Design and Simulation of Discrete-Time Cellular Neural Network by

haremboingAI and Robotics

Oct 20, 2013 (4 years and 2 months ago)

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D
e
sign and Simulation of Discrete
-
Time Cellular Neural Network

by

N
egative
D
ifferential

R
esistance

Devices


Yaw
-
Hwang Chen,
Long
-
Xian Su
,

Kwang
-
Jow Gan,

Cher
-
Shiung Tsai, Dong
-
Shong Liang,
Chi
-
Pin
Chen
,
溫俊明
and
塗俊達


Department of Electronic Engineering, Kun

Shan University of Technology

(NSC93
-
2215
-
E
-
168
-
002)

Abstract

Resonant tunneling diodes(RTD

s) have found
various application in high
-
speed digital and
analog circuits due to their
specific

advantages
associated with the unique folded
-
back
negative diffe
rential resistance (NDR) I
-
V
characteristics.

In this paper we
realize
d negative differential
resistance (NDR) I
-
V curve of RTD by
n
egative
d
iff
e
rential

r
esistance

d
evices
.

The
NDR device is composed of
metal
-
oxide

semiconductor

field
-
effect

transistor (MO
S)
devices
.

The discrete
-
time cellular neural
network cell is composed of NDR devices.
Therefore, the DT
-
CNN can be fabricated by
standard CMOS process.

I.

Introduction

The
cellular
n
eural
n
e
t
work
s wer
e invented by
Chua and Yang in

1988. It is in order to sol
ve
real
-
world problems in image processing,
robotics, motion video and many other
complex computational problems.
Th
er
efore

evokes the widespread discussion

and there
have been
documented

in the first two
IEEE International Workshops on C
ell
ular

N
eural
N
etwork
s and their Application in
1992, while retained the two basic concepts of
local connectedness and analog circuit
dynamics.

Definition: The CNN is a

i)


2
-
, 3
-
, or n
-
dimensional array of

ii)

mainly identical dynamical systems,
called cells, which satisfies
two properties:

iii)

most interactions are local with a finite
radius
r

,and

iv)

all state variables are continuous valued
signals.

A typical example of a cell

of a
c
ellular

n
eural

n
etwork
s is shown in figure 1,
where the suffices
u, x
,

a
nd
y

denote the
input, state, and output respectively.
Therefore

node voltage
,
and

are defined input, state, and output voltage
respectively.



is a linear capacit
or;

and

are
linear resistors;
I

is an independent current
source;


and


are
linear voltage
controlled

current sources
with the characteristics
which


=

(1)

and


=
.
(2)


(3)

is a piecewise
-
linear voltage controlled
current source;

is

a time
-
invariant
independent voltage source.

The circuit equations of a cell which satisfy
KCL and KVL are easily derived as follow:

State equation

is


(4)

Where
and

are the
non
linear cloning templates.

Output equation is


(5)

Input equation is


(6)

Constraint conditions

are

. (7)

Parameter assumptions are


(8)

where
,

and

i
s the neighbor set of
.



Fig.1. It

is an example of a cell circuit.


II. The
Λ
-
type

NDR Device


A
Λ
-
type MOS
-
NDR device is composed of
t
hree NMOS

transistors.

This circuit is shown
in figure 2.
In the region 2, V
DS

exceeds the
threshold voltage of Q
3

and Q
3

changes from
cutoff state to saturation state. In the
meanwhile, V
GS

will g
o down and current
from

drain to source of Q
2

also goes down.
This is the
reas
on why there is a
negative
differential resistance

in the region 2.





Fig.
2.
A
Λ
-
type

NDR device circuit

is
composed of three NMOS
.


The
Λ
-
type I
-
V characteristics and the

operation point

are shown in figure
3 and
table1 of each transistor.







Fig.3.
It

is the

I
-
V curve of
Λ
-
type
.

Table 1. This table

shows the operating point
V
DS

Q
1

Q
2

Q
3

V
DS

< V
T

Saturation

Linear

Cut
-
off

V
DS
= V
GS
+V
T

Saturation

Linear→

Saturation

Saturation

V
GS
≤V
DS
+V
T


Saturation

Linear

Saturation

I

V




(1)

(2)

(3)

of each transistor for a
NDR device
.

III. The Inverter based on
Λ
-
type

NDR Device

T
he inverter
is constructed by

a N
MOS

device
and

a MOS
-
NDR device which are
connected parallel
. T
he total current I
total

is
the sum of the currents flowed through
the
MOS
-
NDR and NMOS devices

: I
total

=

I
NDR

+

I
MOS
.

Since I
MOS

can be

modulated by the gate
voltage

(V
G
),

so is

I
t
otal
, as show in figure

4.



Fig.4. The peak current of
Λ
-
type MOS
-
NDR

de
vice can be controlled by the V
G

voltage.


Our inverter circuit design is based on
two

series
-
connected MOS
-
NDR devices
as
shown in figure

5.

This circuit is so called the
monostable
-
bistable transition logic element

(MOBILE)
. The input node is located
at the
V
G

gate. The output node is located between
the two MOS
-
NDR devices. When
the bias
V
S

is bigger than

twice peak voltage (
2V
P
), but is
smaller than twice valley voltage (2V
V
), there
is two possible stable points (
bistable
) that
respect the low a
nd high states (corresponding
to

0


and

1

), respectively.
A small
difference between the peak currents of the

series
-
connected

NDR devices det
ermines the
state
which the circuit will stay stably
. By
suitably determining the parameters of
devices and
cir
cuits
, figure 6 shows the
simulated results for the inverter.


Fig. 5. I
nverter circuit design based on the
MOBILE.



Fig. 6. These are the simulated results for the
inverter.


IV. The MOBILE CNN

T
he cell circuit configuration of a DT
-
CNN
implemented

with MOBILE

s. Here, the cell
with positive feedback and an inverting
MOBILE at the output is show in Fig 7.The
state of MOBILE are clocked with the V
A
clock, the states of inverter are clocked with
the V
B

clock. V
A
and V
B
are
complementary

clocks. Hence,

the output A is
complementary

with output B. The cell outputs with clock are
on the control. Since output values can be
latched when clock is high and is changeable
when clock is low. The cell circuit is
con
trol
led and driven by input
, self
-
feedback
and c
lock. The cell can adjust branch in
parallel with the load
ing

MOS
-
NDR to
generate different outputs. The simulating
results of
the DT
-
CNN are shown in the
figure
8.

We can see the outputs of cells will
remain stably only within a few iterative
process. The

cell of DT
-
CNN based on

MOS
-

NDR device is as good as RTD
-
based cell. It
a
lso can be manufa
ctured by stand CMOS
process.






















Fig.7 It

is the circuit
al

configuration of
DT
-
CNN implemented with MOBILE

s. A
cell
consist
s with positive feedback and
inverting MOBILE at the output.



Fig
. 8.
These are simulating results for the
DT
-
CNN. The traces show the time
evaluation of the output voltage

of the cells.
The evaluation of the cell

s states was
illustrated schematically in the upper inset.
Here, the black pixels indicate
d

cell state is 1
and white pixels indicate
d

cell state is 0.


V. Conclusions

We have designed a d
iscrete
-
t
ime
c
ellular

n
eural

n
et
work

(DT
-
CNN) based on the
Λ
-
type
NDR
-
based devices and circuits
according to the standard 0.35
μm
CMOS
process.
The I
-
V characteristics of the

NDR
device could be controlled by the V
g

voltage.
Hence, it is eas
ier to control than RTD
DT
-
CNN.



References

1. L.O.

Chua and L.

Yang

,

Cellular Neural
Networks

Theory

,
IEEE Transactions on
circuit
s and systems, vol.35, no.10, pp.1257
-
1272, October
1988.

2. L.
O. Chua and Patrick Thiran,

An Analytic
Method for Design Simple Cellular Neural
Networks

, IE
EE Transactions on circuits and

systems,
vol.38, no.11, pp. 1332
-

1341,
November

1991

3. L.O. Chua and T. Roska,

The CNN
Paradigm

, IEEE Transactions on circuits and
systems
-
I: Fundamental Theory
and Application
,
vol.40, no.3, March 1993.

4. L.
O. Ch
ua,

Simplicial RTD
-
Based Cellular
Nonlinear Networks

, IEEE Transactions on
circuits and systems
-
I: Fundamental Theory and
Application, vol.50, no.4, April 2003.

5.
T. K. Liang, S. Y. Wang, K. J. Gan, C. S. Tsai,
C. C. Hsiao and F. C. Chiang,


Design and
O


O
u
t
p
u
t
A

o u t p u t B


V
A

V
B

o u t p u t A

V
A

I
n p u t f r o m

t h e n e i g h b o r i n g
ce
lls

Simulation of Voltage Controlled Oscillator
With High Frequency by Differential Resistance
Devices and Integrated Circuits

, ASTC, 2004.

6. K.

Maezawa, T.

Akeyoshi and T. Mizutani,

Function and Application of Monostable

-
Bistable Transition Log
ic Elements
(MOBILEs) Having Multiple
-
Inputer
Terminals

, IEEE Transactions on Electron
Devices, vol.

41, no.

2, February 1994.