# Algebra for Bode plots...



## SteveR (May 20, 2007)

I'm having trouble re-arranging equations for RLC circuits into a form typically used for Bode plots.

For example, see NCEES practice exam problem #114. A series RLC circuit is given. I have no problem writing the I(s)= equation for this circuit:

I(s) =(50/s)/(10 + S*.005 + 5000/s)

But this form does not lend itself to simple interpretation for a Bode plot. The final form is:

I(s) = 10,000/(S+1000)^2

My problem is knowing what algebraic transformations I need to do to get from this:

I(s) = (50/s)/(10 + S*.005 + 5000/s)

To this:

I(s) = 10,000/(S+1000)^2

Reading their solution I am clear on what they did, however, that does not help me with other problems. When looking at the raw equation written directly fromt he schematic, what are the steps you should typically go through to get the equation into the more simplified form? I"m guessing it is something like "remove fraction from denominator/numerator, change decimals to whole numbers, factor, etc., but when I try actually doing it, I don't get the equations where they need to be to write a Bode plot.


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## benbo (May 20, 2007)

Multiply both top and bottom by 200*S. The key is that you want to get rid of the 1/S in the denominator, and after that you want to eliminate the coefficient of the S^2 term in the denominator. That's the algebra for this problem, I think. There are also other ways to do this that would get rid of the 10,000 term in the denominator, but I don't want to confuse you.


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## singlespeed (May 21, 2007)

benbo said:


> The key is that you want to get rid of the 1/S in the denominator, and after that you want to eliminate the coefficient of the S^2 term in the denominator.


I agree - the basic goal is to get a polynomial in the standard form in the denominator. Practice will help you recognize where you need to go and how to get there.


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## SteveR (Jun 24, 2007)

singlespeed said:


> I agree - the basic goal is to get a polynomial in the standard form in the denominator. Practice will help you recognize where you need to go and how to get there.



Thanks, that helps...now I need to find more practice problems.


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