Objective:
This experiment is about the implementation and testing of low-pass, high-pass, and band-pass filters. The frequency response of each filter is analyzed using Bode plots. The properties of passive devices will be used to explain the response.
Equipment List:
EQUIPMENT
Oscilloscope
2 Function Generators
COMPONENTS
1µF Capacitors
1 kΩ Resistors
Relevant Theory/Background Information:
A low-pass filter is a filter that allows frequencies below a cut-off frequency while filtering out frequencies above this cut-off frequency. For a simple series RC circuit, a low-pass filter can be created by connecting the input signal to the resistor and taking the output from the capacitor. The cut-off frequency f0 for the RC circuit is:
f0=12πRC
A high-pass filter is a filter that allows frequencies above a cut-off frequency while filtering out frequencies below this cut-off frequency. For a simple series CR circuit, a high-pass filter can be created by connecting the input signal to the capacitor and taking the output from the resistor. The cut-off frequency f0 for this high-pass filter has the same formula as the low-pass filter.
A band-pass filter is a filter that allows a certain band of frequencies that is bordered by a low-cut-off frequency and a high-cut-off frequency. All frequency values that are not within the band are filtered out. A band-pass filter can be generated by cascading a low-pass filter and a high-pass filter in which the cut-off of the low-pass filter is greater than the cut-off of the high-pass filter.
Experimental Data/Analysis:
PART A
The circuit diagram of the low-pass filter is shown in the following figure.
The measured voltages for the AC sweep of the filter are shown in the following table.
The output is taken from the capacitor. For low frequencies, the capacitor acts as an open circuit. Thus, effectively, the input is directly passed to the output. As the frequency increases, the capacitor slowly becomes a short circuit. Effectively, its impedance decreases, and by voltage division the voltage across the capacitor also decreases.
The corresponding Bode plot is shown in the next figure.
The Bode plot shows that the filter response allows low frequencies and attenuates higher frequencies.
An example of a low-pass filter is a wall. If somebody is playing music from another room that is closed, usually only the low frequency sounds are easily heard while the high frequencies are attenuated or even eliminated totally.
PART B
The following figure shows the circuit diagram of the high-pass filter tested in the experiment.
The results of the voltage measurements are tabulated in the following.
The output is taken from the resistor. At zero frequency, the capacitor acts as an open circuit; the impedance is infinite. As the frequency increases, the capacitor’s impedance becomes finite and approaches zero. Thus, there will be increasing voltage passed to the resistor as the frequency increases until a point wherein the capacitor acts effectively as a short circuit.
The corresponding Bode plot for the high-pass filter is shown in the following.
The high pass filter response allows the higher frequencies while it attenuates the lower frequencies.
An example of a high-pass filter is a DC choke. A DC choke filters out the DC component in a signal. A straightforward implementation of a DC choke is a single series capacitor. A DC choke is used in order to eliminate DC offset voltages that are undesirable in certain systems.
PART C
The circuit diagram of the band-pass filter is as follows:
The table of measured output voltages for this circuit is shown in the following.
The band-pass circuit in this experiment is simply a cascade of a low-pass and a high-pass circuit in which the cut-off of the high-pass filter is lower than the cut-off of the low-pass filter. At DC, both capacitors are open, thus there is no voltage passed to the output. As the frequency increases, since the high-pass filter has a higher capacitance than the low-pass filter, its capacitance reaches short circuit condition first, achieving a high-pass response on the lower frequencies. As the frequencies reach the cut-off of the low-pass filter, the capacitance of the low-pass filter slowly reaches short circuit condition, thus a low-pas filter response is achieved on the higher frequencies.
The corresponding Bode plot of these results is shown in the next figure.
The band-pass filter response shows that it only allows certain frequencies within a specified band. All the other frequency values that are not inside the band are attenuated.
An example of a band-pass filter is an audio equalizer. An audio equalizer only allows frequencies at a certain band. It balances the gains for different frequency values in order to achieve the desired acoustics. In balancing the gains, some frequencies are attenuated and some are boosted, depending on the desired sound.
Conclusion:
This experiment has successfully modeled and implemented low-pass, high-pass, and band-pass filters using only resistors and capacitors. The Bode plots acquired have verified the frequency response of the filters.
