Final answer:
The transfer function for a CR circuit is derived using Kirchhoff's laws and Laplace transforms, resulting in the form H(s) = 1/(1+sRC), where R is resistance, C is capacitance, and s is the complex frequency variable.
Step-by-step explanation:
The transfer function for a CR circuit (capacitor-resistor circuit), which is a first-order system, can be found by analyzing the circuit's differential equation that relates the input voltage to the output voltage across the capacitor.
This involves using Kirchhoff's laws to derive an equation for charge and current as functions of time and then transforming this into the s-domain using Laplace transforms.
The result is a transfer function in the form of H(s) = 1/(1+sRC), where R is the resistance, C is the capacitance, and s is the complex frequency variable in the Laplace transforms.
The transfer function characterizes the frequency response of the circuit and can be used to understand how the circuit behaves under different input conditions.