Download Can Biology Inspire Better Circuit Design? Soumyajit Mandal

Can Biology Inspire Better Circuit Design?
The RF Cochlea as a Case Study
Soumyajit Mandal
[email protected]
Overview
ƒ
ƒ
ƒ
ƒ
Introduction
Biologically-inspired systems
The RF cochlea
Conclusion
Motivations
ƒ Emulation: Biology solves problems that computers have
difficulty with
ƒ Adaptation
ƒ Pattern recognition
ƒ Low-power, real time computation
ƒ Computation: Biological models can be simulated faster in
hardware
Challenges
ƒ Modeling challenges
ƒ Parameter values hard to obtain
ƒ Fidelity hard to verify
ƒ Figuring out reasonable simplifications is hard
ƒ As computational media, biology and silicon are very different
ƒ Neuronal networks are 3D, silicon is planar
ƒ Neural networks are hybrid state machines
The human auditory periphery
Biological cochlea numbers
Dynamic range
Power dissipation
120 dB at input
~14μW (estimated)
Power supply voltage
Volume
Detection threshold at 3 kHz
Frequency range
Outlet taps
Filter bandwidths
Phase locking threshold
~150 mV
~35mm x 1cm x 1 cm
0.05 Å at eardrum
20 Hz – 20 kHz
~35,000
~1/3 Octave
~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
ƒ Biology has evolved a broadband spectrum analyzer with
ƒ Extremely low power consumption
ƒ High dynamic range
ƒ High resolution (~1Hz around 2KHz)
ƒ Binaural hearing allows
ƒ Precise arrival time discrimination (to within 10μs)
ƒ Spatial localization of sound sources
Conventional spectrum analyzers
ƒ Essentially a swept-tuned superheterodyne receiver
ƒ IF filter sets resolution bandwidth (RBW)
ƒ Sweep time proportional to 1/(RBW)2
ƒ Trade-off between speed and precision
ƒ Substantial speedup by using an FFT (instead of an analog IF filter) for
small resolution bandwidths
Spectrum analyzers: prior engineering versus
biology
ƒ 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
ƒ 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
ƒ 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
ƒ 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
ƒ The cochlea is a long fluid-filled tube separated into three parts by two
membranes
ƒ Human cochleas are about 3.5mm long
ƒ Coiled into 3.5 turns to save space
ƒ 1mm in diameter
ƒ Oval and round windows couple sound in and out
ƒ Fluid – membrane interactions set up traveling wave from base to apex
Cross-section of the cochlea
ƒ Cochlea powered by ionic
gradient between perilymph and
endolymph
Perilymph
Endolymph
ƒ Provides a quiet power supply
isolated from blood circulation
ƒ Basilar membrane
ƒ Supports traveling wave
ƒ Supports organ of Corti
Perilymph
ƒ Reissner’s membrane has no
mechanical function
ƒ Interface with 25,000 endings of
the auditory (eighth cranial) nerve
Organ of Corti
ƒ Contains mechanisms for
ƒ Signal transduction (inner hair cells)
ƒ Active cochlear amplification (outer hair cells)
ƒ Neural coding of auditory information (spiral ganglion cells)
ƒ Stereocilia (hairs) used for sensing
ƒ Actuation and amplification mechanism unclear
The basilar membrane
ƒ Properties of basilar membrane change (taper) exponentially with position
(from base to apex)
ƒ Width increases (from 50 to 500μm)
ƒ Stiffness decreases
ƒ Hence resonant frequency of the fluid – membrane system also depends
exponentially on position along the cochlea
ƒ Spectral analysis!
Wave motion
Tonotopic map: exponential scaling
Frequency–to–place transform
Cochlear frequency responses
ƒ Frequency responses of live cochleas are sharper & have more gain
ƒ Implies presence of an active cochlear amplifier
ƒ Spatial responses look very similar to frequency responses (frequency-toplace transform)
Gain control
ƒ Strong compressive nonlinearity
present in cochlear response with
sound level
ƒ Effects of compressive gain
control
ƒ Enhanced dynamic range
ƒ Two-tone suppression (masking)
ƒ Models of cochlear damping
versus local signal amplitude |A|
d ( A ) ≡ λ1 + σ 1 ⋅ log A
“log law”
d ( A ) ≡ λ2 + σ 2 ⋅ A
“power of 1 law”
d ( A ) ≡ λ3 + σ 3 ⋅ A
2
“power of 2 law”
Experimental cochlear frequency responses
versus input amplitude (sound pressure
level (SPL) in dB)
Gain control (continued)
ƒ Simple model: feedback loop with
compressive nonlinearity
ƒ Behavior
ƒ Linear at small and large amplitudes
ƒ Strongly compressive in between
Beyond the cochlea
Auditory nerve connections in the cochlea
ƒ 10 nerve endings per inner hair cell
ƒ ~20dB dynamic range in firing rate per
nerve fiber
ƒ Smart neural coding to increase total
output dynamic range
The auditory pathway
Why an RF cochlea?
ƒ Silicon cochleas have been built at audio frequencies, but
operating at RF has several advantages
ƒ Availability of true (passive) inductors at RF frequencies
ƒ Reduced noise
ƒ Improved performance because of new theoretical insights
ƒ Several possible applications
ƒ Fast, wideband real-time spectrum analysis
ƒ Front end for wideband radio receivers
ƒ As a distributed “RF laser”
ƒ Proposed implementation
ƒ Operating frequency range
ƒ 8GHz – 800MHz (bidirectional)
ƒ 6GHz – 450MHz (unidirectional)
ƒ Over 60dB of input dynamic range
Cochlear models
Two dimensional model
One dimensional models
ƒ Fluid mass modeled as network of inductors or resistors
ƒ Basilar membrane modeled by complex impedance
ƒ Simplifications
ƒ 1D models: if a single propagating wave mode is considered
ƒ A cascade of unidirectional filters: if reflected waves are ignored
Bidirectional RF cochlea
RF cochlea chip die photos
Unidirectional
Bidirectional
Spatial responses
0
8 GHz
-10
Output voltage (dB)
-20
-30
1GHz
-40
-50
-60
-70
5
10
15
20
25
30
Stage Number
35
40
45
Two-tone responses
-10
5
-20
10
Stage number
15
-30
20
-40
25
30
-50
35
-60
40
45
-70
20
40
60
80
100
Varying the negative resistance
0
5.3 GHz
3.5 GHz
-10
2.3 GHz
Output voltage (dB)
-20
1.5 GHz
-30
-40
-50
-60
-70
0
10
20
30
Stage number
40
8 GHz
Driving the cochlea unstable
1
25
2
Frequency (GHz)
20
3
15
4
10
5
6
5
7
0
8
0.6
0.65
0.7
0.75
Active element bias (V)
0.8
A video of the RF cochlea in action
Faculty members in related areas
ƒ Harvard-MIT division of Health Sciences and Technology (HST)
ƒ Prof. Dennis Freeman (Cochlear micro-mechanics)
ƒ Profs. Christopher Shera, Bertrand Delgutte and Donald Eddington (Auditory
physics)
ƒ Prof. Roger Mark (Modeling & control of complex physiological systems)
ƒ
ƒ
ƒ
ƒ
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)
ƒ Prof. Scott Manalis (Nanoscale sensing)
ƒ Many others ...
Other info
ƒ Useful classes
ƒ
ƒ
ƒ
ƒ
ƒ
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
ƒ Companies of interest
ƒ Implanted devices: Medtronic, Advanced Bionics
ƒ Biomedical systems: GE, Philips
ƒ 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
Bidirectional Cochlear Model
dP
= − jω L ( x ) ⋅U
dx
dU
P
=−
dx
Z ( jω, x )
P
U
L(x)
Z(jω, x)
– pressure (voltage)
– volume velocity (current)
– liquid mass (inductance)
– Basilar Membrane (BM)
impedance
The definition of the cochlea Transfer Function (TF) is
TF ( jω , x ) ≡
I out ( x )
1 dU
1
P
=−
=
U (0)
U ( 0 ) dx U ( 0 ) Z ( jω , x )
Scaling of the Cochlea
ƒ
The liquid mass, or inductance, L(x) increases exponentially with position x:
L ( x ) = L0 ⋅ e
where
ƒ
ƒ
L0
is the inductance per unit length on the basal end of the cochlea
l
is the cochlea taper coefficient
ωc ( x ) = ωc (0) ⋅ e
The Center Frequency (CF):
where
x/l
ωc (0)
−x/l
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:
ωn ( x, ω ) ≡
ω
ωc ( x )
=
ω
ωc ( 0 ) ⋅ e
−x/l
sn ≡ jωn
WKB Analytical Solution
•
The ODE for the pressure, or voltage, P is
d 2P
2
=
k
( sn ) ⋅ P
2
dsn
•
2
2
l
⋅
ω
0
⋅
L
)
(
N
0
c
≡
k 2 ( sn ) =
sn ⋅ Z ( sn )
sn ⋅ Z n ( sn )
The WKB-approximate solution for the cochlea TF is
( )
sn
⎛
⎞
3/ 2
TF ( sn ) ∝ sn ⋅ k ( sn ) ⋅ exp ⎜ − ∫ k sn′ dsn′ ⎟
⎜
⎟
0
⎝
⎠
•
Ignoring the pre-exponent dependencies,
d
d
log TF (ωn )
k ( jωn ) ≈ −
Phase {TF (ωn )} + j ⋅
dωn
dωn
•
Now, by knowing the experimental cochlea collective response, we can
calculate k(jωn) and snZn(sn), and therefore design the cochlea section
Designing Zn(sn) to be a Rational Function
Want Z n to be a rational function so that it can be easily implemented
The simplest possible rational
function is
sn ⋅ Z n ( sn )
s
(
=
2
n
s + sn
2
n
d = 0.1
μ = 0.76
Q = 3.8
Pole-zero diagram of snZn(sn)
+ 2dsn + 1)
μ
Q
2
+ μ2
We tweak these
parameters to obtain
a desirable cochlea
frequency response
Frequency Response of snZn
ƒ Double zero in snZn close to the jω
axis vital for collective gain
ƒ snZn close to zero for a range of
frequencies around ωn = 1
ƒ Several stages contribute gain
ƒ Real part of Zn < 0 for ωn < 1
ƒ Traveling wave amplitude
increases before CF
ƒ Zn cannot be completely passive
Modified Cochlear Architectures
ƒ Possible modifications
ƒ (a) Reverse the mechanical – to – electrical mapping convention
ƒ (b) Use a low pass to high pass (s → 1/s) transformation
ƒ Problems
ƒ (a) Need to synthesize complex floating, bidirectional impedance
ƒ (b) High frequencies have to travel the whole length of the cochlea
Synthesizing the Cochlear Impedance
k=
M
L1 L2
ƒ Use coupled resonator topology to synthesize Zn
ƒ Suitable for IC implementation
ƒ Computer-based optimization using Mathematica™ used to find
component values
ƒ Single active element required – R1 must be negative
ƒ Additional synthesis constraints
ƒ |k| < 0.8 so that an integrated transformer can be used
ƒ C1 & C2 > Cmin to absorb parasitic capacitances from inductors and resistors
Negative Resistance Circuits
Cross-coupled differential pair
Capacitive source degeneration
Inductive gate degeneration
Coupled inductors
Problem: these circuits cannot synthesize floating negative resistors
Cochlear Transfer Functions
ƒ Input impedance of the cochlea
ƒ Resistive over the operating
frequency range
ƒ Reactive otherwise
ƒ Frequency scaling
ƒ Impedance scaling
Spatial transfer functions
Termination Issues
System eigenvalues with (A) single terminating impedance
(B) distributed terminal layer
ƒ
Instabilities due to reflections from
ƒ Apical termination
ƒ Inter-stage impedance mismatch
ƒ
ƒ
ƒ
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)
Unidirectional Cochlea with Improved Section TF
•
The TF of the n-th section is
⎛ sn
⎞
TFn = exp ⎜ − ∫ k ( s ) ds ⎟
⎜ s
⎟
n
−
1
⎝
⎠
TFn ≈ exp ( − k ( sn ) ⋅ ( sn − sn −1 ) )
1
TFn ≈
1 + k ( sn ) ⋅ ( sn − sn −1 )
•
The TF of the n-th section of the cochlea with Noct sections per octave is
Vout ,n
Vin ,n
1
=
sn ⋅ ( sn + μ )
N ln 2
1+
⋅ 2
N oct sn + 2d (Vout ,n ) ⋅ sn + 1
Unidirectional Cochlea with Improved Section TF
•
The WKB-approximate solution for the cochlea TF is
( )
sn
⎛
⎞
3/ 2
′
′
TF ( sn ) ∝ sn ⋅ k ( sn ) ⋅ exp ⎜ − ∫ k sn dsn ⎟
⎜
⎟
⎝ 0
⎠
•
Ignoring the pre-exponent dependencies,
⎛ sj
⎞
TF ( sn ) = ∏ exp ⎜ − ∫ k ( s ) ds ⎟
⎜ s
⎟
j =1
⎝ j−1
⎠
n
•
Already looks like a cascade of filters,
with the TF of the n-th section being
⎛ sn
⎞
TFn = exp ⎜ − ∫ k ( s ) ds ⎟
⎜ s
⎟
−
1
⎝ n
⎠
Action of a filter cascade
Preliminary specifications for the RF cochlea
Parameter
Unidirectional
Bidirectional
Fabrication technology
UMC 0.13µm CMOS
UMC 0.13µm CMOS
Stages per octave
12 (17 / e-fold)
14 (20 / e-fold)
Number of stages
50
50
Frequency range
7GHz – 400MHz
9GHz – 800MHz
Transfer function Q3dB
~5
15
Transfer function gain
~ 20dB
0dB
Output noise
< 2mVrms
< 300µVrms
Maximum input signal
700mVrms
700mVrms
Input-referred dynamic range
71dB
67dB
Input impedance
50Ω
50Ω
Maximum scan clock speed
10MHz
10MHz
Power consumption
75mA @ 1.0V
120mA @ 1.5V
‘Traditional’ software radio consumes 7W just for a 9-bit, 10GHz ADC
Frequency responses
0
Stage 46
-10
Output voltage (dB)
-20
Stage 6
-30
-40
-50
-60
-70 0
10
Frequency (GHz)
Compression curves
0
fmax
-10
Output voltage (dB)
-20
-30
fmax/1.5
fmax/2.3
fmax/3.5
fmax/5.3
-40
-50
-60
-70
-60
-50
-40
-30
-20
Input power level (dBm)
-10
0
Varying the line loss cancellation
0
3.0 GHz
-10
Output voltage (dB)
-20
1.3 GHz
-30
-40
-50
-60
-70
0
10
20
30
Stage number
40