How Do You Determine the Critical Frequency in a Bode Plot Equation?

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SUMMARY

The critical frequency in a Bode plot can be determined by analyzing the transfer function given by the equation 2/((jw)^2 + 54jw + 44). To find the critical frequency, substitute s = jω into the equation and factor the denominator. The roots of the denominator must be real to identify the corner frequency accurately. This process eliminates any imaginary components that may arise during calculations.

PREREQUISITES
  • Understanding of Bode plots and frequency response analysis
  • Familiarity with complex numbers and the substitution s = jω
  • Knowledge of polynomial factorization techniques
  • Experience with control systems and transfer functions
NEXT STEPS
  • Study the process of finding critical frequencies in transfer functions
  • Learn about the significance of corner frequencies in Bode plots
  • Explore polynomial root-finding methods for real roots
  • Investigate the impact of damping ratios on frequency response
USEFUL FOR

Electrical engineers, control systems analysts, and students studying signal processing or frequency response techniques will benefit from this discussion.

fractal01
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Given an equation like 2/((jw)^2 +54jw +44), how would you find the critical frequency?

I am getting a umaginary number and I am sure this is not true, please help!
 
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fractal01 said:
Given an equation like 2/((jw)^2 +54jw +44), how would you find the critical frequency?

I am getting a umaginary number and I am sure this is not true, please help!

Let s = jω and write your equation using s. You should be able to factor the denominator and hence pick out any critical frequencies (I'm assuming that by 'critical frequency' you also mean 'corner frequency' for the Bode plot). (Also, the roots of the denominator should be real).
 
fractal01 said:
Given an equation like 2/((jw)^2 +54jw +44), how would you find the critical frequency?

I am getting a umaginary number and I am sure this is not true, please help!

What equation?
 

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