MATLAB: Electrical Systems

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Figure below shows a circuit made up of two RC circuits. Find the dynamic equations of the system.

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$\%$ Variables KVL$1$ KVL$2$ eqn$1$ eqn$2$ ee

$\%$ for symbolic declaration R$1$ R$2$ C$1$ C$2$ ee e$1($t$)$ e$2($t$)$ De$1($t$)$ De$2($t$)$

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De$1=$diff$(e1)$

De$2=$diff$(e2)$

$\%$ Write the KCL equation for node voltage, e$1.$

$\%.$ Use Ohm's law and the current through a capacitor to rewrite the KCL equation for node voltage, e$1,$ in terms of ee$,$ e$1,$ e$2,$ R$1,$ R$2,$ and C$1.$

KVL$1=$

$\%$ Write the $KCL$ equation for the node voltage, e$2.$

$\%$ Use Ohm's law and the current through a capacitor to rewrite the KCL equation for node voltage, e$2,$ in termis of e$1,$ e$2,$ R$2,$ and C$2.$

KVL$2=$

$\%$ Solve equation for ee$.$

eqn$1=$

$\%$ Solve equation for e$1.$

egn $2=$

$\%$ Use algebra to substitute one equation into the other and solve for the dynamic equation.

eqn$1$ eqn $1,$ Ihs $($eqn$2),$ rhs $($eqn$2))$

$e=rhs(eqn1)$

$\%$ simplify equation to solve for the dynamic equation.

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