saimani lab 9 - TITLE: LAB-9: Fourier Analysis and Filter...

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TITLE: LAB-9: Fourier Analysis and Filter Design NAME: SAIMANI KUMAR M.N.V (11554210) SECTION: 062 PARTNER: Ravneet Kaur TA: Kaloyan Popov DATE PERFORMED: 27 th Nov 2009 DATE DUE: 2 nd Dec 2009 DATE RECEIVED:
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Objective: The objective of this experiment is to learn about Fourier Series and design a third-order low pass filter. A periodic signal is passed through the filter and the effect of the filter on the signal is observed. The low pass filter is built and the output signal is captured on the oscilloscope and the frequency response of the filter is captured using LabVIEW. PSpice is also used to simulate the circuit and plot the input and output voltages obtained along with the frequency response of the filter. Maple is also used to calculate the coefficients of the Fourier Series of the output signal when the periodic square wave is passed through the filter, and also to display its plot. The frequency responses obtained from all the three methods is compared. Circuit Diagrams: Fig. 1: Circuit Diagram of a third-order low pass filter with R=60, L=38.8mH, C1=4.34uF and C2=13.016 uF and a cut-off frequency at f c =320Hz
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Figure 2: Schematic diagram of the Third-Order Low Pass Filter with R1 =60, L=38.8mH, the resistance of the inductor = 50, C1=4.34 uF and C2=13.016 uF and a cut-off frequency at f c =320Hz. A 1V square wave of a frequency of 320 Hz is applied as input.
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Figure 3: Schematic diagram of the Third-Order Low Pass Filter to perform transient analysis with R1 =60, L=38.8mH, the resistance of the inductor = 50, C1=4.34 uF and C2=13.016 uF and cut-off frequency at f c =320Hz. A 1V square wave of a frequency of 320 Hz is applied as input.
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Data Sheet: Part 1 : First, the third order filter designed as shown in the Sample Calculations section (See Figure 1) is constructed, and a unit square wave having a frequency of 400Hz is applied as its input. The measured values of the resistances and capacitances used in the third-order filter are: R1 =60, L=38.8mH, C1=4.34 uF and C2=13.016 uF The voltage gain is calculated which is the ratio of the output voltage to the input voltage. The voltage gain in dB is calculated at each of the above three frequencies using the equation: Equation 1 The voltage gain obtained at each of these frequencies is tabulated as follows: Input Frequency (Hz) Gain (V/V) Gain (dB) 32.000 0.950 -0.445 320.00 0.299 -10.49 3200.0 0.021 -33.55 Table 1: The gains at each of the frequencies the sine waveform is applied to the low- pass filter As observed from the above table, the voltage gain is the highest and is almost close to unity when the input signal has the lowest frequency. This means that the output signal is passed through the filter without attenuation. As the frequency of the input signal is increased to 320 Hz which is the corner frequency of the low pass filter, the voltage gain is reduced by almost 65%. The voltage gain becomes 0 when an input signal has a high frequency meaning that the signal is
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saimani lab 9 - TITLE: LAB-9: Fourier Analysis and Filter...

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