Homework help: Transfer Function and Half Power Frequency

[Khesahn]

Homework Statement

I made a quick drawing of the circuit, and I apologize because I am not good at using the computer to draw circuits! Anyway, in this particular circuit R=200Ω , and L=5mH.

For part a I am supposed to find the Transfer Function H(jw) = (Vout/Vin) in terms of ω.

For part b I am supposed to find the 1/2 power frequency for this filter in hertz.

Homework Equations

None given

The Attempt at a Solution

For part a, I believe I am correct in my thinking here. I used (Vout/Vin) = Zr/(Zr+Zl) which would give me:

H(jw)= R/(R+jωL), and this would be my transfer function. I believe this is correct.

On part B I am a little confused. I am setting the magnitude of my transfer function equal to 1/√2. Therefore I would have:

[ R / √(R^2 + (ωL)^2)] = 1/√2.

After multiplying things out and simplifying my equation here, I came up with that ω=R/L. This would give me ω=(200/.005), which means ω=40000.

Considering I am supposed to find this in Hertz, I used ω=2∏f, therefore f= ω/2∏.

This would give me f = 6366Hz. Am I doing this correctly? I have one of those feelings where I am not going about this in the right way.

Thanks for your help.http://i47.tinypic.com/o5apt0.gif

 

[gneill]

Your method and results look fine.