Instrumentation Dr. Xiaofeng Wu 1 1

Note Quiz 1: Date: 02/05/2013 Time: 1 hour

Differential Equation with Capacitor or Inductor

Laplace Transfer Function Differential operator S

First Order Filters Low pass filter: High pass filter:

Second Order Filters Low pass filter High pass filter Band pass filter Band stop (Notch) filter

Example 1 The circuit diagram as shown is a second order band-pass filter. Design this filter to have k=1, ω0=1000 rad/s and Q=1. If Vs(t)=u(t), find v0(t) for time t>0.

Inverse Laplace Transform

Laplace Transform Pairs (p665)

Example 2 Find the inverse Laplace transform of

Example 1 The circuit diagram as shown is a second order band-pass filter. Design this filter to have k=1, ω0=1000 rad/s and Q=1. If Vs(t)=u(t), find v0(t) for time t>0.