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The objective of this Lab activity is to: 1. Construct a Band Pass Filter by cascading a low pass filter and a high pass filter and obtain the frequency response of the filter.
A Band Pass Filter allows a specific range of frequencies to pass, while blocking or attenuating lower and higher frequencies. It passes frequencies between the two cut-off frequencies while attenuating frequencies outside the cut-off frequencies.
One typical application of a band pass filter is in Audio Signal Processing, where a specific range of frequencies of sound are desired while attenuating the rest. Another application is in the selection of a specific signal from a range of signals in communication systems.
A band pass filter may be constructed by cascading a High Pass RL filter with a roll-off frequency fL and a Low Pass RC filter with a roll-off frequency fH, such that :
The Lower cut-off frequency is given as:
The higher cut-off frequency is given as:
The Band Width of frequencies passed is given by:
All the frequencies below fLand above fH are attenuated and the frequencies between are passed by the filter.
Figure 1: Band Pass Filter circuit
We can also use the formula for the LC resonance to calculate the center frequency of the band pass filter, the resonant frequency ωo is given by:
To show how a circuit responds to a range of frequencies a plot of the magnitude ( amplitude ) of the output voltage of the filter as a function of the frequency can be drawn. It is generally used to characterize the range of frequencies in which the filter is designed to operate within. Figure 2 shows a typical frequency response of a Band Pass filter.
Figure 2: Band Pass Filter Frequency Response
ADALM2000 Active Learning Module
Solder-less breadboard, and jumper wire kit
1 1.0 KΩ resistor
1 0.047 µF capacitor
1 10 mH inductor
Build the circuit presented in Figure 3 on the solderless breadboard.
Figure 3: Band Pass Filter circuit
Figure 4: Breadboard connections of the Band Pass Filter circuit
The band pass filter frequency response can be plotted using the Network Analyzer tool. Compute the center frequency of the filter using equation (4). According to this you will set the start and stop frequencies of the logarithmic sweep. For this filter the center frequency is 7.3 KHz. In the network analyzer set the start frequency at 1 KHz and the stop frequency at 20 KHz. Set the minimum phase at -90 the maximum phase at 90. Magnitude axis can be set from -30 dB to 10dB. In Figure 5 is presented the transfer function of the filter obtained by running the network analyzer.
Figure 5: Frequency response of Band pass filter circuit
In the Signal Generator tool, on Channel 1, generate a waveform with the frequency value in the pass band of the filter and analyze it's response. Observe on the oscilloscope channel 1 the input signal and the output signal on channel 2. In Figure 6 you can see the filter input and output for a 7kHz sine waveform.
Figure 6: Input and output signals of Band pass filter circuit for 7kHz input frequency
Compute the cut-off frequencies for each Band Pass filter constructed using the formula in equations (1) and (2). Compare these theoretical values to the ones obtained from the experiment and provide suitable explanation for any differences.
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