44
to the amazingly enhanced processing speed in cellular neural networks. Each cell is made
up of a linear capacitor, a non-linear Voltage-controlled current source and a few resistive
linear circuit elements, as shown in Figure 5-2 [104].
Figure
5-2: Basic architecture of CNN cell: the equivalent electrical circuit
In Figure 5-2,
C
is a linear capacitor;
R
and
R
are linear resistors;
I
is an independent
voltage source;
I
and
I
are linear voltage controlled
current sources with the
characteristics
I (i, j; k, l) = A(i, j; k, l)u
and
I (i, j; k, l) = B(i, j; k, l)u
for all
C(i, j)ЄN(i, j);
I
is a piecewise-linear voltage-controlled current source. Applying
Kirchhoff’s Current Law
(KCL) and
Kirchhoff’s Voltage Law
(KVL),
the following state
equation of CNN can be derived.
(5-1)
𝑥̇
,
= −𝑥
,
+
𝐴(𝑖, 𝑗; 𝑘, 𝑙)𝑦
,
+
( , )∈ ( , )
𝐵(𝑖, 𝑗; 𝑘, 𝑙)𝑢
,
+
( , )∈ ( , )
𝐼
Where
x
is the state of the cell C (i,j); A(i,j;k,l) and B(i,j;k,l) are the feedback and control
templates respectively for all cells C(k,l) in the neighborhood N(i,j) of cell C(i,j).
The output equation is given as:
45
(5-2)
y =
1
2
( 𝑥 + 1 − 𝑥 − 1 )
The feedback template (A), the control template (B) and the Bias (I) are all core parts of a
CNN processor concept and contribute to the determination its output for a given input.
