2_MAE 334Woodward - lab5

2_MAE 334Woodward - lab5 - The low pass filter drawn in...

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MAE 334 – LAB 5 2 The low pass filter drawn in Figure 1 can be modeled as a first order differential equation of the form: F y dt dy RC = + If F(t) is the input signal and y(t) the output. This equation has the following general solution: = t RC t d e RC F t y / ) ( 1 ) ( ) ( (4) following equations (1), (2) and (3) we conclude / 1 0 () 00 tRC et ht RC t = < (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 delta or 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=0 is 1. + = ε δ 1 ) ( dt t Therefore ε can be as small as we please. If we subject our filter to an impulse function,
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