1. Twin T Notch Filter

2. Noise
White noise
Equal 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.

3. Twin T Notch Filter
Design an adjustable Twin T notch filter to remove the 60 Hz signal.
Application note
As shown in passive filters experiment, the parasitic resistance of an inductor limits the bandwidth of an RLC notch filter.

4. Twin T Notch Filter
Operates 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.

5. Twin T Circuit

6. Redrawn to highlight T’s
Zo1 io
io1
Zo2
io2

7. At the center frequency
Ideally, io1 - io2 = 180 and magnitude of Zo1 = Zo2 at the center frequency of the Twin-T filter.
This will force Vo = 0V at f = fo.

8. Adjustable Twin T Notch Filter

9. Transfer Function
where 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.

10. Twin 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.

11. PSpice 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 kW
Plot the power as a function of frequency
Macro in Trace/Add Trace is DB()
Determine center frequency, , and bandwidth,
for each value of R
Bandwidth is the difference in frequency between the -3dB points of the output signal.
Calculate Q where

12. Measurements 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 kW
Calculate the Q of the filter

13. Velleman 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.

14. MATLAB code
In 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

15. Waveform 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.

16. To Output the Waveform Click on MORE FUNC. Click on LIB
A pop-up window open.
Click on LIB
Find the correct library file name (AMWave, if you didn’t change it) in directory: c://Velleman/PCSGU250_DLL/lib
Set the frequency to 60 Hz.
Set the amplitude to obtain accurate voltage measurements.

17. Bode Plot
To 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.