Circuit Theory/Complex Frequency Examples/example15

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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

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

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:

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