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### Phase shift oscillator equations way different in other book

Posted: Wed Jan 24, 2007 3:10 pm
Hi I am a electronics technician that came across equation confusion from various books for the three network phase shift oscillator circuit.One book"hints and kinks by QST"says f=(tan 60 deg)/2prc=1.73/6,28 rc=
0.28/rc. Another book "electricity,electronics and electromagnetic principles" by Robert Boylestad says: fo=1/(2xpi x square root of 6 x rc) =1/(2xpi x tan 180deg xrc);and the last book "Introduction To electronic Circuit Design" by Richard Spencer says : f=(square root of 6 /rc)/(2 x pi).
Which equation will give the correct answer? I think it's Boylestads book but when I rearrange the equation to solve for c I get :
c = 25330/fo^2 6r . I would really like to know the correct answer. I will build the circuit as in the Hints And Kinks Book and make measurements to see if their correct or not. Tim Rasch [email protected]

Posted: Wed Jan 24, 2007 3:14 pm
Hi Tim,

Could you post the circuit somewhere? That's the only way we can
tell what circuit you are dealing with.

Posted: Wed Jan 24, 2007 4:19 pm
Mr Al,I can't send the circuit from protolab or spice program .I will try to describe the network : it's a three resistor network with 10k in series and three caps .1uf going to ground from each resistor node and a output resistor from the resistor string ,10k going to -input of ua741. there is a adjustable resistor 1meg going from - input to output pin 6 of the ua741 op amp. Thats the complete oscillator circuit except for the +- vcc of 9v.
I think I have found the correct equation on the internet:F= 1/(2xpi rc )x 2.4494897 So the QST book is wrong !!! :they calculated the frequency based on 60 degrees instead of 180 degrees of the total phase shift network. Tim Rasch [email protected]

Posted: Wed Jan 24, 2007 9:00 pm
Timothy Rasch wrote:Mr Al,I can't send the circuit from protolab or spice program .I will try to describe the network : it's a three resistor network with 10k in series and three caps .1uf going to ground from each resistor node and a output resistor from the resistor string ,10k going to -input of ua741. there is a adjustable resistor 1meg going from - input to output pin 6 of the ua741 op amp. Thats the complete oscillator circuit except for the +- vcc of 9v.
I think I have found the correct equation on the internet:F= 1/(2xpi rc )x 2.4494897 So the QST book is wrong !!! :they calculated the frequency based on 60 degrees instead of 180 degrees of the total phase shift network. Tim Rasch [email protected]
Tim, I'm lazy. I simulated the RC network and got 2.44955 as the constant. probably close enough to the equation you found for government work. This assumes that the op amp has infinite bandwidth - not a very good assumption, especially with a 741, but at this frequency (~390Hz), probably OK.