Simple transfer function question

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SUMMARY

The transfer function for the given RLC circuit, where all impedances are in series and Vo is across the resistor, is derived as H(s) = s/(s^2 + 1 + s). Assuming R, C, and L are all equal to 1, the frequency response is expressed as H(ω) = jω/(−ω^2 + 1 + jω). The magnitude of the transfer function is calculated as |H(ω)| = ω/sqrt(ω^4 + ω^2 + 1). The user expresses uncertainty regarding the accuracy of the magnitude calculation.

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tadm123
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Homework Statement


Find the transfer function of an RLC circuilt and the magnitude. (All the impedances are in series) and the Vo is in the R. Vi is the source voltage.


Homework Equations





The Attempt at a Solution



So transfer function of the circuit => Vo/Vi = R/ (sL+1/sC + R)

solving all this and assuming that R=C=L=1
I get

H(s)= s/(s^2+1+s)

H(ω)= jω/(j^2*ω^2+1+j*ω)

For the magnitud I get :

|H(ω)|= ω/sqr(ω^4+ω^2+1)

But I think the magnitude is wrong, please help.
 
Last edited:
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Hi tadm123. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif


Remember that j^2 = -1
 
Last edited by a moderator:
tadm123 said:
assuming that R=C=L=1



whence this assumption?
 

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