http://pspice.narod.ru

Tрансформатор


Оторвать бы руки тому, кто так решает задачи. Однако это возможно!

Рис. 1. Схемат рансaформатора
[Maple Metafile]

>    restart:with(MSpice):ESolve(D,`TX-PSpiceFiles/SCHEMATIC1/SCHEMATIC1.net`);

`Дифференциальная система Кирхгофа {ODE}`

1/L2*int(-VOUT(t)-M*diff(JL1(t),t),t)-VOUT(t)/R2 = 0

(sin(omega*t)-V1(t))/R1+1/L1*int(-V1(t)-M*diff(JL2(t),t),t) = 0

1/L2*int(-V4(t),t)+(-V4(t)+M*diff(JL1(t),t))/R2 = 0

1/L1*int(-V3(t),t)+(sin(omega*t)-V3(t)+M*diff(JL2(t),t))/R1 = 0

`Граничные условия {ISc}`

{VOUT(0) = 0, V1(0) = 0, V4(0) = 0, V3(0) = 0}

``

MSpice v8.44:   http://pspicelib.narod.ru

Заданы узлы: {VINP} Источники: [нет источников]

Решениe: dsolve(ODE union ISc):  assign(%);

``

>    ODE:=diff(ODE,t):for i from 1 by 1 to nops(ODE) do print(eval(ODE[i])): end do;

-V4(t)/L2+(-diff(V4(t),t)-M*diff(V3(t),t)/L1)/R2

-V3(t)/L1+(cos(omega*t)*omega-diff(V3(t),t)-M*diff(V4(t),t)/L2)/R1

(cos(omega*t)*omega-diff(V1(t),t))/R1+(-V1(t)+M*V4(t)/L2)/L1

(-VOUT(t)+M*V3(t)/L1)/L2-diff(VOUT(t),t)/R2

>    dsolve(ODE union ISc): assign(%): OUT:=simplify(VOUT(t),'size');

OUT := exp(-R2/L2*t)*Int(-1/2*M/(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L1^2*R2^2)/L2*(((-L1^2*R2^2-L2^2*R1^2-2*R1*R2*M^2)*(L1^2*R2^2+(-2*L2*L1+4*M^2)*R1*R2+L2^2*R1^2)^(1/2)+(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L...
OUT := exp(-R2/L2*t)*Int(-1/2*M/(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L1^2*R2^2)/L2*(((-L1^2*R2^2-L2^2*R1^2-2*R1*R2*M^2)*(L1^2*R2^2+(-2*L2*L1+4*M^2)*R1*R2+L2^2*R1^2)^(1/2)+(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L...
OUT := exp(-R2/L2*t)*Int(-1/2*M/(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L1^2*R2^2)/L2*(((-L1^2*R2^2-L2^2*R1^2-2*R1*R2*M^2)*(L1^2*R2^2+(-2*L2*L1+4*M^2)*R1*R2+L2^2*R1^2)^(1/2)+(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L...
OUT := exp(-R2/L2*t)*Int(-1/2*M/(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L1^2*R2^2)/L2*(((-L1^2*R2^2-L2^2*R1^2-2*R1*R2*M^2)*(L1^2*R2^2+(-2*L2*L1+4*M^2)*R1*R2+L2^2*R1^2)^(1/2)+(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L...
OUT := exp(-R2/L2*t)*Int(-1/2*M/(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L1^2*R2^2)/L2*(((-L1^2*R2^2-L2^2*R1^2-2*R1*R2*M^2)*(L1^2*R2^2+(-2*L2*L1+4*M^2)*R1*R2+L2^2*R1^2)^(1/2)+(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L...
OUT := exp(-R2/L2*t)*Int(-1/2*M/(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L1^2*R2^2)/L2*(((-L1^2*R2^2-L2^2*R1^2-2*R1*R2*M^2)*(L1^2*R2^2+(-2*L2*L1+4*M^2)*R1*R2+L2^2*R1^2)^(1/2)+(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L...
OUT := exp(-R2/L2*t)*Int(-1/2*M/(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L1^2*R2^2)/L2*(((-L1^2*R2^2-L2^2*R1^2-2*R1*R2*M^2)*(L1^2*R2^2+(-2*L2*L1+4*M^2)*R1*R2+L2^2*R1^2)^(1/2)+(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L...
OUT := exp(-R2/L2*t)*Int(-1/2*M/(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L1^2*R2^2)/L2*(((-L1^2*R2^2-L2^2*R1^2-2*R1*R2*M^2)*(L1^2*R2^2+(-2*L2*L1+4*M^2)*R1*R2+L2^2*R1^2)^(1/2)+(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L...
OUT := exp(-R2/L2*t)*Int(-1/2*M/(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L1^2*R2^2)/L2*(((-L1^2*R2^2-L2^2*R1^2-2*R1*R2*M^2)*(L1^2*R2^2+(-2*L2*L1+4*M^2)*R1*R2+L2^2*R1^2)^(1/2)+(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L...
OUT := exp(-R2/L2*t)*Int(-1/2*M/(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L1^2*R2^2)/L2*(((-L1^2*R2^2-L2^2*R1^2-2*R1*R2*M^2)*(L1^2*R2^2+(-2*L2*L1+4*M^2)*R1*R2+L2^2*R1^2)^(1/2)+(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L...
OUT := exp(-R2/L2*t)*Int(-1/2*M/(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L1^2*R2^2)/L2*(((-L1^2*R2^2-L2^2*R1^2-2*R1*R2*M^2)*(L1^2*R2^2+(-2*L2*L1+4*M^2)*R1*R2+L2^2*R1^2)^(1/2)+(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L...
OUT := exp(-R2/L2*t)*Int(-1/2*M/(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L1^2*R2^2)/L2*(((-L1^2*R2^2-L2^2*R1^2-2*R1*R2*M^2)*(L1^2*R2^2+(-2*L2*L1+4*M^2)*R1*R2+L2^2*R1^2)^(1/2)+(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L...
OUT := exp(-R2/L2*t)*Int(-1/2*M/(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L1^2*R2^2)/L2*(((-L1^2*R2^2-L2^2*R1^2-2*R1*R2*M^2)*(L1^2*R2^2+(-2*L2*L1+4*M^2)*R1*R2+L2^2*R1^2)^(1/2)+(L2^2*R1^2-2*R2*(L2*L1-2*M^2)*R1+L...

>    Values(DC,RLCIV,["Vin"]); M:=0.5: omega:=300: Vin:=sin(omega*t): OUT:=evalf(OUT);

Ввод номиналов компонентов:   

R2 := .10e5, "10K"

L2 := 1, "1"

L1 := 1, "1"

R1 := 1, "1"

eqE2 := -M*diff(JL1(t),t)

eqVin := sin(omega*t)

eqE1 := -M*diff(JL2(t),t)

OUT := exp(-.10e5*t)*Int(-16.29652658*exp(9999.000025*_z1)-37.48589882*exp(-3333.666692*_z1)+.1665721585e-6*(325090000.*cos(300.*_z1)+.3002025000e11*sin(300.*_z1))*exp(.10e5*_z1),_z1 = 0. .. t)
OUT := exp(-.10e5*t)*Int(-16.29652658*exp(9999.000025*_z1)-37.48589882*exp(-3333.666692*_z1)+.1665721585e-6*(325090000.*cos(300.*_z1)+.3002025000e11*sin(300.*_z1))*exp(.10e5*_z1),_z1 = 0. .. t)

>    ploth([Vin,OUT],t=0..0.2,"2) Напряжение на входе и выходе del[Vin(t),OUT(t)]");

[Maple Plot]

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