Solving for Bode Critical Frequency: Guide and Equation Explanation

  • Thread starter Thread starter fractal01
  • Start date Start date
  • Tags Tags
    Bode Frequency
Click For Summary
SUMMARY

The discussion focuses on determining the critical frequency from a given Bode plot represented by the transfer function G(jω) = 2/(-ω² + 162jω + 320). The user initially misinterprets the equation leading to an invalid solution involving the square root of a negative number. The correct approach involves substituting s = jω, transforming the transfer function to G(s) = 2/(s² + 162s + 320), which reveals that the denominator has negative-valued roots corresponding to the angular frequencies of interest.

PREREQUISITES
  • Understanding of Bode plots and their significance in control systems.
  • Familiarity with transfer functions and their representations.
  • Knowledge of complex numbers and their manipulation in engineering contexts.
  • Basic concepts of root finding in polynomial equations.
NEXT STEPS
  • Study the derivation and interpretation of Bode plots in control theory.
  • Learn about the Routh-Hurwitz stability criterion for analyzing system stability.
  • Explore the use of MATLAB for plotting Bode diagrams and analyzing transfer functions.
  • Investigate the implications of pole locations on system response and stability.
USEFUL FOR

Control engineers, electrical engineers, and students studying system dynamics who need to analyze and interpret Bode plots and transfer functions.

fractal01
Messages
13
Reaction score
1
I am given a bode plot and have to label the cutoff frequency on there.
G(jw)=2/(-w^2 +162jw +320)

I got this equation where w is the critical frequency:
70922=81^2 + (170 -(w^2/4))

I am sure that this is wrong since I get the sqrt of a negative number for w.

It would be really great if someone could help!
 
Physics news on Phys.org
-ω2 is equivalent to (jω)2. So let s = jω and your transfer function becomes:
$$\frac{2}{s^2 + 162s + 320}$$
The denominator has a pair of negative valued roots which should correspond to (angular) frequencies of interest.
 

Similar threads

Engineering How Can I Find the H-infinity Norm of a Transfer Function?
  • · Replies 1 ·
Replies
1
Views
3K
Engineering How do I draw the Bode diagram of this transfer function?
  • · Replies 3 ·
Replies
3
Views
3K
Identifying type of feedback by looking at bode plot
  • · Replies 1 ·
Replies
1
Views
2K
Engineering Bode plot for active low pass filters
  • · Replies 9 ·
Replies
9
Views
5K
PLL - How to find all the gains of a PI corrector and fix Ki ? MATLAB
  • · Replies 2 ·
Replies
2
Views
2K
Bode plots and crossover frequency
  • · Replies 4 ·
Replies
4
Views
8K
How to find cutoff frequencies from Bode plot?
  • · Replies 2 ·
Replies
2
Views
30K
Bode Plot Matlab Homework: High Pass Filter
  • · Replies 3 ·
Replies
3
Views
4K
Engineering Analyzing the Nyquist Curve for a 5th Order System
  • · Replies 3 ·
Replies
3
Views
2K
Get transfer function from bode plot
  • · Replies 1 ·
Replies
1
Views
4K