US 7,454,725 B2 · Apparatus and computer readable medium having program for analyzing distributed constant in a transmission line

An apparatus for analyzing a distributed constant in a transmission line, comprising:

an input section for inputting distributed parameters for each line segment virtually and arbitrarily divided in said transmission line to be analyzed;
an arithmetic operation section for calculating characteristic data of said transmission line by performing a predetermined arithmetic operation based on said distributed parameters input from said input section;
and
an output section for outputting the characteristic data,
wherein said distributed parameters input from said input section include a distributed self-inductance Li, a distributed resistance Ri, and a distributed capacitance ci and a distributed conductance gi in relation to a reference potential plane in said transmission line, and a distributed mutual inductance Mij, a distributed capacitance Cij, and a distributed conductance Gij between said transmission line and another transmission line,
wherein said arithmetic operation section calculates the characteristic data in said transmission line by solving a differential equation regarding electromagnetic interaction of said each line segment based on predetermined distributed parameters being input from the input section, and
wherein said arithmetic operation section comprises a secondary simultaneous differential equations as represented in a following formula 1 regarding electromagnetic interaction of said each line segment with the voltage V(θ) of said each line segment in said transmission line as an unknown variable (in the formula 1, V(θ) is a column vector of n×1 as represented in a following formula 2, Z is an impedance matrix created based on said distributed parameters as represented in a following formula 3, Y is an admittance matrix created based on said distributed parameters as represented in a following formula 4), in which said secondary simultaneous differential equations as represented in the formula 1 are solved by obtaining the eigenvalues yi2 (i=1 to n:
n is a virtually divided number of line segments) of a complex coefficient matrix −ZY with said impedance matrix Z and said admittance matrix Y, thereby acquiring a general solution (pi, qi are arbitrary constants, and ui (i=1 to n) are eigenvectors corresponding to said eigenvalues γi2) of voltage and current I(θ) as represented in a following formula 5 and a following formula 6a or 6b at a limited position on said each line segment
ⅆ
2
ⅆ
θ
2
⁢
V
⁡
(
θ
)
=
-
ZY
·
V
⁡
(
θ
)
(
Formula
⁢
⁢
1
)
V
⁡
(
θ
)
=
(
υ
1
⁡
(
θ
)
υ
2
⁡
(
θ
)
⋮
υ
n
⁡
(
θ
)
)
(
Formula
⁢
⁢
2
)
Z
=
(
(
R
1
+
j
⁢
⁢
ω
⁢
⁢
L
1
)
j
⁢
⁢
ω
⁢
⁢
M
12
⋯
j
⁢
⁢
ω
⁢
⁢
M
1
⁢
n
j
⁢
⁢
ω
⁢
⁢
M
21
(
R
2
+
j
⁢
⁢
ω
⁢
⁢
L
2
)
⋯
j
⁢
⁢
ω
⁢
⁢
M
2
⁢
n
⋮
⋮
⋰
⋮
j
⁢
⁢
ω
⁢
⁢
M
n1
j
⁢
⁢
ω
⁢
⁢
M
n2
⋯
(
R
n
+
j
⁢
⁢
ω
⁢
⁢
L
n
)
)
(
Formula
⁢
⁢
3
)
Y
=
(
ξ
2
(
G
12
+
j
⁢
⁢
ω
⁢
⁢
G
12
)
⋯
(
G
1
⁢
n
+
j
⁢
⁢
ω
⁢
⁢
C
1
⁢
n
)
(
G
21
+
j
⁢
⁢
ω
⁢
⁢
C
21
)
ξ
2
⋯
(
G
2
⁢
n
+
j
⁢
⁢
ω
⁢
⁢
C
2
⁢
n
)
⋮
⋮
⋰
⋮
(
G
n1
+
j
⁢
⁢
ω
⁢
⁢
C
n1
)
(
G
n2
+
j
⁢
⁢
ω
⁢
⁢
C
n2
)
⋯
ξ
n
)
⁢
⁢
wherein
,
⁢
ξ
j
=
-
{
(
g
j
+
j
⁢
⁢
ω
⁢
⁢
c
j
)
+
∑
k
=
1
,
k
≠
j
n
⁢
(
G
jk
+
j
⁢
⁢
ω
⁢
⁢
C
jk
)
}
(
Formula
⁢
⁢
4
)
V
⁡
(
θ
)
=
∑
i
=
2
n
⁢
(
p
i
⁢
⁢
cos
⁢
⁢
h
⁡
(
γ
i
⁢
θ
)
+
q
i
⁢
sin
⁢
⁢
h
⁡
(
γ
i
⁢
θ
)
)
⁢
u
i
⁢
(
Formula
⁢
⁢
5
)
I
⁡
(
θ
)
=
Y
⁢
∫
V
⁡
(
θ
)
⁢
ⅆ
θ
⁢
=
Y
⁢
∑
i
=
1
n
⁢
1
γ
i
⁢
{
p
i
⁢
⁢
sin
⁢
⁢
h
⁡
(
γ
i
⁢
θ
)
+
q
i
⁢
⁢
cos
⁢
⁢
h
⁡
(
γ
i
⁢
θ
)
}
⁢
u
i
⁢
⁢
⁢
or
,
(
Formula
⁢
⁢
6
⁢
a
)
I
⁡
(
θ
)
=
-
Z
-
1
⁢
∑
i
=
1
n
⁢
γ
i
⁢
{
p
1
⁢
⁢
sin
⁢
⁢
h
⁡
(
γ
1
⁢
θ
)
+
q
1
⁢
cos
⁢
⁢
h1
⁡
(
γ
1
⁢
θ
)
}
⁢
d
⁢
⁢
θ
.
(
Formula
⁢
⁢
6
⁢
b
)

529 more elements

A computer-readable medium storing a computer-executable program for instructing an apparatus for performing a method for analyzing a distributed constant in a transmission line,

wherein said apparatus comprises
an input section for inputting distributed parameters for each line segment virtually and arbitrarily divided in said transmission line to be analyzed;
an arithmetic operation section for calculating characteristic data of said transmission line by performing a predetermined arithmetic operation based on said distributed parameters input from said input section;
and
an output section for outputting the characteristic data,
wherein said distributed parameters input from said input section include a distributed self-inductance Li, a distributed resistance Ri, and a distributed capacitance ci and a distributed conductance gi in relation to a reference potential plane in said transmission line, and a distributed mutual inductance Mij, a distributed capacitance Crij, and a distributed conductance Gij between said transmission line and another transmission line,
wherein said arithmetic operation section calculates the characteristic data in said transmission line by solving a differential equation regarding electromagnetic interaction of said each line segment based on predetermined distributed parameters being input from the input section, and
wherein said arithmetic operation section comprises a secondary simultaneous differential equations as represented in a following formula 1 regarding electromagnetic interaction of said each line segment with the voltage V(θ) of said each line segment in said transmission line as an unknown variable (in the formula 1, V(θ) is a column vector of n×1 as represented in a following formula 2, Z is an impedance matrix created based on said distributed parameters as represented in a following formula 3, Y is an admittance matrix created based on said distributed parameters as represented in a following formula 4), in which said secondary simultaneous differential equations as represented in the formula 1 are solved by obtaining the eigenvalues γi2 (i=1 to n:
n is a virtually divided number of line segments) of a complex coefficient matrix −ZY with said impedance matrix Z and said admittance matrix Y, thereby acquiring a general solution (pi, qi are arbitrary constants, and ui (i=1 to n) are eigenvectors corresponding to said eigenvalues γi2) of voltage and current I(θ) as represented in a following formula 5 and a following formula 6a or 6b at a limited position on said each line segment
ⅆ
2
ⅆ
θ
2
⁢
V
⁡
(
θ
)
=
-
ZY
·
V
⁡
(
θ
)
(
Formula
⁢
⁢
1
)
V
⁡
(
θ
)
=
(
υ
1
⁡
(
θ
)
υ
2
⁡
(
θ
)
⋮
υ
n
⁡
(
θ
)
)
(
Formula
⁢
⁢
2
)
Z
=
(
(
R
1
+
j
⁢
⁢
ω
⁢
⁢
L
1
)
j
⁢
⁢
ω
⁢
⁢
M
12
⋯
j
⁢
⁢
ω
⁢
⁢
M
1
⁢
n
j
⁢
⁢
ω
⁢
⁢
M
21
(
R
2
+
j
⁢
⁢
ω
⁢
⁢
L
2
)
⋯
j
⁢
⁢
ω
⁢
⁢
M
2
⁢
n
⋮
⋮
⋰
⋮
j
⁢
⁢
ω
⁢
⁢
M
n1
j
⁢
⁢
ω
⁢
⁢
M
n2
⋯
(
R
n
+
j
⁢
⁢
ω
⁢
⁢
L
n
)
)
(
Formula
⁢
⁢
3
)
Y
=
(
ξ
1
(
G
12
+
j
⁢
⁢
ω
⁢
⁢
C
12
)
⋯
(
G
1
⁢
n
+
j
⁢
⁢
ω
⁢
⁢
C
1
⁢
n
)
(
G
21
+
j
⁢
⁢
ω
⁢
⁢
C
21
)
ξ
2
⋯
(
G
2
⁢
n
+
j
⁢
⁢
ω
⁢
⁢
C
2
⁢
n
)
⋮
⋮
⋰
⋮
(
G
n1
+
j
⁢
⁢
ω
⁢
⁢
C
n1
)
(
G
n2
+
j
⁢
⁢
ω
⁢
⁢
C
n2
)
⋯
ξ
n
)
⁢
⁢
wherein
,
⁢
ξ
j
=
-
{
(
g
j
+
j
⁢
⁢
ω
⁢
⁢
c
j
)
+
∑
k
=
1
,
k
≠
j
n
⁢
(
G
jk
+
j
⁢
⁢
ω
⁢
⁢
C
jk
)
}
(
Formula
⁢
⁢
4
)
V
⁡
(
θ
)
=
∑
i
=
1
n
⁢
(
p
i
⁢
⁢
cos
⁢
⁢
h
⁡
(
γ
i
⁢
θ
)
+
q
i
⁢
sin
⁢
⁢
h
⁡
(
γ
i
⁢
θ
)
)
⁢
u
i
⁢
(
Formula
⁢
⁢
5
)
I
⁡
(
θ
)
=
Y
⁢
∫
V
⁡
(
θ
)
⁢
ⅆ
θ
⁢
=
Y
⁢
∑
i
=
1
n
⁢
1
γ
i
⁢
{
p
i
⁢
⁢
sin
⁢
⁢
h
⁡
(
γ
i
⁢
θ
)
+
q
i
⁢
⁢
cos
⁢
⁢
h
⁡
(
γ
i
⁢
θ
)
}
⁢
u
i
⁢
⁢
⁢
or
,
(
Formula
⁢
⁢
6
⁢
a
)
I
⁡
(
θ
)
=
-
Z
-
1
⁢
∑
i
=
1
n
⁢
γ
i
⁢
{
p
1
⁢
⁢
sin
⁢
⁢
h
⁡
(
γ
i
⁢
θ
)
+
q
1
⁢
cos
⁢
⁢
h
⁡
(
γ
1
⁢
θ
)
}
⁢
d
⁢
⁢
θ
(
Formula
⁢
⁢
6
⁢
b
)
wherein said arithmetic operation section comprises a computer, and wherein the method comprises:
setting up the secondary simultaneous differential equations as represented in the formula 1 regarding electromagnetic interaction of said each line segment with the voltage V(θ) of said each line segment virtually and arbitrarily divided in said transmission line to be analyzed as the unknown variable (in the formula 1, V(θ) is the column vector of n×1 as represented in the formula 2, Z is the impedance matrix created based on said distributed parameters as represented in the formula 3, Y is the admittance matrix created based on said distributed parameters as represented in the formula 4), and
solving said secondary simultaneous differential equations as represented in the formula 1 by obtaining the eigenvalues γi2 (i=1 to n:
n is the virtually divided number of line segments) of the complex coefficient matrix −ZY with said impedance matrix Z and said admittance matrix Y from a distributed self-inductance Li, a distributed resistance Ri, and a distributed capacitance ci and a distributed conductance gi in relation to a reference potential plane in said transmission line, and a distributed mutual inductance Mij, a distributed capacitance cij, and a distributed conductance Gij between said transmission line and another transmission line, which are input from said input section, thereby acquiring a general solution (pi, qi are arbitrary constants, and ui (i=1 to n) are eigenvectors corresponding to said eigenvalues γi2) of voltage and current as represented in the formula 5 and the formula 6a or 6b at a limited position on said each line segment.

533 more elements

A computer-readable medium storing a computer-executable program for instructing an apparatus for performing a method for analyzing a distributed constant in a transmission line,

wherein said apparatus comprises
an input section for inputting distributed parameters for each line segment virtually and arbitrarily divided in said transmission line to be analyzed;
an arithmetic operation section for calculating characteristic data of said transmission line by performing a predetermined arithmetic operation based on said distributed parameters input from said input section;
and
an output section for outputting the characteristic data,
wherein said distributed parameters input from said input section include a distributed self-inductance Li, a distributed resistance Ri, and a distributed capacitance ci and a distributed conductance gi in relation to a reference potential plane in said transmission line, and a distributed mutual inductance Mij, a distributed capacitance Cij, and a distributed conductance Gij between said transmission line and another transmission line,
wherein said arithmetic operation section calculates the characteristic data in said transmission line by solving a differential equation regarding electromagnetic interaction of said each line segment based on predetermined distributed parameters being input from the input section, and
wherein said arithmetic operation section comprises a secondary simultaneous differential equations as represented in a following formula 1 regarding electromagnetic interaction of said each line segment with the voltage V(θ) of said each line segment in said transmission line as an unknown variable (in the formula 1, v(θ) is a column vector of n×1 as represented in a following formula 2, Z is an impedance matrix created based on said distributed parameters as represented in a following formula 3, Y is an admittance matrix created based on said distributed parameters as represented in a following formula 4), in which said secondary simultaneous differential equations as represented in the formula 1 are solved by obtaining the eigenvalues γi2 (i=1 to n:
n is a virtually divided number of line segments) of a complex coefficient matrix −ZY with said impedance matrix Z and said admittance matrix Y, thereby acquiring a general solution (Pi, qi are arbitrary constants, and ui (i=1 to n) are eigenvectors corresponding to said eigenvalues γi2) of voltage and current I(θ) as represented in a following formula 5 and a following formula 6a or 6b at a limited position on said each line segment
ⅆ
2
ⅆ
θ
2
⁢
V
⁡
(
θ
)
=
-
ZY
·
V
⁡
(
θ
)
(
Formula
⁢
⁢
1
)
V
⁡
(
θ
)
=
(
υ
1
⁡
(
θ
)
υ
2
⁡
(
θ
)
⋮
υ
n
⁡
(
θ
)
)
(
Formula
⁢
⁢
2
)
Z
=
(
(
R
2
+
jωL
2
)
jω
⁢
⁢
M
22
…
jω
⁢
⁢
M
1
⁢
n
jω
⁢
⁢
M
n
(
R
2
+
jω
⁢
⁢
L
2
)
…
jω
⁢
⁢
M
2
⁢
n
⋮
⋮
⋰
⋮
jω
⁢
⁢
M
n
⁢
⁢
1
jω
⁢
⁢
M
n
⁢
⁢
2
…
(
R
n
+
jω
⁢
⁢
L
n
)
)
(
Formula
⁢
⁢
3
)
Y
=
(
ξ
2
(
G
12
+
jω
⁢
⁢
C
12
)
…
(
G
1
⁢
n
+
jω
⁢
⁢
C
1
⁢
n
)
(
G
22
+
jω
⁢
⁢
C
22
)
ξ
2
…
(
G
2
⁢
n
+
jω
⁢
⁢
C
2
⁢
n
)
⋮
⋮
⋰
⋮
(
G
n
⁢
⁢
1
+
jω
⁢
⁢
C
n
⁢
⁢
2
)
(
G
n
⁢
⁢
2
+
jω
⁢
⁢
C
n
⁢
⁢
2
)
…
ξ
n
)
⁢
⁢
wherein
,
ξ
j
=
-
{
(
g
j
+
jω
⁢
⁢
c
j
)
+
∑
k
=
3
,
k
≠
3
n
⁢
(
G
jk
+
jω
⁢
⁢
C
jk
)
}
(
Formula
⁢
⁢
4
)
V
⁡
(
θ
)
=
∑
i
=
1
n
⁢
(
p
i
⁢
cosh
⁡
(
γ
i
⁢
θ
)
+
g
i
⁢
sinh
⁡
(
γ
i
⁢
θ
)
)
⁢
u
i
(
Formula
⁢
⁢
5
)
I
⁡
(
θ
)
=
⁢
Y
⁢
∫
V
⁡
(
θ
)
⁢
ⅆ
θ
=
⁢
Y
⁢
∑
i
=
1
n
⁢
1
γ
i
⁢
{
p
i
⁢
sinh
⁡
(
γ
i
⁢
θ
)
+
q
i
⁢
cosh
⁡
(
γ
i
⁢
θ
)
}
⁢
u
1
⁢
⁢
or
,
(
Formula
⁢
⁢
6
⁢
a
)
I
⁡
(
θ
)
=
-
Z
-
1
⁢
∑
i
=
1
n
⁢
γ
i
⁢
{
p
i
⁢
sinh
⁡
(
γ
⁢
i
⁢
θ
)
+
q
i
⁢
cosh
⁡
(
γ
i
⁢
θ
)
}
⁢
ⅆ
θ
(
Formula
⁢
⁢
6
⁢
b
)
wherein said arithmetic operation section comprises a computer, and wherein the method comprises:
setting up linearly simultaneous differential equations as represented in a following formula 10 regarding electromagnetic interaction of said each line segment with the voltage V(θ) and current I(θ) of said each line segment virtually and arbitrarily divided in said transmission line to be analyzed as unknown variables (in the formula 10, W(θ) matrix containing V(θ)n×1 and I(θ)n×1 as represented in a following formula 11, A is a matrix as represented in a following formula 12 containing the impedance matrix Z created based on said distributed parameters as represented in the formula 3 and the admittance matrix Y created based on said distributed parameters as represented in the formula 4), and
solving said linearly simultaneous differential equations as represented in the formula 10 by obtaining 2n eigenvalues γi (i=1 to 2n) of said matrix A from a distributed self-inductance Li, a distributed resistance Ri, and a distributed capacitance ci and a distributed conductance gi in relation to a reference potential plane in said transmission line, and a distributed mutual inductance Mij, a distributed capacitance Cij, and a distributed conductance Gij between said transmission line and another transmission line, which are input from said input section, thereby acquiring a general solution (αi (i=1 to 2n) are arbitrary constants, and ui (i=1 to 2n) are eigenvectors corresponding to said eigenvalues γi) of voltage and current as represented in a following formula 13
ⅆ
ⅆ
θ
⁢
W
⁡
(
θ
)
=
A
·
W
⁡
(
θ
)
(
Formula
⁢
⁢
10
)
W
⁡
(
θ
)
=
(
V
⁡
(
θ
)
n
×
1
I
⁡
(
θ
)
n
×
1
)
=
(
υ
1
⁡
(
θ
)
υ
2
⁡
(
θ
)
⋮
υ
n
⁡
(
θ
)
i
1
⁡
(
θ
)
i
2
⁡
(
θ
)
⋮
i
n
⁡
(
θ
)
)
(
Formula
⁢
⁢
11
)
A
=
(
0
n
×
n
-
Z
Y
0
n
×
n
)
2
⁢
n
×
2
⁢
n
(
Formula
⁢
⁢
12
)
W
⁡
(
θ
)
=
∑
i
=
1
2
⁢
n
⁢
α
i
⁢
ⅇ
γ
⁢
⁢
i
⁢
⁢
θ
⁢
u
i
.
(
Formula
⁢
⁢
13
)

628 more elements

Apparatus and computer readable medium having program for analyzing distributed constant in a transmission line

Life of this patent

Apparatus and computer readable medium having program for analyzing distributed constant in a transmission line

Life of this patent

Abstract

Claims18