the frequency of oscillation of a rc phaseshift oscillator is
where N is the number of rc stages....
please tell me how we can arrive at this expression ..... i can't find out a proper derivation...thanks in advance..
The expression (for a high-pass RC oscillator) is correct for N=3. If you increase the number of RC stages, the oscillation frequency increases. So the general expression is obviously wrong.
thank you .. can u please tell me how to select R and C accordingly for 4 stage rc to get 180 degree phase shift ,say for 1KHz frequency??
and also.. in 3 stage .. can i assume C and find R using the above eqn.. or should there be any other relation between r and c for 180 degree phase shift ?
As said, the frequency expression for the 3 stage RC-oscillator in the link is correct, you'll also find it at Wikipedia (with an exact derivation). But the network equations for the coupled RC circuit are rather long winded. Thus I prefer a simulator (e.g. LTSpice) to calculate the transmission function and oscillation frequency.
thank you .. can u please tell me how to select R and C accordingly for 4 stage rc to get 180 degree phase shift ,say for 1KHz frequency??
and also.. in 3 stage .. can i assume C and find R using the above eqn.. or should there be any other relation between r and c for 180 degree phase shift ?
An expression for the 4 stage network is given there:
"Calculate R to complement C at oscillation frequency. There is no trivial way to estimate the oscillation frequency better than within a factor of two or so short of using the derived equations. A 3-section RC uses f = 1 / (2 * pi * SQRT(6) * R * C), but we have a four section RC, so we use the following: *
f = 1 / (2 * pi * SQRT(10 / 7) * R * C) (for a 4-section RC)
R = 1 / (2 * pi * SQRT(10 / 7) * f * C)"
You can also find a description of a method for solving the network here:
Hi Electrician, the given formula for the 4-element phase shift oscillator is not correct. The factor in the denominator D must be: SQRT(7/10)
In case somebody is interested in the derivation - here it is:
The transfer function H(s) for 4 equal RC sections (T=RC) in series can be calculated (by hand or using a symbolic analyzer ) to be:
There are two possible ways to arrange a 4 stage phase shift network using equal Rs and Cs; see the image. You have obtained a result for one of them. Repeat your calculations for the other topology and compare the results. Then look again at the circuit in the web page:
**broken link removed**
and tell me if you still think there is an error there.
I used the free version of SIMetrix SIMPLIS to look at phase shift vs frequency for the two circuits you showed in post 9, with R=10K and C=100nF.
One of the formulas predicted F=190.23Hz, while the other predicted F=133.16. In the simulation, those were the frequencies where phase shift=180 degrees for the two circuits. So - good agreement between theory and simulation.
If you're looking for good free simulation software, I recommend SIMetrix SIMPLIS.
Free simulation software I've tried:
CircuitMaker "student edition":
Very easy to use, with a nice user interface, but has serious bugs - sometimes gives wildly wrong answers.
LTSpice:
Very good but difficult to use - has a user interface from hell IMHO.
SIMetrix SIMPLIS:
Good and easy to use - best of both worlds.
There are two possible ways to arrange a 4 stage phase shift network using equal Rs and Cs; see the image. You have obtained a result for one of them. Repeat your calculations for the other topology and compare the results. Then look again at the circuit in the web page:
and tell me if you still think there is an error there.
OK, I see - and I agree that the formula cited by you was for a high-pass phase shift network.
On the other hand, I must confess, thinking of a phase shift oscillator only the low-pass version comes into my mind immediately (because of its advantages if compared with the high-pass version).
Therefore, I have derived the formula for this kind of phase shift network only. But, of course, the same principle can be applied for the high-pass section.
By the way: In post#8 once I have used the term "resonant frequency". This obviously is not correct. It is simply the "oscillation frequency".
LvW