Can Biology Inspire Better Circuit Design? The RF Cochlea as a Case Study

Soumyajit Mandalsoumya@mit.edu

Overview

IntroductionBiologically-inspired systemsThe RF cochleaConclusion

Motivations

Emulation: Biology solves problems that computers have difficulty with

AdaptationPattern recognitionLow-power, real time computation

Computation: Biological models can be simulated faster in hardware

Challenges

Modeling challengesParameter values hard to obtainFidelity hard to verifyFiguring out reasonable simplifications is hard

As computational media, biology and silicon are very differentNeuronal networks are 3D, silicon is planarNeural networks are hybrid state machines

The human auditory periphery

Biological cochlea numbers

Dynamic range 120 dB at inputPower dissipation ~14μW (estimated)

Power supply voltage ~150 mVVolume ~35mm x 1cm x 1 cmDetection threshold at 3 kHz 0.05 Å at eardrumFrequency range 20 Hz – 20 kHzOutlet taps ~35,000Filter bandwidths ~1/3 OctavePhase locking threshold ~5 kHz

Information is reported with enough fidelity so that the auditory system has thresholds forITD discrimination at ~10 μsFreq. discrimination at 2 Hz (at 1kHz)Loudness discrimination ~1 dB

The bottom line

Biology has evolved a broadband spectrum analyzer withExtremely low power consumptionHigh dynamic rangeHigh resolution (~1Hz around 2KHz)

Binaural hearing allowsPrecise arrival time discrimination (to within 10μs)Spatial localization of sound sources

Conventional spectrum analyzers

Essentially a swept-tuned superheterodyne receiverIF filter sets resolution bandwidth (RBW)Sweep time proportional to 1/(RBW)2

Trade-off between speed and precisionSubstantial 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 complexity

Real time?

FFT O(N log(N)) O(N log(N)) No

Swept-sine O(N2) O(1) No

Analog filter bank O(N) O(N2) 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 membranesHuman cochleas are about 3.5mm long

Coiled into 3.5 turns to save space1mm in diameter

Oval and round windows couple sound in and outFluid – 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 isolated from blood circulation

Basilar membrane Supports traveling waveSupports organ of Corti

Reissner’s membrane has no mechanical functionInterface with 25,000 endings of the auditory (eighth cranial) nerve

Perilymph

Perilymph

Endolymph

Organ of Corti

Contains mechanisms forSignal transduction (inner hair cells)Active cochlear amplification (outer hair cells)Neural coding of auditory information (spiral ganglion cells)

Stereocilia (hairs) used for sensingActuation 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 500μm)Stiffness decreases

Hence resonant frequency of the fluid – membrane system also depends exponentially on position along the cochlea

Spectral analysis!

Wave motion

Tonotopic map: exponential scaling

Frequency–to–place transform

Cochlear frequency responses

Frequency responses of live cochleas are sharper & have more gain Implies presence of an active cochlear amplifierSpatial responses look very similar to frequency responses (frequency-to-place transform)

Gain control

Strong compressive nonlinearity present in cochlear response with sound levelEffects of compressive gain control

Enhanced dynamic rangeTwo-tone suppression (masking)

Models of cochlear damping versus local signal amplitude |A|

Experimental cochlear frequency responses versus input amplitude (sound pressure level (SPL) in dB)

( ) 1 1 logd A Aλ σ≡ + ⋅

( ) 2 2d A Aλ σ≡ + ⋅

( ) 23 3d A Aλ σ≡ + ⋅

“log law”

“power of 1 law”

“power of 2 law”

Gain control (continued)

Simple model: feedback loop with compressive nonlinearityBehavior

Linear at small and large amplitudesStrongly compressive in between

Beyond the cochlea

10 nerve endings per inner hair cell~20dB dynamic range in firing rate per nerve fiberSmart neural coding to increase total output dynamic range

The auditory pathway

Auditory nerve connections in the cochlea

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 frequenciesReduced noise

Improved performance because of new theoretical insightsSeveral possible applications

Fast, wideband real-time spectrum analysisFront end for wideband radio receiversAs a distributed “RF laser”

Proposed implementationOperating frequency range

8GHz – 800MHz (bidirectional)6GHz – 450MHz (unidirectional)

Over 60dB of input dynamic range

Cochlear models

Fluid mass modeled as network of inductors or resistorsBasilar membrane modeled by complex impedanceSimplifications

1D models: if a single propagating wave mode is considered A cascade of unidirectional filters: if reflected waves are ignored

One dimensional models

Two dimensional model

Bidirectional RF cochlea

RF cochlea chip die photos

Unidirectional

Bidirectional

Spatial responses

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Two-tone responses

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Varying the negative resistance

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2.3 GHz3.5 GHz

8 GHz5.3 GHz

Driving the cochlea unstable

Active element bias (V)

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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 classesCircuit design: 6.101, 6.301, 6.331, 6.374, 6.376, 6.775, 6.776Control systems: 6.011, 6.302, 6.241Bioelectronics: 6.021J, 6.022J, 6.023J, 6.024J, 6.121MEMS: 6.777Biomedical systems: 6.971

Companies of interestImplanted devices: Medtronic, Advanced BionicsBiomedical systems: GE, PhilipsMany others!

Computational Intelligence for Understanding Earth SystemsSai Ravela, MIT EAPS

Tuesday, Dec. 45:30-6:30 PM

Room 34-401A(dinner to follow)

Backup slides

Cochlear models

The definition of the cochlea Transfer Function (TF) is

Bidirectional Cochlear Model

( )dP j L x Udx

ω= − ⋅

( ),dU Pdx Z j xω

= −

( ) ( )( ) ( ) ( ) ( )

1 1,0 0 0 ,

outI x dU PTF j xU U dx U Z j x

ωω

≡ = − =

P – pressure (voltage)U – volume velocity (current)L(x) – liquid mass (inductance)Z(jω, x) – Basilar Membrane (BM)

impedance

The Center Frequency (CF):

where is the CF on the basal end of the cochlea

In the real cochlea the BM impedance Z(jω,x) as well as U, P and TF depend only on the following combination of x and ω:

where is the inductance per unit length on the basal end of the cochlea

is the cochlea taper coefficient

The liquid mass, or inductance, L(x) increases exponentially with position x:

Scaling of the Cochlea

l

(0)cω

0L

/( ) (0)c c

x lx eω ω −= ⋅

( ) 0

/x lL Lx e= ⋅

( ) ( ) ( ) /,0n x l

c c

xx e

ω ωω ωω ω −≡ =

⋅ n ns jω≡

WKB Analytical Solution

( ) ( ) ( )3/ 2

0

expns

n n n n nTF s s k s k s ds⎛ ⎞

′ ′∝ ⋅ ⋅ −⎜ ⎟⎜ ⎟⎝ ⎠∫

• The WKB-approximate solution for the cochlea TF is

( ) ( ) ( )logn n nn n

d dk j Phase TF j TFd d

ω ω ωω ω

≈ − + ⋅

• Ignoring the pre-exponent dependencies,

• Now, by knowing the experimental cochlea collective response, we can calculate k(jωn) and snZn(sn), and therefore design the cochlea section

( )2

22 nn

d P k s Pds

= ⋅ ( ) ( )( ) ( )

2 202 0c

nn n n n n

l L Nk ss Z s s Z sω⋅ ⋅

= ≡⋅ ⋅

• The ODE for the pressure, or voltage, P is

Designing Zn(sn) to be a Rational Function

The simplest possible rational function is

( ) ( )22

2 2

2 1

0.10.763.8

n nn n n

n n

s dss Z s

s sQ

d

Q

μ μ

μ

+ +⋅ =

+ +

===

We tweak these parameters to obtain a desirable cochlea frequency response

Pole-zero diagram of snZn(sn)

Want Z n to be a rational function so that it can be easily implemented

Frequency Response of snZn

Double zero in snZn close to the jωaxis vital for collective gain

snZn close to zero for a range of frequencies around ωn = 1Several stages contribute gain

Real part of Zn < 0 for ωn < 1 Traveling wave amplitude increases before CFZn cannot be completely passive

Modified Cochlear Architectures

Possible modifications(a) Reverse the mechanical – to – electrical mapping convention(b) Use a low pass to high pass (s → 1/s) transformation

Problems(a) Need to synthesize complex floating, bidirectional impedance(b) High frequencies have to travel the whole length of the cochlea

Synthesizing the Cochlear Impedance

Use coupled resonator topology to synthesize Zn

Suitable for IC implementationComputer-based optimization using Mathematica™ used to find component valuesSingle active element required – R1 must be negativeAdditional synthesis constraints

|k| < 0.8 so that an integrated transformer can be usedC1 & C2 > Cmin to absorb parasitic capacitances from inductors and resistors

1 2

MkL L

=

Negative Resistance CircuitsCross-coupled differential pair Inductive gate degeneration

Coupled inductorsCapacitive source degeneration

Problem: these circuits cannot synthesize floating negative resistors

Cochlear Transfer Functions

Input impedance of the cochleaResistive over the operating frequency rangeReactive otherwise

Frequency scaling

Impedance scaling

Spatial transfer functions

Termination Issues

Instabilities due to reflections from Apical terminationInter-stage impedance mismatch

Causes spontaneous oto-acoustic emissions (SPOAE’s) in biological cochleasSimilar to how a laser worksReduce apical reflections by using a perfectly matched terminating layer (PML)

System eigenvalues with (A) single terminating impedance (B) distributed terminal layer

Unidirectional Cochlea with Improved Section TF

( )

( ) ( )( )

( ) ( )

1

1

1

exp

exp

11

n

n

s

ns

n n n n

nn n n

TF k s ds

TF k s s s

TFk s s s

−

−

−

⎛ ⎞= −⎜ ⎟⎜ ⎟

⎝ ⎠≈ − ⋅ −

≈+ ⋅ −

∫

• The TF of the n-th section is

• The TF of the n-th section of the cochlea with Noct sections per octave is

( )( )

,

,2

,

1ln 21

2 1

out n

n nin n

oct n out n n

Vs sV N

N s d V sμ

=⋅ +

+ ⋅+ ⋅ +

Unidirectional Cochlea with Improved Section TF

( ) ( ) ( )3/ 2

0

expns

n n n n nTF s s k s k s ds⎛ ⎞

′ ′∝ ⋅ ⋅ −⎜ ⎟⎜ ⎟⎝ ⎠∫

( ) ( )11

expj

j

sn

nj s

TF s k s ds−

=

⎛ ⎞⎜ ⎟= −⎜ ⎟⎝ ⎠

∏ ∫

( )1

expn

n

s

ns

TF k s ds−

⎛ ⎞= −⎜ ⎟⎜ ⎟

⎝ ⎠∫

• Ignoring the pre-exponent dependencies,

• Already looks like a cascade of filters, with the TF of the n-th section being

• The WKB-approximate solution for the cochlea TF is

Action of a filter cascade

Preliminary specifications for the RF cochlea

Parameter Unidirectional Bidirectional

Fabrication technology UMC 0.13µm CMOS UMC 0.13µm CMOS

Maximum input signal 700mVrms 700mVrms

12 (17 / e-fold)

50

7GHz – 400MHz

~ 5

~ 20dB

< 2mVrms

71dB

Input impedance 50Ω 50Ω

Maximum scan clock speed 10MHz 10MHz

75mA @ 1.0V

Stages per octave 14 (20 / e-fold)

Number of stages 50

Frequency range 9GHz – 800MHz

Transfer function Q3dB 15

Transfer function gain 0dB

Output noise < 300µVrms

Input-referred dynamic range 67dB

Power consumption 120mA @ 1.5V

‘Traditional’ software radio consumes 7W just for a 9-bit, 10GHz ADC

Frequency responses

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Compression curves

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fmax

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fmax/5.3

Varying the line loss cancellation

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