Can Biology Inspire Better Circuit Design? The RF Cochlea as a Case - - PowerPoint PPT Presentation

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 Power dissipation ~14μW (estimated) 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 ITD discrimination at ~10 μs

• 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 10μs) 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 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

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 isolated from blood circulation

• Basilar membrane

Supports traveling wave Supports organ of Corti

• Reissner’s membrane has no

mechanical function

• Interface with 25,000 endings of

the auditory (eighth cranial) nerve

Perilymph Perilymph Endolymph

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 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 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|

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

( )

1 1 log

d A A λ σ ≡ + ⋅

( )

2 2

d A A λ σ ≡ + ⋅

( )

2 3 3

d A A λ σ ≡ + ⋅

“log law” “power of 1 law” “power of 2 law”

Gain control (continued)

• Simple model: feedback loop with

compressive nonlinearity

• Behavior

Linear at small and large amplitudes Strongly compressive in between

Beyond the cochlea

• 10 nerve endings per inner hair cell
• ~20dB dynamic range in firing rate per

nerve fiber

• Smart neural coding to increase total
• utput dynamic range

The auditory pathway Auditory nerve connections in the cochlea

Why an RF cochlea? Silicon cochleas have been built at audio frequencies, but

• perating 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

• 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 One dimensional models Two dimensional model

Bidirectional RF cochlea

RF cochlea chip die photos Unidirectional Bidirectional

Spatial responses

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Stage Number Output voltage (dB) 8 GHz 1GHz

Tw o-tone responses

Stage number 20 40 60 80 100 5 10 15 20 25 30 35 40 45

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Varying the negative resistance

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Stage number Output voltage (dB) 1.5 GHz 2.3 GHz 3.5 GHz 8 GHz 5.3 GHz

Driving the cochlea unstable

Active element bias (V) Frequency (GHz) 0.6 0.65 0.7 0.75 0.8 1 2 3 4 5 6 7 8

5 10 15 20 25

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 5:30-6:30 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 U dx ω = − ⋅

( )

, dU P dx Z j x ω = −

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

1 1 , ,

• ut

I x dU P TF j x U U dx U Z j x ω ω ≡ = − = 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)

c

ω

L

/

( ) (0)

c c

x l

x

e

ω ω

−

= ⋅

( )

/ x l

L L

x e

=

⋅

( ) ( ) ( )

/

,

n x l c c

x x e ω ω ω ω ω ω

−

≡ = ⋅

n n

s jω ≡

WKB Analytical Solution

( ) ( )

( )

3/2

exp

n

s n n n n n

TF s s k s k s ds ⎛ ⎞ ′ ′ ∝ ⋅ ⋅ − ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

∫

• The WKB-approximate solution for the cochlea TF is

( ) ( )

{ }

( )

log

n n n n n

d d k j Phase TF j TF d d ω ω ω ω 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 2 2 n n

d P k s P ds = ⋅

( ) ( ) ( ) ( )

2 2 2 c n n n n n n

l L N k s s Z s s Z s ω ⋅ ⋅ = ≡ ⋅ ⋅

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

Designing Z n(sn) to be a Rational Function The simplest possible rational function is

( )

( )

2 2 2 2

2 1 0.1 0.76 3.8

n n n n n n n

s ds s Z s s s Q 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 jω

axis vital for collective gain

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

• Real part of Zn < 0 for ωn < 1

Traveling wave amplitude increases before CF Zn 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 implementation
• Computer-based optimization using Mathematica™ used to find

component values

• Single active element required – R1 must be negative
• Additional synthesis constraints

|k| < 0.8 so that an integrated transformer can be used C1 & C2 > Cmin to absorb parasitic capacitances from inductors and resistors

1 2

M k L L =

Negative Resistance Circuits

Cross-coupled differential pair Inductive gate degeneration Coupled inductors Capacitive source degeneration

Problem: these circuits cannot synthesize floating negative resistors

Cochlear Transfer Functions

• Input impedance of the cochlea

Resistive over the operating frequency range Reactive otherwise

• Frequency scaling
• Impedance scaling

Spatial transfer functions

Termination Issues

• Instabilities due to reflections from
• Apical termination
• Inter-stage impedance mismatch
• Causes spontaneous oto-acoustic emissions (SPOAE’s) in biological cochleas
• Similar to how a laser works
• Reduce apical reflections by using a perfectly matched terminating layer (PML)

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

Unidirectional Cochlea w ith Improved Section TF

( ) ( ) ( )

( )

( ) ( )

1

1 1

exp exp 1 1

n n

s n s n n n n n n n n

TF k s ds TF k s s s TF k 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 ,

1 ln 2 1 2 1

• ut n

n n in n

• ct

n

• ut n

n

V s s V N N s d V s μ = ⋅ + + ⋅ + ⋅ +

Unidirectional Cochlea w ith Improved Section TF

( ) ( )

( )

3/2

exp

n

s n n n n n

TF s s k s k s ds ⎛ ⎞ ′ ′ ∝ ⋅ ⋅ − ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

∫

( ) ( )

1

1

exp

j j

s n n j s

TF s k s ds

−

=

⎛ ⎞ ⎜ ⎟ = − ⎜ ⎟ ⎝ ⎠

∏ ∫

( )

1

exp

n n

s n s

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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Frequency (GHz) Output voltage (dB) Stage 46 Stage 6

Compression curves

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Input power level (dBm) Output voltage (dB) fmax fmax/1.5 fmax/2.3 fmax/3.5 fmax/5.3

Varying the line loss cancellation

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Stage number Output voltage (dB) 3.0 GHz 1.3 GHz