Hardware Reference
In-Depth Information
For a sequence of electrodes E
Df
e
1
;e
2
;:::;e
n
g
, control pin mapping can
be written as
Pin
.E/
Df
p
.1/
;p
.2/
;:::;p
.n/
g
,wherep
.k/
is the pin that is
connected to electrode e
k
.
Pin
.E/ is defined as a control pin assignment sequence.
In [
53
], the researchers found that the unwanted movement/spliting of droplets
can be avoided if the pin assignment sequence P
Df
p
1
;p
2
;:::;p
n
g
satisfies the
following constraints:
Constraint 1:
8
p
i
2
P
and
8
p
j
2
P
where
p
i
D
p
j
and
i
¤
j
,
j
j
i
j
3
.
Constraint 2:
8
p
i
2
P
and
8
p
j
2
P
,if
p
i
D
p
j
and
i
¤
j
,
f
p
i 1
;p
i C1
g\
f
p
j 1
;p
j C1
gD;
.
Based on the above constraints, the pin assignment configurations can be
determined. It is
al
so
pr
oven t
h
at an m
n pin-constrained cross-referencing biochip
requires only
p
2.
p
m
C
p
n/ pins. In [
53
], a droplet routing method for cross-
referencing biochips also was developed to maximize the degree of parallelism for
fluidic operations. Even though the cross-referencing design of biochips can reduce
the number of control pins, it results in increased fabrication cost since both the top
and bottom plates of the cross-referencing biochip contain electrode rows/columns.
For a low-cost biochip that contains a discrete array of electrodes on the bottom
plate, an alternative method to reduce the number of control pins is to connect
multiple electrodes on the bottom plate directly to the same control pin. In [
54
],
the researchers used a combinational logic circuit to generate control signals for the
biochip, and thus the number of control pins was reduced significantly. The concept
of a biochip with a logic control circuit is illustrated in the following example.
Let us assume that we have a 3
3 electrode array, and the electrodes are written
as E
1
, E
2
, ..., E
9
. Figure
1.16
a shows the actuation signals that are to be applied
on these electrodes, with “1”, “0”, and “*” representing “activated”, “deactivated”,
or “don't care” status of an electrode at a specific time, respectively. Electrodes that
possess compatible actuation sequences can be assigned to the same control pin.
In this example, E
1
and E
9
have compatible actuation sequences, so they can be
connected to the same control pin, as shown in Fig.
1.16
b. This design is named as
the “broadcast addressing scheme” of biochips [
43
].
However, if an actuation sequence of an electrode is to be generated as output
signal from a logic function, the number of control pins for the electrode array can
be reduced to two. Figure
1.16
c presents the logic functions that correspond to the
electrodes. Each electrode, E
i
, is assigned a logic function f.E
i
/, e.g., f.E
1
/
D
x
0
.
The example above presents the implementation of a logic circuit that can reduce
the number of control pins significantly. In [
54
], the researchers further developed
a scalable, heuristic approach to generate a control logic circuit for reducing the
number of control pins.
