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Date Posted: 7/22/2008 1:41:52 AM  Status: Live
Low-pass filter
Course Textbook Chapter Problem
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Question Details:
The figures below show the response of a passive Low-Pass Filter.

a) Specify the values of R and C so that the filter has the frequency response shown
above.
b) If the sensor signal (input to the filter) is:
vsensor(t) = 0.1 + 0.9 sin (2t) + 1.8 sin (100t) + 0.2 sin (500t)[V]
Estimate the filter output, vout(t).
[Hint: use the plot to find amplitude & phase at the different forcing frequencies.]
c) Estimate the RMS power consumed in the filter.

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Date Posted: 7/22/2008 6:10:45 AM  Status: Live
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Response:
Given magnitude plot :
 
    
 
From the above plot maximum voltage gain
At cutoff frequency the gain can be reduced to 0.707.
From the graph we can say that cutoff frequency
Cutoff frequency of a RC low pass filter
(a)
Assume  then
 
(b)
Given sensor input
This signal is having a dc voltage 0.1 whose frequency = 0 rad/s.
And this having three harmonic signals with frequencies 2rad/s, 100rad/s and 500rad/s.
Due to cutoff frequency of the filter;
 and  components will be blocked. (in ideal case)
And 0.1 and  components will be allowed. (in ideal case)
So output signal  
In practical case (in practical case) 
 
(c)
RMS power consumed by the filter =
                                                   = .
 
I hope this will helps you..................
 



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