Transfer function of Op-Amp circuit

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Discussion Overview

The discussion revolves around the transfer function of an operational amplifier (op-amp) circuit, focusing on the challenges of deriving the transfer function in terms of frequency (ω) and preparing Bode plots. Participants explore mathematical manipulations, the use of Laplace transforms, and the implications of different forms of the transfer function for Bode plotting.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in converting impedance to frequency (ω) for their transfer function.
  • Another participant suggests that the gain expression already contains ω and questions the original poster's approach.
  • There is a discussion about the necessity of using Laplace transforms, with some arguing that it is not required for Bode plots.
  • Participants debate the correct form of the transfer function for Bode plotting, emphasizing that the numerator should be in terms of jw and the denominator should be real.
  • Concerns are raised about the range of frequencies on the semilog plot, with one participant noting that critical values exceed the available cycles.
  • Another participant mentions the importance of maintaining the correct form of the transfer function and avoiding unnecessary substitutions.
  • There is confusion about the significance of a pole at ω=1 and its implications for the slope of the Bode plot.
  • Participants discuss the need to sketch Bode plots based on given values and the importance of accurately representing the gain and phase characteristics.

Areas of Agreement / Disagreement

Participants do not reach consensus on the necessity of using Laplace transforms, the interpretation of the pole at the origin, and the correct approach to preparing Bode plots. Multiple competing views remain regarding the mathematical manipulations required for the transfer function.

Contextual Notes

Limitations include potential missing assumptions about the familiarity with Laplace transforms and Bode plot conventions. There are unresolved mathematical steps in the derivation of the transfer function and its representation in the frequency domain.

  • #31
Maylis said:
View attachment 69736

Just to show you what was going on in my head.

Some great news as a result of telling me to find the magnitude at w=10^7 rad/s. I just imputed the function into my calculator, and I discovered that my calculator is able to find the magnitude of complex expressions. Then I just did 20 log [magnitude] and got 60 dB! I never knew.

Coolsville!
But - I literally can't make he
 
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  • #32
Maylis said:
View attachment 69736

Just to show you what was going on in my head.

Some great news as a result of telling me to find the magnitude at w=10^7 rad/s. I just imputed the function into my calculator, and I discovered that my calculator is able to find the magnitude of complex expressions. Then I just did 20 log [magnitude] and got 60 dB! I never knew.

Coolsville! Do you undrstand why w=1e7 is a good choice? Not too big, not too small? That's critical.

But - I literally can't make heads or tails of your latest attachment. It's sideways & half is missing.
 
  • #33
No I was just showing the number 10 on top with the db underneath that was all the image was supposed to be.

Does the phase plot look good?
 

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