I don't normally like to generate a wall o' text and scare people away, but since the questions were asked...
As with any oscillator it's necessary to get 360° phase shift around the feedback loop. In the classic phase shift oscillator the three phase shift networks provide a total phase shift of 180° at a frequency determined by the RC time constants. The gain stage provides an additional 180° phase inversion plus sufficient loop gain to give oscillation at that frequency. In theory, two RC networks are able to give almost 180° phase shift. In practice, 3 networks are always used to ensure operation. Because the 3rd RC network need provide only a small amount of phase shift, it's perfectly acceptable to have it as a fixed network, and adjust only the other two. So, a dual gang potentiometer is fine. This will still give a good range of adjustment. In my particular application, I only needed to go from about 250 to 1000 Hz, but a wider range of adjustment should be possible. I think a 10:1 frequency ratio should be achievable. And of course, the minimum and maximum frequencies of the oscillator can be changed by using different component values.
Explain why you have use the diode with this fashion.
The back to back diodes look very much like a clipper, which would be counterproductive in a sine wave oscillator. It's better to think of them as non linear resistors combined with the series capacitor to give a non linear RC network. What they do is provide increasingly aggressive attenuation to harmonics while leaving the fundamental alone. Thus, they eliminate distortion, rather than add to it. The series capacitor needs to be sized to suit the frequency range of the oscillator for this to work correctly.
I dislike the extremely simple single resistor biasing the transistor so one with high hFE is saturated and one with low hFE is cutoff. It also happens as the battery runs down.
Sure, your sinewave looks excellent. But at a frequency not shown and a level also not shown. Change either and it stops oscillating or the diodes show their clipping action.
Lowpass filters work in a phase-shift oscillator made with an opamp because its input impedance is much higher than a transistor, its distortion is much less than a transistor and its voltage gain is much higher.
To address Audioguru's comments:
I agree that the single resistor biasing goes against traditional 'good' design practice. The reason why I did this was twofold:
1. I needed to operate this from a single 5 volt supply and still get a reasonable output amplitude. Using a more conventional phase splitter type bias arrangement would give more stable bias, but would limit the output amplitude. (Since the supply voltage in the current application is higher, there's no reason why the bias arrangement couldn't be changed.)
2. Modern components have a much smaller variance of parameters than they did years ago when these biasing arrangements were first analyzed. So, we don't see as much variation in HFE as we did back in our youth. Thus, the single resistor between collector and base is nowhere near as bad as we were taught to believe. With the transistor that is specified, there's little risk of problems. On the other hand if you use an unmarked general purpose transistor from Uncle Fred's House o' Parts, then there are no guarantees.
As for the use of lag filters rather than lead filters, I've never seen it done anywhere in the literature. I have tried it in my own experiments, and it's never worked. One of the problems is that this arrangement is stable at DC, and so there is no need for the circuit to oscillate. If you are aware of a phase shift oscillator that uses lag networks, I am truly interested in seeing it.
Frequency range for this specific example is as I indicated in the previous post: 250-1000 Hz. Amplitude is fairly constant across that range at about 3.5 Vp-p with a 5 volt supply. Across that range, the waveform is very clean, and looks the same as the one I posted.
Regarding the back to back diode thing, see my comments above.
I just want to say that I don't randomly post dubious circuits I've found on the 'net. However, if I happen to have a simple circuit that I know performs very well, such as this one, then I will post it. If you want to replace the single transistor with an op amp, then go right ahead. I don't have a problem with it. It should perform well either way.
The primary reason why I do post very simple one transistor circuits such as this one is that I believe the purpose of this forum should be to educate. And, transistors are the fundamental building blocks of electronic circuits. While op amps certainly have their uses, they are like the electronic version of french fries. Anyone can take frozen french fries out of the freezer and throw them in the oven, and maybe try to convince themselves they are a chef, but if you handed the same person a potato and a potato peeler they would likely starve to death. The transistor is the unpeeled potato of electronics. You can do amazing things with them that are not greasy at all.
Also, I should point out that the OP has never explicitly stated the required frequency range for his application. This is important to know. If we're talking GHz, then everything that's gone before is all for naught.