Основы компьютерного проектирования и моделирования радиоэлектронных систем: Программа, методические указания и контрольные вопросы

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  • 2007

    ,

  • 2

    02.02.07. 20.02.07. 60 84 1/16. . . . . . 1,56. .. . 1,5.

    100 .

    190000, , . ., 67

    , 2007

    . . . .

    . . : ; . .

    . , , , . .

    .

  • 3

    , . .

    : , ,

    ;

    () ;

    ;

    .

    , ; , .

    , , , .

    , , , , , .

    , .

    , : ; ; ; ;

  • 4

    ; ; .

    . , .

    . . .

  • 5

    1. ,

    1.1.

    , , ; .

    , , , , .

    1.2.

    :

    ;

    ; ; ;

    . :

    () ;

    ;

    .

    , , .

  • 6

    . . 1.

    1

    2.

    1. .

    . . . . . , . .

    : 1, 2. [1, . 723; 2, . 1236; 6, . 38].

    1. .2.

    .3. .

    2. 3 .

    . , . . . .

    K

    9 )63(77 21 21 14 1

  • 7

    : 1, 2. [1, . 62101; 2, . 8596; 3, . 71113, 178228; 6,

    . 817, 3139].

    1. , .

    2. , , , .

    3. , .

    3. . ().

    . . , , . . .

    : 2, 2. [1, . 102137; 2, . 97114; 3, . 129140; 6, . 17

    30, 5172; 9, . 136143, 174186].

    1. .2. ,

    , .3.

    .4. LU.

    4. . .

    .

  • 8

    . . . .

    : 2, 2. [1, . 285289; 7, . 333].

    1. , , .

    2. .

    3. .4. , ,

    .

    5. .

    . . . . .

    : 1, 3. [7, . 3396].

    1. .2. .3.

    .

    6. . ,

    . . .

  • 9

    . .

    : 1, 2. [1, . 233268; 7, . 2433; 8, . 316; 9, . 157162,

    170173].

    1. .

    2. .3. , .

    7. ., .

    Z. .

    : 2, 2. [9, . 435451].

    1. , .

    2. Z.3. .

    8. () .

    . . . .

    : 2, 2. [1, . 460471; 2, . 223234].

  • 10

    1. .2.

    .3. .

    2.2. ,

    , , , .

    1. .

    6 7. : 4, 4, [10, 11].

    2.

    . MatLab 6.5.

    : 4, 4. [10, 11].

    3.

    , MathLab.

    : 4, 4. [10, 11].

  • 11

    3.

    , [12]:

    1. .2. . , ,

    . . 0, 10 .

    3.1. 1

    1. ?2.

    .3. ?4.

    . . 10 1.

    5. ?6. .7. = ,

    ( ); ( ; 10 1).

    8. Z = XAY, , X Y , .

    3 3 1:

    1 2 3 4 53 2 5 1 7 3 4 3 2 2 1 6 2 4 81 4 7 2 5 6 1 5 3 3 2 1 3 1 56 1 2 1 3 2 3 7 1 5 4 3 4 2 3

    6 7 8 9 013 1 6 1 2 1 4 1 3 2 3 5 2 3 42 4 1 7 5 3 3 5 7 1 2 4 4 1 25 7 2 3 6 2 2 3 1 6 1 3 8 5 3

  • 12

    3.2. 2

    . :

    ; ; ; ; ; ; ;

    () (C, L); : 30

    ;

    . min(0,2...0,5) .h =

    . [2, 7]. , , 1: R6, 300 300 ; L8, 0.5 0,5 , C3, 0.5 0,5 .

  • 13

    4.

    2

    4.1.

    , , . . .

  • 14

    , , . . . , . . (,) , , , .

    (. 1). .

    1. , , : , , , , . , 0.

    2. , . : , , , , (E, C, R, L, I).

    3. (. 2), . , .

    4. , . , .

    5. , .

    . ,

    , (. 3).

    . 1. . 2.

    1 2 3 4

    1

    R3 R4 R6

    R5

    L7

    I8C2

  • 15

    , , , , .

    (. 3). n , m, m = n 1. , . 2, m = n 1 == 5 1 = 4.

    E1,2, R3, R4, R5, R6, L7, I8 (. . 1) 1%2%3%4%5%6%7%8. , . 1%2%4%6 (. 3).

    . 4 1%2%4%6, 3%5%7%8. , .

    , . (E, C, R, L, I) .

    , , , .

    . 4.

    . 3.

  • 16

    4.2.

    , . . 5, (A, B, C, D). .

    , . , . . 5, A, B, C, D .

    , , . , .

    1 0 0 0 1 0 0 00 1 0 0 1 1 0 1

    0 0 1 0 0 1 1 10 0 0 1 0 0 1 1

    C

    = A

    (1)

    ij : ij = +1, j% i , , ; ij = 1, j i% , , ; aij = 0, j i .

    . 5. : ;

  • 17

    : . , ij , E. F.

    ,

    = |E F|. (2)

    , : j Ij j , i , i . , , . (. 5, )

    1 3

    2 3 5 8

    4 5 7 8

    6 7 8

    0,0,0,

    0.

    i ii i i ii i i i

    i i i

    = + = + =

    + + =

    (3)

    (3) , .

    (3)

    1

    2

    4

    6

    3

    5

    7

    8

    1 0 0 0 1 0 0 00 0 0 0 1 1 0 1

    00 0 1 0 0 1 1 10 0 0 1 0 0 1 1

    iiiiiiii

    = (4)

    0,C =A I (5)

    I .

  • 18

    I .

    (5) , . (5) (3).

    I : I I.

    TT1 2 4 6 3 5 7 8 ,

    B

    Xi i i i i i i i= = II

    I(6)

    (6) (2) (5)

    , ,BC B X X BX

    = = + = +I I E F EI FI FI II

    (7)

    .XI = Fi

    (7) .

    31

    2 5

    4 7

    6 8

    1 0 0 0 1 1 0 1

    , 0 1 1 1 0 0 1 1

    iii ii ii i

    =

    4.3.

    (. . 4). , 3 , 5 , 7 , 8 D . . , .

    , , . , , :

  • 19

    1 1 0 0 1 0 0 00 1 1 0 0 1 0 0

    .0 0 1 1 0 0 1 00 0 1 1 0 0 0 1

    =

    A (8)

    ij : ij = +1, j% , ij = 1, j , ij = 0, j .

    , , , , F, (FT).

    , .

    j u j , . 1,2 ... 8, u1, u2, ..., u8

    1 2 3

    2 4 5

    4 6 7

    2 4 6 8

    0,0,0,

    0.

    u u uu u uu u u

    u u u u

    + + = + + = + =

    + =

    (9)

    (9) U:

    1

    2

    4

    6

    3

    5

    7

    8

    1 1 0 0 1 0 0 00 1 1 0 0 1 0 0

    0 ,0 0 1 1 0 0 1 00 1 1 1 0 0 0 1

    uuuuuuuu

    =

    (10)

    A U = 0. (11)

  • 20

    U .

    (11) , . (11) (9).

    U : U U:

    T1 2 4 6 3 5 7 8 .

    Bu u u u u u u u= = UUU

    (12)

    (12) (8) (11) T T T

    , ,B

    B X B XX

    = = + = +UA U F E F U EU F U UU

    T .X B=U F U (13)

    (13) . (13)

    3 1

    5 2

    47

    68

    1 1 0 0 0 1 1 0

    . 0 0 1 1 0 1 1 1

    u uu u

    uuuu

    =

    4.4.

    (7) (13), ,

    T

    0.

    0

    =

    FI IU UF

    (14)

    . (14) , F, . 1.2, . F .

  • 21

    4.5.

    , L, (14) . L U. . , m n , , . . , m + n.

    ( ) ( ); .l l c cd du Li i Cudt dt= =

    ( )0 0 ( ) ,0 0

    c

    l l

    d td tdt dt

    = = =C C xui SxL Lu i

    1

    2

    1

    2

    0 ... 00 ... 0

    0. . . .0 0 ...0

    .0 0 ... 0

    0 ... 00

    . . . .0 0 ...

    n

    n

    C

    CL

    L

    L

    = =CSL

    I F, I = FI , I = FI. U = F

    TU, UL = FL

    TU, FC FLT F FT,

    .

    (14), iL uC . y(t).

    1( ) ( ( ), ( )),x t f X t A t= (15)

  • 22

    2( ) ( ( ), ( )).f X t t=y t A (16)

    (t) , .

    () (15) (16) .

    uC iL,, , , , . uC iL y, . . . , , , : x(uC1, iL1). uC1 iL1, , y(t), (15) , uC2,iL2 . . t1, t2, ..., tk. t = ti ti1 , . .

    :

    331

    2 3 5 85

    4 5 7 87

    6 8 7 8

    1 0 0 0 1 1 0 1

    , 0 1 1 1 0 0 1 1

    RRE

    C R RR

    R R LL

    R L

    iiii i i iii i i iii i i i

    = =

    (17)

    3 1 21

    2 425

    4 4 67

    68 2 4 6

    1 1 0 0 0 1 1 0

    . 0 0 1 1 0 1 1 1

    R CE

    C RCR

    R R RL

    R C R R

    u E uuu uuu

    u u uuuu u u u

    = = +

    + +

    (18)

    iL7 , uC2. iR3,

  • 23

    iR5, uR4, uR6, (17), (18) . ,

    iR3 = uR3/R3 = (E1 uC2)(R3)1,

    iR5 = uR5/R5 = (uC2 uR4)(R5)1,

    uR4 = iR4R4 = (iR5 iL7 i8)R4.

    uR4 iR5,

    iR5 = [uC2 (iR5 iL7 i8)R4](R5)1.

    iR5

    iR5 = (uC2 + iL7R4 + i8R4)R51 (1 + R4R51)1.

    uR4 = R4iR4 = R4[(uC2 + iL7R4 + i8R4)R51 (1 + R4R51)1iL7i8],

    uR6 = R6iR6 = R6(iL7i8).

    C2 L7:

    2 72 7, ,

    C LC L

    du dii C u L

    dt dt= =

    :

    ( )( ) ( )

    122

    121

    112 7 8 8

    2

    1 32 ,

    4 4 5 1 4 5

    C L

    duC i

    dt

    E u RC

    u i R i R R R R i

    = =

    = + + + +

    ( ) ( )( )

    177

    112 7 8 7 81

    7 8

    7

    4 4 4 5 1 4 57 .

    6

    LL

    C L L

    L

    diL u

    dt

    R u i R i R R R R i iL

    R i i

    = =

    + + + + = +

    (19)

  • 24

    .

    ( ) ( )

    ( ) ( )

    2 22

    7 77

    1,

    1.

    u n u nut h

    i n i nit h

    =

    =

    =t h : ( ) ( )2 7,u n i n n : ( ) ( )2 71 , 1u n i n (n1) .

    (19),

    ( ) ( )( )( )

    ( )( ) ( )

    2 2

    12

    12 11

    87 8

    1

    1 1 3

    2 ,15 1 4 5

    1 4 4L

    u n u n

    E u n R

    hC u nR R R i

    i n R i R

    = +

    + + + + + +

    ( ) ( )( ) ( )( ) ( )( )

    ( )( )

    17 7

    112 7 8

    7 8

    7 8

    1 7

    1 1 4 4 5 1 4 54

    ,1

    6 1

    C L

    L

    L

    i n i n h L

    u n i n R i R R R RR

    i n i

    R i n i

    = +

    + + + + +

    +

    ( ) ( )2 70 0, 0 0.C Lu i= =

    4.6.

    MatLAB.% 1 % e1=10;e2=20;c3=0.5e6;c4=0.2e6;r5=500;r6=300;r7=1000;l8=0.5;i9=50e3;h=7e6;% uc3=zeros(1,1000);uc4=zeros(1,1000);i8=zeros(1,1000);%

  • 25

    for i=2:1000 uc3(1,i)=uc3(1,i1)+h/c3*((e2uc3(1,i1))/r5+... (e2uc3(1,i1)uc4(1,i1))/r6uc3(1,i1)/r7i8(1,i1)i9); uc4(1,i)=uc4(1,i1)+h/c4*((e2uc4(1,i1)uc3(1,i1))/r6); i8(1,i)=i8(1,i1)+h/l8*(e1+e2+uc3(1,i1)); end% i=1:1:1000;plot(i,uc3,'r',i,uc4,'g')gridtitle(' 3 4');xlabel('t, h=7e6');ylabel('uc3, uc4')figureplot(i,i8,'b')gridtitle(' L8');xlabel('t, h=7e6');ylabel('i8')

    . 6

    . 6. 1

    3 4uc3, uc4 u

    5

    0

    5

    10

    15

    20

    25

    300 100 200 300 400 500 600 700 800 900 t, h = 7e6

    L8i8 i

    0

    0.01

    0.02

    0.03

    0.04

    0.05

    0.060 100 200 300 400 500 600 700 800 900 t, h = 7e6

  • 26

    4.7.

    1. .2. ?3. ?4. ?5. ?6. ?7. , .8. ?

    1. . ., . . . . .: . ., 2001. 479 .

    2. . . /. . . . ., 2001. 360 .

    3. . . MICROCAP6. .: , 2001. 344 .

    4. . . . .: . ., 1986.

    5. . . . .: , 1987. 127 .

    6. . ., . . : . /. ., 1987. 75 .

    7. . . /. .,1983. 72 .

    8. . ., . . . , /. ., 1992.28 .

    9. . . Design Lab 8.0 .: , 1999. 735 .

    10. : , . . /.: . . , . . ; . ., 1997. 16 .

    11. : .. /.: . . , . . ; . ., 2004. 67 .

    12. . ., . . MatLAB . .: , 2005. 320 .

  • 27

    ............................................................................ 31. , ........ 5

    1.1. ................................. 51.2. ..................................... 5

    2. .................................................. 63. ...................................................... 11

    3.1. 1 .......................................... 113.2. 2 .......................................... 12

    4. 2 .................................................................. 13

    4.1. ................................... 134.2. ................................. 164.3. ........................................ 184.4. .................................. 204.5. ................... 214.6. .......... 244.7. ............................................... 26

    .................................................. 26

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