a better sine wave

  
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This one is actually a bit simpler to explain: the op-amp is set up with 25. 50x amplification, i. e almost a comparator (with 50x amplification, a 50 mV input above or below the 2. 5V will drive the output to its limit). And indeed, the output signal of the op-amp looks somewhat like a heavily clipped sine wave: The 3 resistors and 3 capacitors crea
a better sine wave - schematic

te 3 RC low-pass  filters in series, removing all the higher frequencies, i. e. harmonics. A fairly clean sine wave comes out at the end, as you can see here: The frequency is determined by phase shifts . Each RC filter changes the phase of its input signal, and it will be by 60 ° at a certain frequency, so that 3 of them in series will then shift it by 180 °. Since the signal is fed back to the -  pin of the op-amp, that`s exactly the proper signal to generate the opposite output, i. e. shifted 180 ° out of 360 °. This analog stuff gets complicated don`t worry too much about it: just pick R and C values to get the right frequency, and make all of them the same. I used 0. 1 µF caps i. s. o. 10 nF caps, i. e. 10x larger than the original circuit. With these values, the oscillation in my setup turned out to occur at just about 440 Hz, i. e. a pure musical A  tone! I did have to increase the gain (1. 5 M © / 55. 2 k © = 27 in the above setup) to force oscillation. I changed RF to 1 M © and RG to 22 k ©, for a gain of 47. This RG value is a bit low, it loads down the last RC section quite a bit. What you`re seeing here is a classical example of a negative feedback loop, which ends up in a very stable state of oscillation. It oscillates because we`re delaying the feedback signal by about 2. 27 ms through the RC chain. So the op-amp constantly overshoots around its mid-point (the 2. 5V applied to the +  input), but does so...



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