平成18年度電気関係学会四国支部連合大会

17 - 17313

Analysis of Plane Circuit Using CNNs
Masayoshi ODA† , Yoshifumi NISHIO† and Akio USHIDA‡
Tokushima University, ‡Tokushima Bunri University

In PEEC aproach, the plane is discretized spatially and modeled bylinear elements, R, L, G and C.
Fig.1. shows the equaivalent circuitof the plane. The parameters of linear elements are determined by thephysical property of the plane andFig. 1. Plane circuit.
the discritization size.
The state equations of the PEEC model are given as follows;
j-1

vi-1,ji-1

jj+1

LRvi,j-1iLRLvi,jR v
i,j+1ii,jLCGRvi+1,jrr
LLdvi,j dτ = −Gr C vi,j +r C ii,j ,dii,jCC
= −Rii,j +(vi−1,j + vi+1,j
dτLL



X
dx1ij

= −x1ij +A1 (i, j; k, l)y1kl

dt


C(k,l)∈Nr (i,j)
X
B1 (i, j; k, l)u1kl+
C(k,l)∈Nr (i,j)

X


C1 (i, j; k, l)y2kl + I1 ,+
C(k,l)∈Nr (i,j)
Xdx2ij
A2 (i, j; k, l)y2kl
 dt = −xi,j +C(k,l)∈Nr (i,j)

X



+B2 (i, j; k, l)u2kl
C(k,l)∈N(i,j)
r

X



+C2 (i, j; k, l)y1kl + I2 .
The behavior of CNNs is defined by the coefficients, calledcloning templates. By comparing two system of equations,
PEEC and CNNs, we can find that both equations have
local connectivity. Hence, we can simulate the phenomenaon the plane using two-layer CNNs.
4. Simulation
Confirming the accuracy of the PEEC model, we measure
the voltage at some points whose distance from an arbitrary
point in Euclidean space is the same. We compare two cases,in the first case, we discretize the plane w = 2.0[mm] andassume the impulse voltage as a point, while another case,
we discretize w = 0.4[mm] and assume the impulse voltage
as an area.
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+ vi,j−1 + vi,j+1 − 4vij ).

If we discretize the plane into n × n small elements, we haveto calculate 2n2 differential equations.
3. Cellular Neural Networks
Cellular Neural Networks (CNNs) have the array structureof the fundamental elements, called cell, which is composedof simple analog circuit. CNNs have been developed as theanalysis method of the partial differential equations andadapted for simulate spatio-temporal phenomena, such as
traveling waves. The concept of the multi-layer CNNs has
been proposed and reported its high processing abilities.
The state equations of the two-layer CNNs are given by as

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(1)

(2)

C(k,l)∈Nr (i,j)

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i+1

follow;

Voltage

1. Introduction
Recently, the operational speed of the integrated circuits
are increasing rapidly. The increase of the operational
speed causes many complicated phenomena, such as thetransmission delay, the power/signal integrity or thepower distribution. In designing the high speed systems,
analyzing the power distribution of the multi-layer printed
circuit bords is very important. Most of the analysis
method of the power distributions are based on the finite
element method. In the finite element method, obtaining
the accrate solution, the number of element become verylarge. It is very time consuming task that calculate thesolution by conventional digital computers. Hence, in thispaper, we simulate the voltage propagation on the plane
using two-layer Cellular Ceural Networks, which are highspeed analog signal processing systems.
2. Plane Circuit
Analysis methods of the power distribution can be classified into three classes by its model accuracy, full-wave
electromagnetic model, modified nodal model and lumpedcircuit model. In our research, we adapt the partial-element
equivalent circuit (PEEC) method.

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Time(a) w = 2.0[mm].
(b) w = 0.4[mm].
Fig. 2. Dirrection difference.

As shown in Fig.2, observed phenomena are different. Thisdifference is resulted in the lattice-like structure of the planecircuit. Obtaining the accurate results, we have to discretize
the plane smaller and to assume the voltage as an area, not
as a point.
5. Conclusion
In this paper, we showed that the power distribution of theprinted circuit board can be analyzed by two-layer CNNs.
Although our research is only the simulation, CNNs will
provide for a solution with higher speed than any oter known
methods.