMR, while the amplitude of the input signal is varied. It can be seen, in Fig. 28 that as the input amplitude increases the gain of the output signal flattens out. The point at which the gain begins to flatten out is controlled . Fig. 29 shows by the level at which the ceiling is set via that for low input intensities the gain increases along with the selectivity of the response as is required by our cochlea model. Fig. 30 shows the transient response of the 5th BMR to a sinusoidal input of amplitude 100 mV and frequency 1.4 kHz set high so that only low -values could be achieved. with In Fig. 30, we reset the output of the resonator at time zero by resetting the output of the ramp generator. From this time we see the amplitude of the output signal grow, resulting in a final gain of approximately 6 dB. Fig. 30 also demonstrates how the DC level of the output signal does not remain constant. This is probably due to mismatch in the impedance matching circuit and is demonstrated even more dramatically in Fig. 31 where we have increased the maximum -value. B. Operation of the Active 2-D Cochlea Following extensive testing of the individual BMRs we configured the chip as a 2-D active cochlea. This was achieved by reconnecting the resistive network and inputting the test signal via the input generator circuit. In this configuration the output from the first few resonators is discarded because they do not 40 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 2, NO. 1, MARCH 2008 Q Fig. 32. Frequency response of the 2-D cochlea with mid- . Fig. 34. Gain of the output of the active 2-D cochlea with varying input intensity. Fig. 35. (a) Amplitude growth for resonator 7. (b) Phase versus frequency for resonator 7 with input 6 and 24 dB. 0 Fig. 33. Frequency response of the 2-D cochlea with high Q and close spacing. have resonators of higher resonant frequencies earlier in the resonator chain and do not display the characteristic steep high-frequency roll-off. Fig. 32 shows the frequency response from resvalue is set to onators 18, 38, and 54 when the maximum a medium level. Only three resonators are shown to improve clarity. In Fig. 32 the sharpness of the frequency response peaks is more obvious at higher frequencies than at lower frequencies. This is also the case in biology where we see sharper tuning at high frequencies and flatter tuning for the low frequencies [20]. The effect of increasing the maximum -value is shown in Fig. 33. In this plot we have not only increased the maximum -value, but also reduced the frequency spacing of the resonators by reducing the voltage difference across the resistive line. The plot shows the output from resonators 11, 19, 26, 33, 44, and 53. Fragnière [7, pp. 85–86, pp. 93–96] showed that it is necessary to reduce the resonant frequency spacing of the resonators when there is the possibility of high -values to avoid instabilities. We found that in addition to improved stability, steeper frequency response curves were obtained with higher gain when the frequency spacing of the resonators was reduced. The density of 180 resonators per octave for the measurement of Fig. 33 was exaggerated to illustrate another point. As the input signal travels from the base to the apex of the resonator chain, the signal is lost to adjacent, basal resonators since such a significant part of their resonant frequencies overlaps. Note, however, that the gain at resonance for resonator 53 is still 6 dB 0 higher than the gain of the resonators in Fig. 32. With fewer resonators per octave less signal would be lost and the gain would be more even across the sections, but too few resonators per octave will lead to instability. The gain of the 2-D cochlea with varying input intensity is shown in Fig. 34. In Fig. 34, we see the output from the 30th resonator for seven different input amplitudes, covering a dynamic range of 40 dB, when the chip is configured as an active 2-D cochlea. While this particular configuration does not exhibit huge gain we can see that lower amplitude signals have higher gain and more selective response when compared to high amplitude input signals. In this case the lowest amplitude signal was 100 times smaller than the highest signal. It also shows that the resonant frequency shifts to the left (i.e., becomes lower) when the strength of the input signal increases. In Fig. 35, we see the amplitude growth data over a 24-dB range (a) and phase data for two different signal intensities (b) for the seventh resonator. The shape of the phase data is very similar to physiological data in [29]. At the centre frequency the phase lag is larger for the 6 dB input than for 24 dB. Specifically the phase accumulation at the centre frequency is and at 6 and 24 dB, respectively. In the biological data higher intensity input signals have a greater delay than the low intensity signals. The slope of the phase curve increases after the centre frequency until it plateaus in both the measured data and the biological data. The phase accumulation is much greater for the biological data than for the chip data, however, our silicon cochlea has a smaller frequency range than HAMILTON et al.: ACTIVE 2-D SILICON COCHLEA 41 Fig. 36. Two-tone suppression with (left) a low-frequency suppressor tone and (right) a high-frequency suppressor tone. Fig. 38. Transient response of the active 2-D cochlea with medium Q. Fig. 37. Frequency spectra at a place (corresponding to the seventh resonator) along the basilar membrane showing odd-order distortion products from the silicon cochlea. the biological cochlea and as such the travelling wave does not travel as far. Physiological experiments with the live cochlea have shown that the magnitude of the output signal in response to a test tone is reduced in the presence of another tone. This phenomenon is called two-tone suppression. Fig. 36 shows the output response of the seventh resonator to a 3.6-kHz test tone in the presence of a 2.5-kHz suppressor tone (left) and a 5-kHz suppressor tone (right) of varying intensities. The -axis shows the intensity of the 3.6-kHz test tone and the -axis shows the output response. When compared to the physiological data [30], we see that in biology the test and suppressor tones are able to cover a much larger dynamic range; over 100 dB. The effect of the suppressor tone is correct, however, with the chip data showing a decrease in response with an increase in the intensity of the suppressor tone. Combinational tones or distortion products are by-products of the nonlinear action of the cochlea. When the cochlea is exposed to two tones which are close to the centre frequency at a particular place along the basilar membrane the frequency spectra of the basilar membrane in response to these tones contains prominent, odd-order distortion products (e.g., 2f1-f2, 3f12f2, 2f2-f1, 3f2-2f1, and so on) [31]. Fig. 37 shows the frequency spectra at resonator 7 when two frequencies of equal intensity are presented simultaneously to the silicon cochlea. In Fig. 39. Transient response of the active 2-D cochlea with high Q. this plot the two test tones (f1 and f2) are selected such that , where the centre frequency of the seventh resonator. Here we see that the odd-ordered distortion products are prominent and this is also the case for biology. Fig. 38 shows the transient response of the 30th BMR to a sinusoid of amplitude 100 mV and frequency 600 Hz with the chip configured as an active 2-D cochlea. In this case, the maximum -value has been set to a medium value as in Fig. 32. In this figure, we see that after the resonator has been reset at time zero the output level adapts in approximately 10 ms and then settles. Changing the settings of the AQC to allow for a higher results in the transient response shown in Fig. 39. Here the output signal adapts in approximately 45 ms. This transient signal is on the edge of stability with the control loop having set the -value to its highest value without limit cycling. VI. DISCUSSION The biological cochlea is believed to include two control loops [19]: a local and virtually instantaneous control loop 42 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 2, NO. 1, MARCH 2008 cochlea. It is believed, however, that biological phenomena such as otoacoustic emissions utilize the ability of the cochlea to facilitate bidirectional and standing waves [21]. VII. CONCLUSION Fig. 40. FFT of transient response from Fig. 39. which is attributed to the action of the OHCs, and a slower control loop which influences the OHCs’ response and operates from higher levels of the auditory pathway via efferent fibres. In our silicon cochlea design, the AQC loop is analogous to the biological local control loop. The transient response shown in Figs. 38 and 39 indicates that adaptation occurs quickly. There is a limit, however, to how quickly the -value can change and still maintain stability in the circuit. The slow biological control loop is not modelled by our silicon cochlea, but its effect would which sets the be similar to that of the control voltage maximum value that the -value can reach. It is important to maintain the -value at the point before the resonator starts limit cycling. There is a small range of -values for which the resonator will oscillate at the resonant frequency. Subsequent increases in the -value will result in oscillations of much lower frequency and this strongly impacts upon the operation of the cochlea which relies on a sequential decrease in resonant frequency from the basal to apical end of the resonator chain. If the -value is set uniformly across the BMR chain, then a high degree of matching in the resonator circuits is desirable. Otherwise, variations among the resonators means that the -value must be tuned down to avoid limit cycling in each and every resonator and this effectively reduces the gain available across the entire cochlea. Ideally, each resonator could be tuned individually, however, this requires too much space on chip. It is more reasonable that independent AQC is applied across various sections of the BMR chain. The need to discard the output of the first few resonators because they do not display high-frequency roll-off is wasteful in terms of chip resources, area, and power consumption. In biology there is likely a similar redundancy, however, a solution where the resistive network is terminated for high frequencies at its basal end might remedy the situation somewhat. No matter what the solution, it is certainly clear that the first few resonators do not require AQC. Termination at the apical end of the cochlea is also important. In Fig. 33, the resonator output curves have a bump between 200 and 300 Hz. This bump is due to standing waves resulting from the lack of a low impedance path to signal ground at low frequencies. Particular care must be taken to ensure correct termination as standing waves will degrade the performance of the In this paper, we have presented an active 2-D silicon cochlea that incorporates some of the nonlinearities present in the biological cochlea. We have discussed the model used to create our cochlea, the circuits used to realize this model and shown results from a fabricated integrated circuit that implements this model. Our results indicate that our 2-D silicon cochlea exhibits many of the nonlinear behaviors of the biological cochlea. These include amplitude growth, large signal compression, two-tone suppression and the presence of distortion products or combinational tones. By building this model we have also discovered a number of possible improvements to our model or the circuits used in its implementation. Future iterations of this design will focus on improving termination and tunability of the AQC in individual or grouped resonators. REFERENCES [1] C. J. Plack, The Sense of Hearing. Mahwah, NJ: Lawrence Erlbaum, 2005. [2] R. F. Lyon and C. Mead, “An analog electronic cochlea,” IEEE Trans. Acoust. Speech Signal Process., vol. 36, no. 7, pp. 1119–1134, Jul. 1988. [3] L. Watts, D. A. Kerns, R. F. Lyon, and C. A. Mead, “Improved implementation of the silicon cochlea,” IEEE J. Solid-State Circuits, vol. 27, no. 5, pp. 692–700, May 1992. [4] A. van Schaik, E. Fragniere, and E. A. 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Kemp, “Otoacoustic emissions, traveling waves and cochlear mechanisms,” Hearing Res., vol. 22, pp. 95–104, 1986. [22] T. J. Hamilton et al., “A basilar membrane resonator for an active 2-D cochlea,” presented at the ISCAS, New Orleans, LA, 2007. [23] S. T. Neely and D. O. Kim, “A model for active elements in cochlear biomechanics,” J. Acoust. Soc. Amer., vol. 79, no. 5, pp. 1472–1480, 1986. [24] J. F. Ashmore et al., “Molecular mechanisms of sound amplification in the mammalian cochlea,” in Proc. Nat. Acad. Sci., 2000, vol. 97, pp. 11759–11764. [25] D. C. Geisler and X. Shan, , P. Dallos, D. C. Geisler, J. M. Matthews, M. A. Ruggero, and C. R. Steele, Eds., “A model for cochlear vibrations based on feedback from motile outer hair cells,” in The Mechanics and Biophysics of Hearing. Berlin, Germany: Springer-Verlag, 1990, pp. 86–95. [26] F. Mammano and R. Nobili, “Biophysics of the cochlea: Linear approximation,” J. Acoust. Soc. Amer., vol. 93, no. 6, pp. 3320–3332, 1993. [27] G. Zweig, “Finding the impedance of the organ of Corti,” J. Acoust. Soc. Amer., vol. 89, no. 3, pp. 1229–1254, 1991. [28] R. F. Lyon, , P. Dallos, Ed., “Automatic gain control in cochlear mechanics,” in The Mechanics and Biophysics of Hearing. New York: Springer-Verlag, 1990, pp. 395–402. [29] M. A. Ruggero, N. C. Rich, A. Recio, S. S. Narayan, and L. Robles, “Basilar-membrane responses to tones at the base of the chinchilla cochlea,” J. Acoust. Soc. Amer., vol. 101, pp. 2151–2163, 1997. [30] M. A. Ruggero, L. Robles, and N. C. Rich, “Two-tone suppression in the basilar membrane of the cochlea: Mechanical basis of auditorynerve rate suppression,” J. Neurophys. vol. 68, no. 4, pp. 1087–1099, May 1992. [31] L. Robles, M. A. Ruggero, and N. C. Rich, “Two-tone distortion on the basilar membrane of the chinchilla cochlea,” J. Neurophys. vol. 77, no. 5, pp. 2385–2399, May 1997. Tara Julia Hamilton (S’97–M’01–SM’05) received the B.E. (engineering) degree from the University of Sydney, Sydney, Australia in 2001 and the M.Eng.Sc. (biomedical) from the University of New South Wales, Australia, in 2003. She is currently working towards a Ph.D. at the University of Sydney. She worked for Cochlear Ltd. as a Quality Assurance Engineer and an Analog IC Design Engineer for four years and was part of the team that invented the world’s first totally implantable cochlear implant. She is a Lecturer in the School of Electrical and Information Engineering, University of Sydney, Australia. Her research interests include neuromorphic engineering, analog integrated circuit design, and biomedical engineering. 43 Craig Jin (M’92) received the M.S. degree in applied physics from the California Institute of Technology, Pasadena, in 1991 and the Ph.D. degree in electrical engineering from the University of Sydney, Sydney, Australia, in 2001. He is a Senior Lecturer in the School of Electrical and Information Engineering, University of Sydney and also a Queen Elizabeth II Fellow. He is a Director of the Computing and Audio Reseach Laboratory at the University of Sydney and also a co-founder of three start-up companies. His research focuses on spatial audio and neuromorphic engineering and he is the author or co-author of more than 50 journal or conference papers in these areas and holds six patents. Dr. Jin has received national recognition in Australia for his invention of a spatial hearing aid. André van Schaik (M’00–SM’02) received the M.Sc. degree in electrical engineering from the University of Twente, Enschede, The Netherlands, in 1990 and the Ph.D. degree in electrical engineering from the Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland, in 1998. He is a Reader in Electrical Engineering in the School of Electrical and Information Engineering, University of Sydney, Sydney, Australia, and an Australian Research Council Queen Elizabeth II Research Fellow. His research focuses on two main areas: neurmorphic engineering and spatial audio. He has authored or co-authored more than 90 papers in these two research areas and is an inventor of more than 25 patents. He is the Director of the Computing and Audio Research Laboratory at the University of Sydney and a co-founder of three start-up companies. Dr. van Schaik is a member of the EPSRC college and a board member of the Institute of Neuromorphic Engineering. He is the Past Chairman of the Sensory Systems Technical Committee of the IEEE Circuits and Systems Society and an Associate Editor for the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS. He is a member of the Analog, BioCAS, and Neural Network Technical Committees of the IEEE Circuits and Systems Society. Jonathan Tapson (M’05) received the B.Sc. degrees in physics and in electrical engineering and the Ph.D. degree from the University of Cape Town, Rondebosch, South Africa, in 1986, 1988, and 1994, respectively. He is Professor of Instrumentation at the University of Cape Town. After spells in industry and in a government research laboratory, he rejoined his alma mater in 1997 and was promoted to Professor in 2003. His research interests include smart sensors, networked instruments, and bio-inspired systems. He serves on the boards of three companies which have spun out from his research work. These operate in areas as diverse as web-based monitoring of industrial machinery, and induction melting of platinum and precious metals in the jewelry industry. He is most proud of Cell-life, Inc., a not-for-profit corporation which uses GSM cellphone technology to provide IT solutions for the HIV/Aids crisis in Africa, and which currently supports over 20 000 patients, including over 2000 children.