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# State Space Equation

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For the given circuit diagram, select the state variables as a subset of nodal current and loop voltage. Also determine the state space equation and transfer function of the circuit. Please look at the attached file for further details.

Kindly give a detailed step by step solution.

https://brainmass.com/engineering/electrical-engineering/state-space-equation-303066

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Please see attached file for the solution to the given problem.

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Solution: The state variables we will use are as follows:

The state-space equations we will have using nodal analysis and mesh analysis are:

The output equation y(t) is equal to:

We will have the following state-space equations in matrix form:

The output equation in matrix form is:

To get the transfer function, we need to get the Laplace transform of each state-space equations and the output equation. We will have:

Since the output requires the inductor current, we will equate the state-space equations in terms of inductor current:

Substitute it to the equation of the output, we have the transfer function of:

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