Can Biology Inspire Better Circuit Design? The RF Cochlea as a Case Study Soumyajit Mandal soumya@mit.edu
Overview � Introduction � Biologically-inspired systems � The RF cochlea � Conclusion
Motivations � Emulation: Biology solves problems that computers have difficulty with � Adaptation � Pattern recognition � Low-power, real time computation � Computation: Biological models can be simulated faster in hardware
Challenges � Modeling challenges � Parameter values hard to obtain � Fidelity hard to verify � Figuring out reasonable simplifications is hard � As computational media, biology and silicon are very different � Neuronal networks are 3D, silicon is planar � Neural networks are hybrid state machines
The human auditory periphery
Biological cochlea numbers Dynamic range 120 dB at input ~14 μ W (estimated) Power dissipation Power supply voltage ~150 mV Volume ~35mm x 1cm x 1 cm Detection threshold at 3 kHz 0.05 Å at eardrum Frequency range 20 Hz – 20 kHz Outlet taps ~35,000 Filter bandwidths ~1/3 Octave Phase locking threshold ~5 kHz Information is reported with enough fidelity so that the auditory system has thresholds for ~10 μ s ITD discrimination at Freq. discrimination at 2 Hz (at 1kHz) Loudness discrimination ~1 dB
The bottom line � Biology has evolved a broadband spectrum analyzer with � Extremely low power consumption � High dynamic range � High resolution (~1Hz around 2KHz) � Binaural hearing allows � Precise arrival time discrimination (to within 10 μ s) � Spatial localization of sound sources
Conventional spectrum analyzers Essentially a swept-tuned superheterodyne receiver � IF filter sets resolution bandwidth (RBW) � Sweep time proportional to 1/(RBW) 2 � � Trade-off between speed and precision Substantial speedup by using an FFT (instead of an analog IF filter) for � small resolution bandwidths
Spectrum analyzers: prior engineering versus biology Trade-off between speed, precision (number of bins N ) and � hardware complexity Topology Acquisition time Hardware Real time? complexity FFT O( N log(N)) O( N log(N) ) No Swept-sine O( N 2 ) O(1) No Analog filter bank O( N ) O( N 2 ) Yes Cochlea O( N ) O( N ) Yes The cochlea is an ultra-wideband spectrum analyzer with extremely fast scan time, low hardware complexity and power consumption, and moderate frequency resolution
Example 1: a silicon cochlea An analog electronic cochlea , Lyon, R.F.; Mead, C.; � Acoustics, Speech, and Signal Processing, IEEE Transactions on, Volume 36, Issue 7, July 1988 Page(s):1119 - 1134
The mammalian retina
Example 2: a silicon retina Silicon retina with correlation-based, velocity-tuned pixels , Delbruck, � T.; Neural Networks, IEEE Transactions on, Volume 4, Issue 3, May 1993 Page(s):529 - 541
Example 3: a silicon muscle fiber An analog VLSI model of muscular contraction , Hudson, T.A.; Bragg, � J.A.; Hasler, P.; DeWeerth, S.P.; Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on , Volume 50, Issue 7, July 2003 Page(s):329 - 342
Example 3: a silicon muscle fiber
The human auditory periphery
Structure of the cochlea The cochlea is a long fluid-filled tube separated into three parts by two � membranes Human cochleas are about 3.5mm long � � Coiled into 3.5 turns to save space � 1mm in diameter Oval and round windows couple sound in and out � Fluid – membrane interactions set up traveling wave from base to apex �
Cross-section of the cochlea Cochlea powered by ionic � gradient between perilymph and endolymph � Provides a quiet power supply Perilymph isolated from blood circulation Basilar membrane � Endolymph � Supports traveling wave � Supports organ of Corti Reissner’s membrane has no � mechanical function Perilymph Interface with 25,000 endings of � the auditory (eighth cranial) nerve
Organ of Corti Contains mechanisms for � � Signal transduction (inner hair cells) � Active cochlear amplification (outer hair cells) � Neural coding of auditory information (spiral ganglion cells) Stereocilia (hairs) used for sensing � Actuation and amplification mechanism unclear �
The basilar membrane Properties of basilar membrane change (taper) exponentially with position � (from base to apex) � Width increases (from 50 to 500 μ m) � Stiffness decreases Hence resonant frequency of the fluid – membrane system also depends � exponentially on position along the cochlea � Spectral analysis!
Wave motion
Frequency–to–place transform Tonotopic map: exponential scaling
Cochlear frequency responses Frequency responses of live cochleas are sharper & have more gain � Implies presence of an active cochlear amplifier � Spatial responses look very similar to frequency responses (frequency-to- � place transform)
Gain control Strong compressive nonlinearity � present in cochlear response with sound level Effects of compressive gain � control � Enhanced dynamic range � Two-tone suppression (masking) Models of cochlear damping � versus local signal amplitude |A| ( ) ≡ λ + σ ⋅ “log law” d A A 1 log 1 Experimental cochlear frequency responses ( ) ≡ λ + σ ⋅ versus input amplitude (sound pressure d A A “power of 1 law” 2 2 level (SPL) in dB) ( ) ≡ λ + σ ⋅ 2 “power of 2 law” d A A 3 3
Gain control (continued) Simple model: feedback loop with � compressive nonlinearity Behavior � � Linear at small and large amplitudes � Strongly compressive in between
Beyond the cochlea Auditory nerve connections in the cochlea 10 nerve endings per inner hair cell � ~20dB dynamic range in firing rate per � nerve fiber The auditory pathway Smart neural coding to increase total � output dynamic range
Why an RF cochlea? � Silicon cochleas have been built at audio frequencies, but operating at RF has several advantages � Availability of true (passive) inductors at RF frequencies � Reduced noise � Improved performance because of new theoretical insights � Several possible applications � Fast, wideband real-time spectrum analysis � Front end for wideband radio receivers � As a distributed “RF laser” � Proposed implementation � Operating frequency range � 8GHz – 800MHz (bidirectional) � 6GHz – 450MHz (unidirectional) � Over 60dB of input dynamic range
Cochlear models Two dimensional model One dimensional models Fluid mass modeled as network of inductors or resistors � Basilar membrane modeled by complex impedance � Simplifications � � 1D models: if a single propagating wave mode is considered � A cascade of unidirectional filters: if reflected waves are ignored
Bidirectional RF cochlea
RF cochlea chip die photos Unidirectional Bidirectional
8 GHz 45 40 35 30 Stage Number 25 20 15 10 Spatial responses 1GHz 5 0 -10 -20 -30 -40 -50 -60 -70 Output voltage (dB)
-10 -20 -30 -40 -50 -60 -70 100 80 60 40 Tw o-tone responses 20 5 10 15 20 25 30 35 40 45 Stage number
Varying the negative resistance 0 8 GHz 5.3 GHz 3.5 GHz -10 2.3 GHz -20 1.5 GHz Output voltage (dB) -30 -40 -50 -60 -70 0 10 20 30 40 Stage number
25 20 15 10 5 0 0.8 0.75 Active element bias (V) Driving the cochlea unstable 0.7 0.65 0.6 1 2 3 4 5 6 7 8 Frequency (GHz)
A video of the RF cochlea in action
Faculty members in related areas Harvard-MIT division of Health Sciences and Technology (HST) � � Prof. Dennis Freeman (Cochlear micro-mechanics) � Profs. Christopher Shera, Bertrand Delgutte and Donald Eddington (Auditory physics) � Prof. Roger Mark (Modeling & control of complex physiological systems) Profs. Joel Voldman & Jongyoon Han (BioMEMS) � Prof. Rahul Sarpeshkar (Analog VLSI and biological systems) � Prof. Joel Dawson (Biomedical circuits and systems) � Prof. George Verghese (Modeling and control of complex physiological � systems) Prof. Scott Manalis (Nanoscale sensing) � Many others ... �
Other info � Useful classes � Circuit design: 6.101, 6.301, 6.331, 6.374, 6.376, 6.775, 6.776 � Control systems: 6.011, 6.302, 6.241 � Bioelectronics: 6.021J, 6.022J, 6.023J, 6.024J, 6.121 � MEMS: 6.777 � Biomedical systems: 6.971 � Companies of interest � Implanted devices: Medtronic, Advanced Bionics � Biomedical systems: GE, Philips � Many others!
Computational Intelligence for Understanding Earth Systems Sai Ravela, MIT EAPS Tuesday, Dec. 4 Room 34-401A 5:30-6:30 PM (dinner to follow)
Backup slides
Cochlear models
Bidirectional Cochlear Model dP ( ) = − ω ⋅ – pressure (voltage) P j L x U – volume velocity (current) dx U – liquid mass (inductance) L(x) dU P Z(j ω , x) – Basilar Membrane (BM) = − impedance ( ) ω dx Z j x , The definition of the cochlea Transfer Function (TF) is ( ) I x dU P 1 1 ( ) ω ≡ = − = out TF j x , ( ) ( ) ( ) ( ) ω U U dx U Z j x 0 0 0 ,
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