Question

Purpose: Use Laplace transforms to find the time domain response of a RLC band-pass filter to step and impulse inputs Vout Vin L=27 mH For the RLC circuit above Find the s-domain transfer function: Find the impulse response h(t) H(s) = Vout(s)/Vin(s) · These operations must be performed by hand using Laplace transforms, do not use MATLAB or a circuit simulator. We will verify your hand calculations in lab. Hints: To find the transfer function, find the equivalent impedance of the inductor and capacitor in the s-domain, then use a voltage divider equation to find Vout(s) Vin(s). To find h(t), you will need to perform partial fraction expansion and then apply inverse Laplace transforms to get back to the time domain. (When I performed the partial fraction expansion, my poles were complex! I also used Mathcad, instead of a calculator, to do my math calculations --which made things very easy.)