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Instrumentation Dr. Xiaofeng Wu 1 1

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

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**Differential Equation with Capacitor or Inductor**

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**Laplace Transfer Function**

Differential operator S

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First Order Filters Low pass filter: High pass filter:

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**Second Order Filters Low pass filter High pass filter Band pass filter**

Band stop (Notch) filter

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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.

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**Inverse Laplace Transform**

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**Laplace Transform Pairs (p665)**

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Example 2 Find the inverse Laplace transform of

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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.

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