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Sallen-Key High Pass Filter on Line Voltage: Looking at Noise - by Robbie

This idea traces back to the book "The Art of Electronics" by Paul Horowitz, Winfield Hill. I enjoy pulling this book out and reading through it from time to time, and I came across this experiement. I did it, but I wasn't happy with the results that a simple, passive filter can provide. I wanted to create something that would reject 60Hz voltage "with extreme prejudice." I use quotes around that phrase because an English professor once told me he would "grade with extreme prejudice if I didn't put the assigment number in the top, right-hand corner of the header."

I still have a passive filter in the circuit, but I am also using two, second-order Sallen-Key active filters to further reject anything below 300Hz. At 300Hz, I think it rejects at -6dB. Using Multisim simulation I estimated that using all three filters, 60Hz should be attenuated by -76dB. There should be around 800nV of ripple at 60Hz. This should be fun!

Design and Calculations:

Quite a bit of math is involved with figuring out filters. Passive filters are really easy. The cutoff frequency is simply: 1/(2PI*RC) where R is in ohms and C is in Farads. This gives you the frequency in Hertz. I want the cutoff frequency to be 300Hz. I'll also go ahead and assume that I will use a .1uF (.0000001F) capacitor. Using the given formula I get a resistor that is close to 5.1k ohms (5100 ohms).

Much more math goes into designing a Sallen-Key filter. I've used CodeCogs Equation Editor to make these easier to read. First we need to convert the cutoff frequency from 300 Hertz to radians per second. Also assume that we will use .1uF capacitors for this as well. If the calculations don't work out, we could always choose a different starting point.

Convert Hertz to radians per second

Convert Hertz to radians per second

Next, we need to select a second order Butterworth low pass prototype. We will then use the low pass to high pass transformation to convert our prototype to the high pass configuration. We will plug in 's' to find our high pass formula.

Butterworth 3dB low pass prototype

low pass to high pass transform

high pass transfer function

high pass transfer function

high pass transfer function

high pass transfer function

b0

b1

Find resistors 1 and 2

Find resistors 3 and 4

Gain

Gain

Gain resistor calculation

R3

R4

We now have all of the calculations to design our Sallen-Key high pass filter. Now we just need to plug our results into a schematic. Some of the results were not standard, so the values may differ a little for the resistors.

The picture below contains the calculations for the 2kHz cutoff filter. Notice a pattern?

Hand calculations for a Sallen-Key with a cutoff of 3kHz

Precautions:

This is a project that deals with mains voltages. Shielding your mains connections in a box is recommended. Informing anyone in your lab that you are working with high voltage is important. Tech-Tut.com and its owners are not responsible for injuries or damages. Perform this experiment at your own risk.

Photos and Diagrams:

Schematic

Transformer diagram

Below is a video showing how to build the circuit on a breadboard. There is no sound or anything remotely entertaining about it. :) It is important to note that I did not have enough 5.1k resistors in my parts bin. I used some loose resistors to make them. I also did not follow my Fritz to the jumper. I didn't want to have to strip that many jumper wires. I just used the long leads to make the connections. Either way you attempt this project, the video or the Fritz should get you there.

Fritz - http://fritzing.org/download/

Bill of Materials:

Results (fc=300Hz):

The below screenshots from my oscilloscope show that there is a little noise on the line, but I'm not really able to pick out anything in particular. The noise level isn't that high in comparison to the voltage level at 60Hz. I think that picking a higher cutoff frequency would provide a better outlook.

5ms per division, 200mV per division 2.5ms per division, 200mV per division 1ms per division, 200mV per division

250us per division, 200mV per division 50ns per division, 50mV per division - could this be noise from my scope? 25ns per division, 50mV per division - could this be noise from my scope?

Results (fc=2kHz):

The 25ns screenshots for the above results was scope noise. When not connected it has a tiny amount of noise. After trying out the circuit with 2kHz as the new cutoff frequency, I found a strong 5kHz frequency on the line voltage. This time the 60Hz was pretty much non-existent. I wonder what kind of information that waveform contains below.

5ms per division, 50mV per division 1ms per division, 50mV per division 1ms per division, 50mV per division - Scrolled horizontally

The first screen shot below shows an FFT from my scope. You can clearly see the 5kHz band. The second screen shot shows some periodic blips, and the third screen shot shows a close up of one of the blips.

FFT 10us per division, 50mV per division 50ns per division, 50mV per division

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