MAE 334 – LAB 5 2The low pass filter drawn in Figure 1 can be modeled as a first order differential equation of the form: FydtdyRC=+If F(t)is the input signal and y(t)the output. This equation has the following general solution: ∫∞−∆−−∆⎥⎦⎤⎢⎣⎡∆=tRCtdeRCFty/)(1)()((4) following equations (1), (2) and (3) we conclude /10()00tRCethtRCt−⎧≥⎪=⎨⎪<⎩……(5) You should recognize this as a standard first order system response function of the same form as used to describe the thermocouple in lab 2 and the calorimeter in lab 3. In this case the time constant, τ, would be RC, the resistance and capacitance values. The Impulse Response of the Low Pass Filter Recall that the deltaor impulse function, δ(t), is zero at all times except t = 0, where it is infinite and that it is infinite in such a way that integral for any time that includes t=0is 1. ∫+−=εδ1)(dttTherefore εcan be as small as we please. If we subject our filter to an impulse function,
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