analysis synthesis of electric circuits

8/18/2019 analysis synthesis of electric circuits

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iRv ==== ! !

dtdv

dvdCv)v(Ci ++++====

dt

di

di

dLi)i(Lv ++++====

" ! #$

! %$

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ckk vEv ====

kv

cv

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cvki

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ckk iHv ====

kv

ci

ckk iFi ====

ki

ci


6/21

0

0

00

ii

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321

====

====

====

====

−−−−++++

++++++++

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++++++++

"

" & ' (

)

1R 4R

3R

8R

37vE

6ES

5IS32vG

* ! +


7/21

0

0

0

0

0

0

00

eev

ev

eev

ev

ev

eev

evev

438

47

326

25

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++++

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−−−−

* ! +

"

" & ' (

)

1R 4R

3R

8R

37vE

6ES

5IS32vG 0eAv T ====−−−−


8/21

−−−−

−−−−

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−−−−

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−−−−

−−−−

−−−−

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1R

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1

1

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9/21

====

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s

oo

e

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10/21

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1R 4R

3R

5IS32vG

52R1

21R1

21

R

1221

R

1

ISe4

)ee(3

0)ee(

3

)e

1

e(Ge

1====++++−−−−−−−−

====−−−−++++−−−−++++

/

ISIS

0

e

e

333

3G

3G

1e Y52

1

R1

R1

R1

R1

2R1

2R1

n ====

====

++++−−−−

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====

,

,

0ISv4

v3

0v3

v2Gv1

0iii0iii

54R

1

3R

1

3R1

31R1

543

321

====−−−−++++−−−−

====++++++++

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====++++++++

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v3

0v3

v2Gv1

0iii0iii

54R

1

3R

1

3R1

31R1

543

321

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====++++++++

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====++++++++

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v3

0v3

v2Gv1

0iii0iii

54R

1

3R

1

3R1

31R1

543

321

====−−−−++++−−−−

====++++++++

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====++++++++

Tv1-in AKAKY −−−−====


11/21

====

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00

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====

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0

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e

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i

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e

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i

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T

T

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,

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12/21

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..

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..k

..

..

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n

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.

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.

.

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k

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..

..

Ykk

kk

n


13/21

"

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3R

8R

37vE

6ES

5IS32vG

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0v8

i

0v8

i

0iISv

4

v

3

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6

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13

R

1

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====

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====++++

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====++++++++

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0v8

i

0v8

i

0iISv

4

v

3

0v3

vGv1

0ii0ii

0iiii

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7

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6

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13

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1

3R1

321R1

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====

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====++++

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====++++++++

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====++++

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====++++++++

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0v8

i

0v8

i

0iISv

4

v

3

0v3

vGv1

0ii0ii

0iiii

0iii

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7

8R1

6

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13

R

1

3R1

321R1

8786

6543

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====−−−−

====

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====++++

====−−−−−−−−++++−−−−

====++++++++

====−−−−++++

====++++

====−−−−−−−−++++−−−−

====++++++++


14/21

====

−−−−

−−−−

−−−−

−−−−

−−−−++++−−−−

−−−−−−−−++++++++

0

ES

00

IS

0

i

i

ee

e

e

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000110

10000100

0100

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6

5

7

6

4

3

2

1

77

R1

R1

R1

R1

R1

R1

R1

R1

2R1

2R1

88

88

433

331

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)

1R 4R

3R

8R

37vE

6ES

5IS32vG

ISAAKAK Tv1-i

====−−−−


15/21

! * , !

* ,/

nnnn

2nn22221nn1212111

bxu

::

:::

bxu.....xu

bxu.....xuxu

====

====++++++++

====++++++++++++

1,1

nn,122,11

1

1n,1n

nn,1n1n1n

n,n

n

n

u

xu.....xub

x

. . . . .

. . . . .

. . . . .

u

xubx

u

b x

−−−−−−−−−−−−====

−−−−====

====

−−−−−−−−

−−−−−−−−

−−−−

j,j

n

1jkkk,jj

j

u

xub

x

++++====

−−−−

====

j,j

1j

1kkk,jj

j

l

xlb

x−−−−

====

−−−−

====

)1n(n21

++++


16/21

)n(nn

)n(n,n

)2(2n

)2(n,22

)2(2,2

)1(

1n

)1(

n,12

)1(

2,11

)1(

1,1

bxa

::

:::

bxa.....xabxa.....xaxa

====++++

====++++++++++++

====++++++++++++

nnn,n22,n11,n

2nn,222,211,21nn,122,111,1

bxa.....xaxa

:::::

:::::

bxa.....xaxa

bxa.....xaxa

====++++++++++++

====++++++++++++

====++++++++++++

)2(nn

)2(n,n2

)2(2,n

)2(2n

)2(n,22

)2(2,2

1nn,122,111,1

bxa.....xa0

::::::::::

bxa.....xa0

bxa.....xaxa

====++++++++++++

====++++++++++++

====++++++++++++

11,1

1,i

i

)2(

i

j,11,1

1,ij,i

)2(j,i

ba

a

bb

aa

aaa

−−−−====

−−−−====

,&.

3

nn3n 23 −−−−++++


17/21

75x5.12x5.12

25.6x25.1x000125.0

21

21

====++++

====++++

52

521

1025.6x1025.1

25.6x25.1x000125.0

××××−−−−====××××−−−−

====++++

9999.4x

0001.1x

2

1

====

====

5x

0x

2

1

====

====

75x5.12x5.1225.6x25.1

212

====++++

====+

+++

5x

1x

21

====

====

!' # + # ! (), -.,

%

/

/


18/21

====

nnn3n2n1

n3333231

n2232221

n1131211

nn

n333

n22322

n1131211

nn3n2nn1

3332

2221

11

a....aaa

:: :;::

a....aaa

a....aaaa....aaa

u....000

:: ::::

u....u00

u....uu0u....uuu

l....lll

:: ::::

0....ll31l

0....0ll0....00l

3 , ! . * , !

2 ! .

. 3 , ! / 4

%56789*:9 *;


19/21

2 .

n1n111

121211

111111

aul: ::

aul

aul

====

====

====

1n11n1

311131

211121

aul: ::

aul

aul

====

====

====

n2n121n222

2313212322

2212212222

aulul:: :: :

aulul

aulul

====++++

====++++

====++++

kk

1k

1ppjipik

ik1k

1ppjkpkjkj

u

ula

l ulau

−−−−

====−−−−

====

−−−−

====−−−−====

n.....1k,n....1ka ++++++++

k....1,n....1u

4 4 4 4

& . /

4 4 4 4

&

23 >

*:79?#8 *;


20/21

n)1r()1c()1c)(1r(1n

1k

1n

1k

1n

1kk kkk

++++−−−−++++−−−−++++−−−−−−−− −−−−

====

−−−−

====

−−−−

====

*,!

:6

/

---

rowth-kinzeros-non#c

rowth-kinzeros-non#r

k

k

====

====

' ! " $ !" #

)k(kk

)k(kj

)k(ik)k(

ij)1k(

ija

aaaa −−−−====

++++

.> zero-nonare a and a )k(kj

)k(ik


21/21

−−−− 1 137 0

0 3 1 0

0 0 2 7

1 2 3 5

& ' ( )

&

A

B

C

A & & ( & ' ' & ( & & ) •

B ' & • ' ' ' •

& ( ' ( ( ( •

B ) ' • &( ) ( • & ) ) • •

Documents

analysis synthesis of electric circuits