Легостаев Н.С., Четвергов К.В. Методы анализа и расчета электронных схем (МАРЭС). Руководство к организации самостоятельной работы
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170
Ρ
RR
identity l
R
()
:= Ρ
RR
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
=
Ρ
LR
matrix l
LN
l
R
, f,
()
:=
Ρ
LR
000000()=
Ρ
LL
identity l
L
()
:= Ρ
LL
1()=
Ρ
y
augment stack Ρ
CC
Ρ
GC
,Ρ
RC
,Ρ
LC
,
()
stack matrix l
CN
l
G
, f,
()
Ρ
GG
,Ρ
RG
,Ρ
LG
,
()
,
()
:=
Ρ
z
augment stack Ρ
CE
Ρ
GE
,Ρ
RE
,Ρ
LE
,
()
stack matrix l
CN
l
G
+ l
R
, f,
()
Ρ
RR
,Ρ
LR
,
()
, stack matrix l
CN
l
G
+ l
R
+ l
L
, f,
()
Ρ
LL
,
()
,
( )
:=
Θ stack augment Π
y
matrix ν l
z
, f,
()
,
()
augment matrix σ l
y
, f,
(
)
Ρ
z
,
(
)
,
()
:=
Θ1 stack augment matrix ν l
y
, f,
()
Π
z
,
()
augment Ρ
y
matrix σ l
z
, f,
()
,
()
,
()
:=
170
171
L
L
L1:= Y
GG
Gsi
0
0
1
rk
⎛
⎜
⎜
⎝
⎞
⎟
⎟
⎠
:= Y
GC
0
0
0
0
0
0
0
0
S
0
0
0
0
0
⎛
⎜
⎝
⎞
⎟
⎠
:=
C
C
C1
0
0
0
0
0
0
0
C2
0
0
0
0
0
0
0
C3
0
0
0
0
0
0
0
Czs
0
0
0
0
0
0
0
Czi
0
0
0
0
0
0
0
Ck
0
0
0
0
0
0
0
Csi
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
:=
Компонентные матрицы
Ρ
y
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1−
1
1
1−
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1−
1−
0
0
1
1
1−
1
1
0
0
0
1
0
0
0
1
1−
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
=Ρ
z
0
0
0
1−
1−
1−
0
1−
1−
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
=
171
172
Y
0
augment stack matrix l
C
l
C
, f,
()
Y
GC
,
()
stack matrix l
C
l
G
, f,
(
)
Y
GG
,
(
)
,
()
:=
N
GE
matrix l
G
l
E
, f,
()
:= N
GR
0
0
0
0
0
0
0
0
0
α
0
0
⎛
⎜
⎝
⎞
⎟
⎠
:= N
GL
matrix l
G
l
L
, f,
()
:=
N
0
augment stack matrix l
C
l
E
, f,
()
N
GE
,
()
stack matrix l
C
l
R
, f,
()
N
GR
,
()
, stack matrix l
C
l
L
, f,
()
N
GL
,
()
,
( )
:=
M
RC
matrix l
R
l
C
, f,
()
:= M
RG
matrix l
R
l
G
, f,
()
:=
M
0
augment stack matrix l
E
l
C
, f,
()
M
RC
, matrix l
L
l
C
, f,
()
,
()
stack matrix l
E
l
G
, f,
()
M
RG
, matrix l
L
l
G
, f,
()
,
()
,
( )
:=
Z
RE
matrix l
R
l
E
, f,
()
:= Z
RL
matrix l
R
l
L
, f,
()
:=
Z
RR
R1
0
0
0
0
0
0
R2
0
0
0
0
0
0
R3
0
0
0
0
0
0
rb
0
0
0
0
0
0
re
0
0
0
0
0
0
Rn
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
:=
Z
0
augmentstack matrixl
E
l
E
, f,
()
Z
RE
, matrixl
L
l
E
, f,
(
)
,
()
stack matrixl
E
l
R
, f,
(
)
Z
RR
, matrixl
L
l
R
, f,
(
)
,
(
)
, stack matrixl
E
l
L
, f,
(
)
Z
RL
, matrixl
L
l
L
, f,
(
)
,
(
)
,
( )
:=
172
173
V
0
stack augment Y
0
N
0
,
()
augment M
0
Z
0
,
(
)
,
()
:=
V
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
510
3−
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
210
6−
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
210
6−
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
110
6
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
400
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
110
4
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
200
0
0
0
0
0
0
0
0
0
0
0
0.98
0
0
0
0
0
5.2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
110
4
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
=
173
174
W
0
V
0
Θ
T
⋅Θ1
T
−:=
W
0
0
0
0
0
0
0
0
0
0
1
−
1−
1−
1−
0
1
−
1−
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
−
1
1
1−
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
− 10
6−
×
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5.002 10
3−
×
0
0
0
1
1
1
−
1
1
0
0
0
0
0
0
0
0
0
2
− 10
6−
×
0
0
0
0
1
1
−
0
0
0
0
0
1
−
1
0
1−
0
0
0
0
0
0
0
0
0
0
0
0
0
1
−
1
0
0
1
−
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
−
0
0
1
−
0
0
0
0
0
0
0
0
1
−
0
0
0
0
0
0
0
0
0
110
6
×
0
0
0
0
0
0
1
−
0
0
0
1
−
0
0
0
0
0
0
400
0
0
0
0
0
1
−
1−
0
0
1−
0
0
0
0
0
0
0
110
4
×
0
0
0
0
0
1
0
1
−
1
1
−
0
0
0
0
0
0
0
200
0
0
0
1
−
1−
0
0
1−
1
0
0
0.98
0
0
0
0
0
5.2
0
0
1
−
1−
1−
0
1
−
0
0
0
0
0
0
0
0
0
0
110
4
×
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
=
Матрицы эквивалентных параметров
174
175
w
p
augment stack C
C
Π
CC
T
⋅ matrix l
G
l
R
+ l
L
+ l
CT
, f,
()
,
⎛
⎝
⎞
⎠
stack matrix l
C
l
G
+ l
R
+ l
LN
, f,
()
L
L
Ρ
LL
T
⋅,
⎛
⎝
⎞
⎠
,
⎛
⎝
⎞
⎠
:=
w
p
510
6−
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3.979 10
8−
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
110
5−
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
110
12−
×
0
0
1
− 10
12−
×
0
0
0
0
0
0
0
0
0
0
0
0
0
510
12−
×
0
110
12−
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
710
12−
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6.366 10
5−
×
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
=
175
176
w
x1
stack submatrixW
0
0, l
y
1−, l
E
, l
E
l
CT
+ 1−,
()
submatrixW
0
l
y
l
E
+, rows W
0
()
1−, l
E
, l
E
l
CT
+ 1−,
(
)
,
( )
:=
w
x2
stack submatrixW
0
0, l
y
1−, cols W
0
()
l
LN
−, cols W
0
()
1−,
()
submatrixW
0
l
y
l
E
+, rows W
0
()
1−, cols W
0
()
l
LN
−, cols W
0
()
1−,
()
,
( )
:=
w
x
augmentw
x1
w
x2
,
()
:=
w
x
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
−
1
1
1
−
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
− 10
6−
×
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5.002 10
3−
×
0
0
1
1
1
−
1
1
0
0
0
0
0
0
0
0
0
2
− 10
6−
×
0
0
0
1
1
−
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
=
176
177
w
0
stack submatrixW
0
0, l
y
1−, l
E
l
CT
+, l
E
l
C
+ l
R
+ l
G
+ 1−,
()
submatrixW
0
l
y
l
E
+, rows W
0
(
)
1−, l
E
l
CT
+, l
E
l
C
+ l
R
+ l
G
+ 1−,
(
)
,
( )
:=
w
0
0
0
0
1
−
1
0
1
−
0
0
0
0
0
0
0
0
0
0
0
0
1
−
1
0
0
1
−
0
0
0
0
0
0
0
0
0
0
0
0
0
1
−
0
0
1
−
0
0
0
0
0
0
0
1
−
0
0
0
0
0
0
0
0
110
6
×
0
0
0
0
0
0
1
−
0
0
0
1
−
0
0
0
0
0
400
0
0
0
0
0
1
−
1−
0
0
1
−
0
0
0
0
0
0
110
4
×
0
0
0
0
0
1
0
1
−
1
1
−
0
0
0
0
0
0
200
0
0
0
1
−
1−
0
0
1
−
1
0
0
0.98
0
0
0
0
5.2
0
0
1
−
1−
1−
0
1
−
0
0
0
0
0
0
0
0
0
110
4
×
0
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
=
177
178
θ
f
stack submatrix W
0
0, l
y
1−, 0, l
E
1−,
()
submatrix W
0
l
y
l
E
+, rows W
0
()
1−, 0, l
E
1−,
(
)
,
( )
:=
θ
1f
stack C
C
Π
EC
T
⋅ matrix l
G
l
R
+ l
L
+ l
E
, f,
()
,
⎛
⎝
⎞
⎠
:=
θ
f
0
0
0
0
0
0
0
0
0
1
−
1−
1−
0
1
−
1−
0
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
=θ
1f
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
=
178
179
w augmentw
p
w
0
,
()
:=
w
510
6−
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3.979 10
8−
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
110
5−
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
110
12−
×
0
0
1
− 10
12−
×
0
0
0
0
0
0
0
0
0
0
0
0
0
510
12−
×
0
110
12−
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
710
12−
×
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6.366 10
5−
×
0
0
0
1
−
1
0
1
−
0
0
0
0
0
0
0
0
0
0
0
0
1
−
1
0
0
1
−
0
0
0
0
0
0
0
0
0
0
0
0
0
1
−
0
0
1
−
0
0
0
0
0
0
0
1
−
0
0
0
0
0
0
0
0
110
6
×
0
0
0
0
0
0
1
−
0
0
0
1
−
0
0
0
0
0
400
0
0
0
0
0
1
−
1−
0
0
1
−
0
0
0
0
0
0
110
4
×
0
0
0
0
0
1
0
1
−
1
1
−
0
0
0
0
0
0
200
0
0
0
1
−
1−
0
0
1
−
1
0
0
0.98
0
0
0
0
5.2
0
0
1
−
1−
1−
0
1
−
0
0
0
0
0
0
0
0
0
110
4
×
0
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
=
179