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.© BrainMass Inc. brainmass.com December 24, 2021, 8:42 pm ad1c9bdddf
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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:© BrainMass Inc. brainmass.com December 24, 2021, 8:42 pm ad1c9bdddf>