4_MAE 334Woodward - lab5

4_MAE 334Woodward - lab5 - Unfortunately it is not always...

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MAE 334 – LAB 5 4 At the filter cutoff frequency the amplitude of the input signal is reduced to 0.707 of the input and the phase is shifted by 45 degrees. The transfer function is commonly displayed on a Bode plot in decibels (dB) = 20 log 10 | H(f) | vs. log 10 ( f/f c ), see Figure 2. Pay particular attention to the -3 dB point on the amplitude plot and the -45 degree point on the phase angle plot. Bode Plot of Single Pole Low Pass Filter -17 -15 -13 -11 -9 -7 -5 -3 -1 1 0.001 0.010 0.100 1.000 10.000 log(2 π fRC) Amplitude (dB) Figure 2. Amplitude of the frequency response function of a passive single pole low pass filter. Phase Angle of Single Pole Low Pass Filter -90 -80 -70 -60 -50 -40 -30 -20 -10 0 0.001 0.010 0.100 1.000 10.000 log(2 π fRC) Phase Angle (degrees) Figure 3. Phase angle of the frequency response function of a passive single pole low pass filter.
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Unformatted text preview: Unfortunately it is not always convenient to create an impulse in the laboratory. Besides, it is often the frequency response function which is desired anyway. Therefore it is useful to inquire as to whether the frequency response function can be obtained directly. It is important to remember that both the frequency response function and the impulse response function contain the same information – if either is known, both are known since they are a Fourier transform pair. Using the properties of the delta function and Fourier transform it can be shown that the output to a sine wave input is: [ ] ( ) ( ) cos 2 ( ) y t H f f t f πφ = + (11)...
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This document was uploaded on 01/03/2011.

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