# Transfer Function of circuit

Discussion in 'Homework Help' started by champ01, Apr 7, 2015.

1. ### champ01 Thread Starter New Member

Aug 22, 2012
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0
Trying to find the transfer func of the circuit attached, in laplace

My answer I got was: Vo(s)/Vi(s) = R1 / (sCR1 + sCR2 + 1)(sL + R1)

Just wondering if anyone can verify my answer?

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2. ### champ01 Thread Starter New Member

Aug 22, 2012
10
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with verification I was just wanting to know if I got the right answer or not, not for anyone to solve it for me.

3. ### t_n_k AAC Fanatic!

Mar 6, 2009
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In reality one has to solve it to verify your result anyway.

As a comment only, perhaps it would have been more informative if you had expanded the function to show a second order polynomial (a*s^2 + b*s +c) in the denominator.

I believe you have an error in what would be the 's' term coefficient in the aforementioned denominator expansion. The 's^2' and constant terms in the expanded denominator polynomial look OK.

4. ### MrAl Distinguished Member

Jun 17, 2014
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515
Hi,

Yes i agree there is something wrong. You should not get a term with R1^2 in it.
Try again, then post result.

Aug 22, 2012
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6. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Still looks incorrect. The negative sign in the final result is puzzling.

7. ### champ01 Thread Starter New Member

Aug 22, 2012
10
0
are my first three equations of circuit analysis correct? could be my algebra needing a brush up

8. ### MrAl Distinguished Member

Jun 17, 2014
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515
Hi,

Sorry that still does not look right.

Also, your final result should be in the form of two polynomials, one numerator and one denominator:

Hs=N/D=(a*s^2+b*s+c)/(d*s^2+e*s+f)

where a and/or b may be zero, and no coefficients will be negative.

9. ### WBahn Moderator

Mar 31, 2012
18,085
4,917

But look at this equation:

Always, always, ALWAYS check your units!

sL has units of impedance
R has units of impedance

what are the units on that last fraction? It's unitless. Can you add a unitless quantity to an impedance?

This means that everything beyond this point (that uses this equation) is guaranteed to be wrong and was a waste of time. ALWAYS track and check your units as you go.

10. ### MrAl Distinguished Member

Jun 17, 2014
2,551
515
Hi,

Yeah it just looks like an algebra problem when equating the far right current i3 to i2.

11. ### champ01 Thread Starter New Member

Aug 22, 2012
10
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I've re-worked again:

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12. ### MrAl Distinguished Member

Jun 17, 2014
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515
Hi,

That may be right, but still not in the right form. You should multiply out the denominator so you have only one polynomial in the denominator and only one in the numerator, with no fractional parts in either.
So this is an example:
5/(s^2*2+3*s+5)

while this is not in proper form yet:
10/(s^2*2/R1+3*s/R1+5)

because of the divisions.

Sometimes you keep the divisions, but that's for a different reason.

Mar 31, 2012
18,085
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