Homework help: Transfer Function and Half Power Frequency

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SUMMARY

The discussion focuses on calculating the Transfer Function H(jω) for a circuit with a resistor (R=200Ω) and an inductor (L=5mH). The transfer function is derived as H(jω) = R/(R+jωL). For the half power frequency, the user sets the magnitude of the transfer function equal to 1/√2, leading to the equation R/√(R² + (ωL)²) = 1/√2. The user correctly calculates ω as 40000 rad/s and converts it to frequency (f) as approximately 6366 Hz using the formula f = ω/(2π).

PREREQUISITES
  • Understanding of transfer functions in electrical circuits
  • Familiarity with complex impedance (Zr and Zl)
  • Knowledge of frequency calculations in terms of angular frequency (ω)
  • Basic circuit analysis involving resistors and inductors
NEXT STEPS
  • Study the concept of Transfer Functions in control systems
  • Learn about the significance of half power frequency in filters
  • Explore complex impedance calculations for RLC circuits
  • Investigate the relationship between angular frequency and frequency in electrical engineering
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in filter design and analysis will benefit from this discussion.

Khesahn
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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
 
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Your method and results look fine.
 

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