Computer-aided design and analysis of circuits and semiconductor – Nanotechnology related integrated circuit design
Reexamination Certificate
2000-03-02
2003-05-20
Smith, Matthew (Department: 2825)
Computer-aided design and analysis of circuits and semiconductor
Nanotechnology related integrated circuit design
C716S030000, C716S030000
Reexamination Certificate
active
06567955
ABSTRACT:
TECHNICAL FIELD
The present invention relates to a method of and a system for carrying out an approximation process for circuit analysis of a distributed constant line. In particular, the present invention relates to a method and a system for approximating a distributed constant line by a lumped constant circuit, with specified accuracy. The present invention also relates to a storage medium that stores a program used therefor.
BACKGROUND ART
With regard to a wiring system such as a printed board or a multilayer wiring board, it is required to carry out circuit analysis concerning whether the circuit realizes desired operation. Conventionally, analysis software has been developed for this object. By designating circuit elements constituting a circuit, a circuit model is specified, and then, the above-mentioned software is used for circuit analysis on a computer.
As LSIs are rapidly improved in their operating speed, a wiring system for transmitting signal between elements is required to have structure capable of transmitting a signal at high speed. To that end, it is necessary to sufficiently understand signal transmission characteristics of a wiring system. In that case, in order to realize high speed transmission, a wiring system should be treated as a transmission line so that its transmission characteristics can be understood accurately.
However, a circuit to be analyzed includes, in addition to transmission lines, circuit elements that should be treated as lumped constants. Thus, lumped constant and distributed constant coexist. However, circuit analysis of a lumped constant/distributed constant mixed system is difficult, since a travelling wave of voltage/current should be treated.
Thus, it is demanded to approximate a distributed constant line by a lumped constant circuit. In the approximation, it is desirable that the degree of accuracy of the approximation be known. Further, when the approximation accuracy becomes higher, a load on the processing becomes larger. Thus, in approximating a distributed constant line by a lumped constant circuit, it is desired that the approximation can be carried out with a required accuracy.
DISCLOSURE OF THE INVENTION
An object of the invention is to provide a process for approximating a distributed constant line by a lumped constant circuit, and, in particular, to provide a method and system for approximating a distributed constant line with a required accuracy, and a storage medium that stores a program used therefor.
To attain the above object, the present invention provides, according to its first mode, a method of approximating a distributed constant line, which employs an information processing apparatus to perform a process of approximating an object distributed constant line by a lumped constant circuit obtained by cascading a given unit lumped constant circuit in n stages, comprising the steps of:
calculating a product &ggr;l of a propagation constant &ggr; of the object distributed constant line and a line length l of the distributed constant line, and storing the product;
calculating cosh &ggr;l and sinh &ggr;l, using the &ggr;l, and storing the cosh &ggr;l and sinh &ggr;l;
calculating a
n
(&ggr;l), b
n
(&ggr;l) and c
n
(&ggr;l) that constitute elements of a transfer matrix of the lumped constant line, from functions a
n
(x), b
n
(x) and c
n
(x) defined by following three expressions:
a
n
(
x
)
=
∑
k
=
0
n
(
n
+
k
-
1
)
!
n
2
k
-
1
(
n
-
k
)
!
x
2
k
(
2
k
)
!
b
n
(
x
)
=
∑
k
=
0
n
-
1
(
n
+
k
)
!
n
2
k
+
1
(
n
-
k
-
1
)
!
x
2
k
+
1
(
2
k
+
1
)
!
c
n
(
x
)
=
∑
k
=
0
n
(
n
2
+
k
2
)
(
n
+
k
-
1
)
!
n
2
k
+
1
(
n
-
k
)
!
x
2
k
+
1
(
2
k
+
1
)
!
putting x=&ggr;l and deciding n as a tentative value, and storing the a
n
(&ggr;l), b
n
(&ggr;l) and c
n
(&ggr;l);
comparing the cosh &ggr;l with a
n
(&ggr;l), sinh &ggr;l with b
n
(&ggr;l), and sinh &ggr;l with c
n
(&ggr;l), respectively, to make a judgment on whether a result of comparison satisfies a predetermined condition, and, when the condition is not satisfied, repeating steps from the step of calculating the a
n
(&ggr;l), b
n
(&ggr;l) and c
n
(&ggr;l), onward, changing the value of the n, until the result of comparison satisfies the condition; and
deciding an approximate circuit, using n when the result of comparison satisfies the condition, in order to decide a lumped constant circuit that is obtained by cascading the unit lumped constant circuit in n stages.
In the above-described method, further, the following modes may be optionally employed.
a) The above-mentioned comparison is carried out by calculating a deviation between the cosh &ggr;l and a
n
(&ggr;l), a deviation between sinh &ggr;l and b
n
(&ggr;l), and a deviation between sinh &ggr;l and c
n
(&ggr;l), respectively, and the result of comparison is obtained as the maximum &dgr; among those deviations; and
a condition that the maximum &dgr; satisfies &dgr;<&egr; for an error tolerance &egr; set in advance is used as the condition to make the judgment.
b) The above-mentioned lumped constant circuit is constituted by cascading a Π circuit as the unit lumped constant circuit in n stages, and the transfer matrix of the lumped constant circuit is given by an expression:
F
Π
=
[
a
n
(
γ
l
)
Z
0
b
n
(
γ
l
)
1
Z
0
c
n
(
γ
l
)
a
n
(
γ
l
)
]
where Z
0
is a characteristic impedance of the distributed constant line.
c) The above-mentioned lumped constant circuit is constituted by cascading a T circuit as the unit lumped constant circuit in n stages, and the transfer matrix of the lumped constant circuit is given by an expression:
F
T
=
[
a
n
(
γ
l
)
Z
0
c
n
(
γ
l
)
1
Z
0
b
n
(
γ
l
)
a
n
(
γ
l
)
]
where Z
0
is a characteristic impedance of the distributed constant line.
d) Input of the error tolerance &egr; is received and stored;
and the received &egr; is used in the condition to decide the value of the n.
e) As the error tolerance &egr;, a plurality of values are received and stored;
and each value of the received &egr; is used in the condition to decide the value of the n corresponding thereto.
Further, a second mode of the present invention provides a method of approximating a distributed constant line, which employs an information processing apparatus to perform a process of approximating an object distributed constant line by a lumped constant circuit obtained by cascading a given unit lumped constant circuit in n stages, comprising the steps of:
receiving input of a value of the n, and storing the value;
calculating a product &ggr;l of a propagation constant &ggr; of the object distributed constant line and a line length l of the distributed constant line, and storing the product;
calculating cosh &ggr;l and sinh &ggr;l, using the &ggr;l, and storing the cosh &ggr;l and sinh &ggr;l;
calculating a
n
(&ggr;l), b
n
(&ggr;l) and c
n
(&ggr;l) that constitute elements of a transfer matrix of the lumped constant line, from functions a
n
(x), b
n
(x) and c
n
(x) defined by following three expressions:
a
n
(
x
)
=
∑
k
=
0
n
(
n
+
k
-
1
)
!
n
2
k
-
1
(
n
-
k
)
!
x
2
k
(
2
k
)
!
b
n
(
x
)
=
∑
k
=
0
n
-
1
(
n
+
k
)
!
n
2
k
+
1
(
n
-
k
-
1
)
!
x
2
k
+
1
(
2
k
+
1
)
!
c
n
(
x
)
=
∑
k
=
0
n
(
n
2
+
k
2
)
(
n
+
k
-
1
)
!
n
2
k
+
1
(
n
-
k
)
!
x
2
k
+
1
(
2
k
+
1
)
!
putting x=&ggr;l and deciding n as the value inputted, and storing the a
n
(&ggr;l), b
n
(&ggr;l) and c
n
(&ggr;l); and
calculating a deviation between the cosh &ggr;l and a
n
(&ggr;l), a deviation between sinh &ggr;l and b
n
(&gg
Dinh Paul
Hitachi Chemical Company Ltd.
Smith Matthew
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