circuit analysisfilterlow passoperational-amplifier
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.
The two filters have similar amplitude responses, but different phase responses. In other words, different harmonics of the original square wave are being delayed (phase shifted) by various amounts by the first filter, but they have a more nearly constant delay (linear phase shift) in the second filter.
While the two waveforms look very different on an oscilloscope, they do actually have essentially the same harmonic content, and will sound very similar if not identical to the ear. Human hearing is actually very insensitive to phase relationships of this sort.
It's relatively difficult to build linear-phase filters in the analog domain, while it's quite easy to do in the digital domain, particularly with an FIR filter. But you need to decide whether the results differ enough in your application in order to make the effort.
"Oscillation frequency" is a term that describes the frequency where the input-output phase relationship is exactly zero degrees i.e. if this filter were part of a circuit used as an oscillator it would oscillate at this frequency. Sometimes oscillation frequency is quoted at 180 degrees phase shift (inverting filter configurations)
It doesn't mean the circuit on its own will oscillate. Look at the results of an RLC low pass filter: -
Clearly this circuit doesn't oscillate but, all the same, it has an oscillation frequency.
Best Answer
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.