2NoiseWhite noiseEqual intensity at all frequencies.60Hz noise is a frequent signal picked up in electronic circuits, most noticeably in audio systems as a low frequency hum that is located between A# (58.27Hz) and B (61.74 Hz).Such applications require a high Q/narrow BW notch filter that will remove the noise without impacting the strength of the signal.
3Twin T Notch FilterDesign an adjustable Twin T notch filter to remove the 60 Hz signal.Application noteAs shown in passive filters experiment, the parasitic resistance of an inductor limits the bandwidth of an RLC notch filter.
4Twin T Notch FilterOperates by phase shifting the signals in the different legs and adding them at the output.At the notch frequency, the signals passing through each leg are 180 degrees out of phase and cancel out to provides a complete null of the signal.Components are required to have values that are very close to the nominal values to achieve a high Q notch at the design frequency.
9Transfer Functionwhere s = jw, w = 1/CR, and a is the fraction of the trim pot resistance R4 that is connected to the input terminal of U2.
10Twin T Filter Use an LM 324 op amp chip. V+ should be +9V, V- should be -9V.Either a 10 kW trim pot or a set of resistors that add up to 10 kW may be used for R4.
11PSpice Use two resistors instead of a trim pot. Perform three simulations of the Twin T notch filter.Set the resistors value to 9k/1k, 5k/5k, and 1 k/9 kWPlot the power as a function of frequencyMacro in Trace/Add Trace is DB()Determine center frequency, , and bandwidth,for each value of RBandwidth is the difference in frequency between the -3dB points of the output signal.Calculate Q where
12Measurements When measuring the characteristics of the Twin T filter Use the Velleman function generator as Vs of the notch filter.Set the voltage so that it does not cause the output of the operational amplifiers in the filter to saturate.Use the Bode Plot at a high resolution to measure the performance of the notch filter around 60 Hz.Measure center frequency and bandwidth of the notch when the trim pot resistance is approximately 1k, 5k, and 9 kWCalculate the Q of the filter
13Velleman Function Generator To create a arbitrary waveshape using MATLAB, you must first install the support package for Velleman PCSGU250. This is available on the MathWorks website.Follow the instructions posted on the Week 9 module to download and install this package.
14MATLAB codeIn the example file – makeSampleLibs.m, which is linked in Week 11 module, lines create a library file called AMWave that can be used by the Velleman scope.The program at the moment creates a wave shape called AMWave that is sin(f)*sin(20f), where f is the frequency that you set on the Velleman function generator.The file is saved under c://Velleman/PCSGU250_DLL/lib
15Waveform for this experiment Modify the makeSampleLibs.m file so that a wave shape created is a sum of three sinusoids with equal amplitudes: sin[(2p55Hz)t]+sin[(2p60Hz)t]+sin[(2p65Hz)t]Write the code so that 60 Hz is the frequency that should be set on the arbitrary function generator.
16To Output the Waveform Click on MORE FUNC. Click on LIB A pop-up window open.Click on LIBFind the correct library file name (AMWave, if you didn’t change it) in directory: c://Velleman/PCSGU250_DLL/libSet the frequency to 60 Hz.Set the amplitude to obtain accurate voltage measurements.
17Bode PlotTo see the notch, you will have to set the Frequency Step Size, located under Options, to a small percentage of the total range when the bandwidth of the notch is small.Note: You can pause the Bode Plot measurement, change the frequency step size, and then unclick the Pause button to vary the speed at which the data is collected.