Solving for 3dB frequency appproximations

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SUMMARY

The discussion focuses on finding the lower cutoff frequency (3dB point) for the transfer function F(s) = s^3 / ((s+12)(s+550)(s+680)). The user is instructed to substitute s with jw and solve for the frequency where the magnitude equals 1/sqrt(2). The challenge lies in handling the imaginary component 'j' and calculating the magnitude of the complex number derived from the transfer function.

PREREQUISITES
  • Understanding of transfer functions in control systems
  • Familiarity with complex numbers and their magnitudes
  • Proficiency in using a TI-84 calculator for complex calculations
  • Knowledge of 3dB frequency concepts in signal processing
NEXT STEPS
  • Learn how to calculate the magnitude of complex numbers in MATLAB
  • Study the application of the Bode plot for frequency response analysis
  • Explore the use of Python libraries like NumPy for solving transfer functions
  • Investigate the implications of 3dB frequency in filter design
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Students in electrical engineering, signal processing enthusiasts, and anyone involved in control systems analysis will benefit from this discussion.

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Homework Statement



I have the transfer function:

F(s) = s^3 / ((s+12)(s+550)(s+680))

Find the lower cutoff frequency (3dB point)

Homework Equations



s = jw

The Attempt at a Solution



I set the equation equal to 1/sqrt(2), use s = jw, and try to solve for the frequency. Now I'm just supposed to "Put it into your calculator and off I go", but what exactly do I put into my calculator? I have a Ti-84, is that able to solve these types of problems?

What's throwing me off is the imaginary term 'j', I'm not exactly sure what to do with it when solving this polynomial.
 
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You need to find the magnitude of a complex number.

It's |a + jb| = sqrt(a^2 + b^2).

So find a and b for your transfer function and set the magnitude = 1/sqrt(2).
 

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