Circuit Theory/Complex Frequency Examples/example15



Find everything give that:
 * $$V_s = 10 * e^{-100t} \cos(6000t)$$

Terminal Relations:
 * $$\mathbb{V}_2 = R_1 * \mathbb{I}_2$$
 * $$\mathbb{I}_3 = C_1 * s * \mathbb{V}_3$$
 * $$\mathbb{V}_1 = L_1 * s * \mathbb{I}_1$$
 * $$\mathbb{V}_4 = R_2 * \mathbb{I}_1$$

Junction Equation:
 * $$\mathbb{I}_1 - \mathbb{I}_2 - \mathbb{I}_3 = 0$$

Loop Equations:
 * $$\mathbb{V}_3 + \mathbb{V}_1 + \mathbb{V}_4 - \mathbb{V}_s = 0$$
 * $$\mathbb{V}_3 - \mathbb{V}_2 = 0$$ (trivial loop)

Complex Frequency:
 * $$ s = -100 + 6000j$$

Complex frequency source:
 * $$ \mathbb{V}_s = 10$$

Solving in the complex frequency domain: