Electrical Systems

Electrical networks are first represented by equivalent circuits consisting of three passive linear components: resistors, capacitors, and inductors.

These components are combined into circuits, with input and output decided, and the transfer function is found using Kirchhoff's laws.

In an RLC circuit, the transfer function that relates the voltage across the capacitor to the input voltage can be derived using Kirchhoff's voltage law.

This yields an integro-differential equation for the network, assuming zero initial conditions.

Variables are initially changed from current to charge, followed by applying the voltage-charge relationship for a capacitor.

Taking the Laplace transform of this equation and simplifying it leads to the transfer function for this circuit.

Impedance is a transfer function similar to resistance but applicable to capacitors and inductors.

Transfer functions can also be obtained using Kirchhoff's current law, using nodal analysis.

The currents in the system are composed of the current flowing through the capacitor and the current that circulates through the series resistor and inductor.

After simplification, the same outcome for the transfer function is achieved.