Simple transfer function question

In summary, the conversation discusses finding the transfer function and magnitude of an RLC circuit with all impedances in series and the output voltage (Vo) in the resistor (R). The equations and attempt at a solution are provided, with the assumption that R, C, and L are all equal to 1. The final magnitude result is questioned and further help is requested.
  • #1
tadm123
14
0

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.
 
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  • #2
Hi tadm123. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif


Remember that j^2 = -1
 
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  • #3
tadm123 said:
assuming that R=C=L=1



whence this assumption?
 

1. What is a transfer function?

A transfer function is a mathematical representation of the relationship between the input and output of a system. It describes how the output of a system changes in response to a change in the input.

2. How is a transfer function related to a system's frequency response?

A transfer function is used to calculate the frequency response of a system. The frequency response shows how a system responds to different frequencies of input signals.

3. What is a simple transfer function?

A simple transfer function is a transfer function that has only one input and one output variable. It is often used to describe simple systems, such as first-order systems.

4. What is the difference between an open-loop and a closed-loop transfer function?

An open-loop transfer function describes the relationship between the input and output of a system without accounting for any feedback or control. A closed-loop transfer function takes into account the effects of feedback and control on the system's output.

5. How is a transfer function used in control systems?

A transfer function is an essential tool in control systems as it allows engineers to design and analyze the behavior of a system. It is used to determine stability, performance, and other characteristics of a control system.

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