Adaptive Log Domain Filters
Using Floating Gate Transistors
Dr. Pamela A. Abshire, Eric Liu Wong, Yiming Zhai and Dr. Marc H. Cohen
Introduction
Significance
¾ Adaptive log domain filter with integrated learning rules
for model reference estimation.
¾ First order low pass filter with on-line learning of gain
and time constant implemented by multiple input floating
gate transistors.
¾ Robust learning rules for both gain and time constant
adaptation derived from adaptive dynamical system
theory .
Simulation and Testing
9First integrated Adaptive IIR filter
(a) - (c) input:
9Lyapunov method for adaptation
Mixture of sine waves at
10kHz, 20kHz, 40kHz,
and 80kHz
9 Low power floating gate computation
(d) - (f) input:
Summation of 14 sine
waves, whose frequency
ratio is an irrational
number 2p 5 , spanning
from 5kHz to 97kHz.
Derivation of Learning Rules
Floating Gate Transistors
Lyapunov method
‹ Floating gate surrounded by an
insulator so electrons are prevented
from escaping.
‹ Voltage inputs to a secondary
control gate couple capacitively
into the floating node to modulate
transistor current.
Find a Lyapunov function
which is:
1. Positive definite
2. Negative definite time
derivative
3. Radially unbounded
Conservation of charge gives:
HSPICE simulation of successful adaptation
The different values Vt correspond to It of 40nA from 0-2ms, 80nA from 2-3ms,
20nA from 3-4ms, 160nA from 4-6ms, and 10nA from 6-8ms.
V
Time constant is inverse proportional to It and gain is proportional to e .
In all cases the error converges to zero, and the model closely tracks the plant.
gain
n
VG
k 1
C kV k
CGSVS
CGDVD
CGBVB
Model reference adaptation
CT
n
k 1
CkVk
n
where
CT
CT
k 1
Ck
Circuit Implementation
We choose
What we have
Unknown plant output & adaptive
estimator output
V (e) = - Ae
Minimize the error to ZERO
2
1
We choose the control laws:
First order low pass filter:
Ax1
ABu
x3 x 2
e2 + e2 + e2
2( 1 2 3 )
To get a negative time derivative:
What we want to do
x1
x 2
V (e) = 1
unknown plant
x3 x4 u adaptive estimator
x
e = - e 2 and e = - e Au
2
1x
3
1
3
For current mode filters:
Error system:
Circuit for both plant and filter
Circuit for computing product
of error and derivative
Circuit for computing temporal derivative
x3
e1 = x2 - x1
output error
e2 = x3 - A
(1/time constant) error
e3 = x4 - B
gain error
u
e2 = x3
0
Summary
※ Robust learning rules based on Lyapunov stability.
※ Log domain IIR filters have simulated cutoff frequencies above
100kHz with power consumption of 23uW.
※ Fabricated filters have measured cutoff frequencies above 20kHz
with power consumption of 170uW.
※ Adaptation is currently being tested.
If we only consider the direction
but not the rate of adaptation:
System dynamics:
e1 = x2 - x1
0
A 0
Testing setup
Fabricated chip
Acknowledgements
e3 = x4
e2 µ - e1 x2 and e3 µ - e1
We thank the MOSIS service for providing chip fabrication through their Educational Research Program. We
thank Gert Cauwenberghs for his guidance as advisor at JHU. P.A. is supported by an NSF CAREER
Award(NSF_EIA-0238061).