Переходные процессы в электрических цепях (E=150 В, L=0,09 Гн, R1=300 Ом, R2=300 Ом, R3=600 Ом, C=5 мкФ, ключ размыкается), страница 4

Величина	t<0	t=0		t®∞
		По законам Кирхгофа	По уравнениям	По законам Кирхгофа	По уравнениям
i1 (t) [A]			0.25		0.125
i2 (t) [A]	0		0.167	0	0
i3(t) [A]			0.083		0.125
uR1(t) [B]			75		37.5
uR2(t) [B]			25		37.5
UR3(t) [В]	0		50		75
UC [B]			75		112.5
UL [B]	0		0	0	0

11. Операторный метод

I3(p)

I2(p)

I1(p)

Составим систему уравнений в операторной форме:

                                                                                                                                                     (69)

Подставим начальные условия:

и преобразуем систему (69) относительно :

                                                                                                                                                     (70)

                                                                                                                                                     (71)

                                                                                                                                                     (71)

                                                                                                                                                     (72)

                                                                                                                                                     (73)

                                                                                                                                                     (74)

                                                                                                                                                     (75)

Перейти от изображения к оригиналу с помощью теоремы разложения (76):

                                                                                                                                                     (76)

Найдём производную полинома F₂:

                                                                                                                                                     (77)

Подставляем корни:

                                                                                                                                                     (78)

                                                                                                                                                     (79)

                                                                                                                                                     (80)

Т. о.                                                                                                                                                      (81)

Формула (81), полученная операторным методом, совпадает с формулой (61), полученной с помощью классического метода.

12. Расчёт методом переменных состояния