Circuit Theory/Complex Frequency Examples/example15

RC parallel, RL series circuit for example 15 circuit theory wikibook .. simple problem with complex frequency

solved with mupad /code/

put in phasor form with matlab /m-file/

Find everything give that:

$V_s=10*e^{-100t}\cos (6000t)$

Terminal Relations:

${𝕍}_2=R_1*{𝕀}_2$

${𝕀}_3=C_1*s*{𝕍}_3$

${𝕍}_1=L_1*s*{𝕀}_1$

${𝕍}_4=R_2*{𝕀}_1$

Junction Equation:

${𝕀}_1-{𝕀}_2-{𝕀}_3=0$

Loop Equations:

${𝕍}_3+{𝕍}_1+{𝕍}_4-{𝕍}_s=0$

${𝕍}_3-{𝕍}_2=0$ (trivial loop)

Complex Frequency:

$s=-100+6000j$

Complex frequency source:

${𝕍}_s=10$

Solving in the complex frequency domain:

Symbol	Magnitude	Radians	Degrees
v1	13.8329	0.0455	2.6061
v2	3.8425	-3.0978	-177.4894
v3	3.8425	-3.0978	-177.4894
v4	0.4611	-1.5270	-87.4894
i1	0.2305	-1.5270	-87.4894
i2	3.8425e-04	-3.0978	-177.4894
i3	0.2305	-1.5253	-87.3939