# Attenuation - two stage RC low‐pass filter

I am having trouble with finding the attenuation and bode diagrams for this circuit below.

This circuit is two stage RC low-pass filters. I have been trying to find resources on how to do them with operational amplifiers (it is my first time using them). Any help is appreciated.

Your circuit shows two cascaded $$\RC\$$ filters. You can determine the transfer function of this simple circuit using the fast analytical circuits techniques or FACTs. Simply reduce the excitation (the input voltage) to 0 V and "look" through the connecting terminals of a capacitor (which is temporarily disconnected) to determine the resistance $$\R\$$ you see. That resistance multiplied by the capacitance forms the individual time constant $$\\tau\$$ you need. The below sketch shows how to do this:

Once you have determined the time constants, you can assemble them in the way I have described in the book I wrote on the subject. The below Mathcad sheet shows the final result:

The op-amp is wired as a voltage follower and shields the filter from the load you will connect on the output. Its presence does not affect the transfer function if we consider a perfect element.

Look up "SALLEN & KEY Butterworth Filters"

• What connection is there between your answer and OP's question? If you were to ask for a kilo of potatoes, would you accept celery, instead? Apr 14, 2020 at 8:03
• The op said he was looking for resources on how to do two stage RC low pass filters with operational amplifiers as it was his first time using them. I simply tried to help by pointing him in the direction of Sallen & Key active filters. If I went into a shop and someone whispered to me that the potatoes were of poor quality then I might just consider having a salad for dinner instead. Apr 14, 2020 at 8:31
• I am having trouble with finding the attenuation and bode diagrams for this circuit below.. Your answer not only does not address OP's question, but is a particular case, Sallen-Key, Buterworth, but there are many other topologies (multiple feedback, Boctor, Friend, Deliyannis, twin-T, Tow-Thomas, ...) and many other filter types (Bessel, Pascal, Legendre, Papoulis, Chebyshev, inverse Chebyshev, Cauer, ...). Also, if I'd want to buy potatoes and someone whipered to me that they are bad, I would go somewhere else for potatoes, that's what I want, not salad. :-) Apr 14, 2020 at 8:42
• When you're a beginner you have to start somewhere and Sallen & Key Butterworth is as good a place as any.You can't try and learn them all at once, it would be overwhelming. And anyway salad would be a much healthier option. You appear to be a little too concerned ;-) Apr 14, 2020 at 8:58
• I didn't downvote, if that's what you meant. But whoever did it, most probably had the same reasons I mentioned. Apr 14, 2020 at 9:33