Engineering Bode Plot Slope based on frequencies

AI Thread Summary
The discussion focuses on determining the Bode plot slope across different frequency ranges, highlighting a gain from 0 to 10^3 ω, another gain from 10^3 to 10^5 ω, and a constant slope from 10^5 ω to infinity. Participants explore how to calculate dB gain using the transfer function's magnitude and the relationship between poles and zeros. The transfer function is derived as H = (-ω^2 LC)/(jω RC - ω^2 LC + 1), with its magnitude calculated for analysis. Identifying poles from the quadratic denominator is crucial, as they dictate the system's frequency response characteristics. Understanding whether poles are real or complex and their damping factors is essential for accurate Bode plot construction.
guyvsdcsniper
Messages
264
Reaction score
37
Homework Statement
Give numerical values of ω that define the ranges where ω can be written as a power law and give the Bode-plot slope in each range, using decibels per dec or oct
Relevant Equations
db=log(v2/v1)
From 0 to ##10^3## ##\omega## there is a dB gain, from ##10^3## to ##10^5## there is another. Finally from ##10^5## to infinity the slope is constant (0).

I know the formula
$$dbV= 20log_{10}\frac{V_2}{V_1}$$

can give me the slope but that is in terms of Volts, but I have frequency and the magnitude of the transfer function. I cant find a formula in my book or online to calculate the dB gain with these two.

Is there an approach to determining the slope of each with the information given in the image?

Screenshot 2023-09-25 at 12.16.55 PM.png
 
Physics news on Phys.org
Have you learned the concepts of "poles" and "zeros" yet, and how they affect the transfer function?
 
berkeman said:
Have you learned the concepts of "poles" and "zeros" yet, and how they affect the transfer function?
I have, each pole corresponds a 6dB/oct gain.

So i'm guessing I would need to take the magnitude of the transfer function and evaluate in the limit of low mid and high frequencies?

I calculated the transfer function to be:
$$H = \frac{-\omega^2 L C}{j\omega RC-\omega^2 LC+1}$$
and then found its magnitude:
$$\lvert{H}\rvert = \frac{\omega^2 LC}{\sqrt{(\omega^4 LC+(\omega LC)^2-2\omega^2 LC+1}}$$

Am I going to have to take the quadratic equation of the denominator to find the poles?
 
guyvsdcsniper said:
Am I going to have to take the quadratic equation of the denominator to find the poles?
Basically yes. But since they haven't given you the component values, the real task here is to recognize the various shapes a quadratic frequency response can take and identify where the poles are from the given plot. Look in your lecture notes about constructing a quadratic bode plot using asymptotes.

Hint: Quadratics always have two poles, identifying whether they are real or complex is an important first step in analysis. If they are complex, then you want to get an idea about the damping (or quality factor Q) to proceed. If they are real, you can treat it as two separate 1st order responses combined together.

This article may be helpful, although it doesn't show the plots.
https://www.physicsforums.com/threads/an-engineers-approach-to-the-quadratic-formula.1053797/
 
  • Like
Likes guyvsdcsniper

Similar threads

Back
Top