RC Network

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electric leazenby

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Mishawaka , IN
I am taking semiconductors in my third year class. In the section called oscillators there is a question that asks: The phase shift components are .02 microfarad capacitors and 15 kilo ohm resistors. At what frequency will the network produce a phase shift of 180 degrees?
My book gives the formula 1/15.39xRC. My instructor said it is brought up every year. Where do they get the constant 15.39? He has offered extra credit if anyone can find out. Thank you
 
Welcome to the Forum. :)

Can you tell us the configuration of the network? And the number of sections in the network?

It has to be more than one section or you could not get that great a phase shift.


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131115-2111 EST

In a network of one resistor and one capacitor the maximum possible phase shift is 90 degrees. By virtue of the answer the question is incomplete. To get useful output you will need at least a three stage RC filter. You might think that two stages will produce 180 degrees, but the output is zero.

Thus, precisely what was the actual question?

A favorite question by A. D. Moore in his senior design class was --- what is the maximum phase shift in an RC network? The usual student answer was 90 degrees. But that is wrong because the word network was used in the question, and that does not limit the network to a single RC.

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131115-2146 EST

Since this is a homework problem I hope no one gives you a direct answer, but you should certainly provide a more complete statement of the problem. Then we might provide you guidance in you thinking.

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The answer is 216.5 Hz. I was trying to find out where the constant 15.39 comes from, because the book does not tell you. Electricians talk found the it is 2x3.14x sqrt of 2x3. Which is great. Still not sure why the sqrt 2x3. Thank you all I appreciate it.
 
131117-1244 EST

electric leazenby:

One can get all sorts of incorrect answers by misapplying an equation or entering the wrong values. Because you use a calculator and get an answer to 5 decimal places does not mean the answer is accurate or correct.

You are correct to question where 15.39 comes from. But you have not yet provided a precise statement of the problem. Until you define the circuit you can not determine where 15.39 comes from or whether it is the correct constant.

Is this an engineering or trade school type of class?

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electric leazenby said:
The answer is 216.5 Hz. I was trying to find out where the constant 15.39 comes from, because the book does not tell you. Electricians talk found the it is 2x3.14x sqrt of 2x3. Which is great. Still not sure why the sqrt 2x3. Thank you all I appreciate it.
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Welcome to the forum.:thumbsup:
 
If you look at the link in bob's post you will see a square root of 2n. The 2 is there because of the math and the 3 is there because it is a three stage network, which you still have not confirmed.

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Thank you all. I appreciate your help, so I will try to answer all your questions. I am a proud third year apprentice for the NJATC/IBEW. Semiconductors was removed from our curiculum. My instructor realizes its importance, so we are taking it anyway; however we have gone through it very fast, because of the rest of our requirements. I did not want to sound stupid explaining the network. There is 3 stages obviously by being numbered. A capacitor in each with a resistor to ground capacitors to base of transistor. Emitter to ground. Collector is parallel to rl then v out.
I plan to continue my education after becoming a JIW. My wife's sister froze to death a few years back. I am more the determined to succeed. The more money I make the more people I can help out. Again thank you all. I hope to be smart enough to pay it forward someday.
 
131117-1945 EST

electric leazenby:

If you have a three stage RC network made up of identical resistors and capacitors, then how much phase shift is required from each stage to achieve a 180 degree total shift?

Given the number of stages, therefore, knowing the phase shift per stage, then approximately at what frequency will a 180 degree phase shift occur for a given set of R and C values?

If you put an operational amplifier between each stage, then what is the exact frequency of oscillation?

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Since this appears to be a school problem or related to one, I will answer with some questions:

1. If, at some specified frequency, the total phase shift must be 180 degrees and each of the three stages will produce an identical phase shift, what must that phase shift be?

2. If I add an amplification stage between two RC stages, will it change the amplitude?
Will it change the phase?
If it changes only the amplitude, will that affect the oscillator frequency?

An ideal amp will have a phase shift of either 0 or 180 degrees. Any other behavior would result from inductive, capacitive, or time delay effects which would make it other than an ideal amplifier or require an external feedback network.

What an op amp can do is prevent the parallel load of the next stage affect the calculated phase shift of the proceeding stage.
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121117-2355 EST

electric leazenby:

Experimentally build the circuit you described, measure the frequency, and see what is the experimental constant. I believe you find it is not 15.39 . Note: you will need to adjust your components to get near the specified values. Within 1% should be OK. 1 % resistors are easy to obtain. Capacitors will need to be sorted and smaller ones paralleled with the larger to create close capacitors. 1% capacitors are too expensive.

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