50 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 54, NO. 1, JANUARY 2007
Fig. 3. The inner hair cell circuit.
a low-pass filter. This half wave-rectified current is as a first ap-
proximation given by
(3)
where
is controlled by and by .
The first-order low-pass filter is a log-domain circuit. Its
transfer function in the Laplace domain is given by
(4)
where
is given by
(5)
and
is given by
(6)
The cutoff frequency of the low-pass filter can be controlled
with
and , which generate bias currents and , re-
spectively. C3, implemented as a pMOS capacitor, should have
been implemented with an nMOS capacitor because the voltage
is quite close to
. Nonetheless, the circuit still operates cor-
rectly as the voltage swing is small and the pMOS capacitor
acts almost linearly. The cutoff was set around 1 kHz as in the
real inner hair cell, modeling the reduction in phase-locking ob-
served on real auditory nerves at frequencies greater than 1 kHz.
The two control signals
and are slightly below to
allow the two pMOS transistors providing
to operate in satu-
ration. Any voltage difference between
and will show
up as a current gain depending exponentially on this difference
as given in (5). In the results shown in this paper, both voltages
were equal to 4.5 V, resulting in a gain of 1.
The biological inner hair cell exhibits adaptation to an on-
going stimulus, therefore it responds more strongly to the onset
of stimulation than the sustained part of the stimulus and its
response is suppressed temporarily after the offset of stimula-
tion. This adaptation has been modeled in [27] but it was con-
sidered too complex and too large for inclusion on the current
chip. However, we intend to include this in future versions.
C. Integrate-and-Fire Neuron for AER
The output current of the IHC (
) is passed through a cur-
rent mirror (not shown) which is cascaded with
, shown
Fig. 4. AER spiking neuron.
in Fig. 4. This point forms the boundary between the analog
front-end and the digital AER circuits. The analog and digital
circuits run on separate power supplies to reduce digital noise on
the analog signals. The wells of the pMOS transistors in Fig. 4
are all tied to the digital
.
When the acknowledge signal (ack) is low,
is integrated
onto the membrane capacitor
of the neuron circuit, which
has a leakage current
controlled by . The spike is gen-
erated by two inverters in series, with positive feedback through
. When a spike is generated, the request line (req) is pulled
low. A high pulse in acknowledgement (ack) resets the neuron
after which it will enter a refractory period with a duration set
by
.
The AER protocol is described in [1]. When a neuron makes
a request (by pulling the req signal low), an on-chip arbiter ar-
bitrates between all neurons making a request, and sends off
each neuron’s address in sequence through two external hand-
shaking signals. Once a neuron’s address has been communi-
cated off-chip, the arbiter sends an acknowledge to the neuron
via the ack signal, which in turn resets the neuron. The AER cir-
cuitry used on our chip is adapted from [1] and has already been
used on a number of chips.
D. AER EAR
The complete system consists of (A) two matched, 32-sec-
tion silicon cochleae, followed by (B) simplified inner hair cell
circuits and (C) spiking neurons and AER interface circuitry to
generate and communicate auditory nerve spikes. It is fabricated
in a 3-metal, 2-poly, 0.5- m CMOS process with a die size of
2.7 mm by 2 mm. Fig. 5 shows the microphotograph of the chip.
III. M
EASUREMENTS
The cutoff frequencies of our second-order sections can be
tuned to a wide range of frequencies, from 50 Hz to 50 kHz or
higher. For the experiments presented here, we adjusted the bias
voltages so that the first section is most responsive to a 15-kHz
input frequency and the last (32nd) section is most responsive to
300 Hz. The quality factor was set to be close to 0.75 as shown
in the simulations in Fig. 2. The offset current, (
in Fig. 3) as
well as the leakage current at the neuron (
in Fig. 4) were
set to zero. Furthermore,
and (Fig. 3) were both set
to 4.5 V, resulting in a low-pass filter gain of 1. These settings
were chosen to simplify the interpretation of the measurement
results.
In biology, the spike rate on the auditory nerve is limited to
about 100 spikes per second, but a number of nerve fibres orig-
inate from the same IHC and many IHCs code for a similar