Can anyone help me out with some values for an Opamp phase shift oscillator

[Skruffyhound]

           Hi, for the last week or so I've been working on phase shift oscillators, after breadboarding Ricks Vibracaster and reading his associated thread with R.G., I started to modify that circuit, changing out pots etc to move the frequency range higher, which to my ear sounds better as at a higher frequency I can get a more "shimmering" type sound.
           I wanted to try an Opamp version, just for interest. I have actually no idea if there is enough gain in a TLO71, for example.
           I actually tried to do the maths on this, but I am frankly out of my depth. Once the RC network becomes unequal the calculations are quite complex. I don't have any triple ganged pots so I'm looking at a double ganged (50k/100k/250k) or single pot version.
           Ideally it should oscillate around 2 to 8hz if I understand correctly, 3 to 7hz is also fine or combinations thereof.
           Can anyone with some software figure out some values of R, C and Pots for me. I have a range of common Opamps and the circuit can be any of the google-able candidates.
           I am also a little confused by the size of R_fb, if it should be 29*(R1) then with the values I've been looking at I end up with 6M4, which seems a little excessive.
           If anyone else is interested there is a very very thorough explanation here http://www.aikenamps.com/ in the tech pages/advanced, although it is all tube related, otherwise I have been breadboarding application note circuits, and checking out this calculator http://hyperphysics.phy-astr.gsu.edu/Hbase/Electronic/oscphas.html  The calculator still has me foxed.
         
           If nothing else perhaps someone could tell me if it's possible to get an Opamp to oscillate at the desired frequency, so I will know if I am barking up the wrong tree or not.
           Thanks Aston 

[frequencycentral]

Bullitt: http://www.thetonegod.com/tech/bullitt/bullitt.html

Figure 6: http://www.ti.com/sc/docs/apps/msp/journal/aug2000/aug_07.pdf

[Skruffyhound]

Thanks Rick, I had actually grazed through Opamps for everyone, but was unsure about the power supply if I ran it on 12v, and pots. I had missed that the frequency range was approximately correct, so I guess I'll breadboard it and start poking it with a stick. Andrew's Bullitt, I hadn't seen.

Still open to other offers

Edit. I just breadboarded it before I noticed the freq. was 1.65 kHz Oops, back in the dark again

[R.G.]

The quick answer is that you take any already-working phase shift oscillator and change the caps.

PSOs work on the Nyquist oscillator basis: the output signal from a nominally-inverting amplifier is put through a lossy network which causes a 180 degree phase shift at some frequency, and this is fed back to the input. This signal is then the correct phase to make the thing oscillate, but it must also be big enough. Since passive phase shift networks have some loss, the amplifier gain must be at least big enough to make up the losses. Overall, the phase shift from amplifier input, through the amplifier, through the phase shift feedback network and back to the input must have a phase shift of 360 degrees (or some multiple of that) and a total signal "gain" of at least unity (can be more) at the frequency where the phase shift is correct.

If the gain is exactly unity at the oscillation must and will be a sinusoid. If it's unity minus some tiny amount, any disturbance (noise, etc) will make it ring, but this will eventually die out. If it's over unity, the oscillation will grow until something limits it. This can be a power supply limit, clipping diodes, automatic gain compensation loop, etc. The more over unity it is at the oscillation frequency, the more distorted the output will be.

The common single-active-device PSOs use purely passive networks, usually three caps in series and three resistors to ground. For the special case where the three caps and three resistors are all equal, the loss in the feedback path is 28/29 of the signal; the amp then needs a gain of 29 to make it oscillate. If the R-C combinations are not all three the same, the loss will be more or less than 28/29, and so the gain needed will be slightly different. Most guitar effects/amps stuff use kind of this approach, but bigger gain than 29. This gets a slightly distorted sine wave, but you have some extra gain to let you diddle with the R-C values away from the "ideal" matched condition and still have it oscillate.

There are ways around this. If you allow yourself to use three active devices, one buffering each R-C network, then you don't get the losses from the RC-networks loading each other down, and the thing will oscillate with much lower gain, and have a much wider range of frequencies from varying R's.

But as I said (and wandered away from...  ) the easiest thing to do is to simply raise/lower all the caps in the phase shift string by the same amount. All 0.22s? Make them all 0.1 and the entire frequency range will be about doubled.

[Skruffyhound]

Thanks for taking the time to explain it to yet another newbie hacker R.G.
I'll get to work on it.
Learning, slowly, but learning 

[R.G.]

Thanks for taking the time to explain it to yet another newbie hacker R.G.
I'll get to work on it.
Learning, slowly, but learning 

Learning is a journey, not a destination. I'm very much still walking the path myself.