Op-Amp w/ Inductor: vO & vS Relationship

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    Inductor Op-amp
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Discussion Overview

The discussion revolves around the relationship between the output voltage (vO) and the input voltage (vS) in an operational amplifier circuit where a capacitor has been replaced by an inductor. Participants explore the implications of this change, particularly in the context of an integrator circuit and the use of the "s domain" for analysis.

Discussion Character

  • Homework-related
  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant describes their homework problem involving an operational amplifier similar to an integrator circuit, noting the challenge of replacing a capacitor with an inductor and seeking guidance on the relationship between vO and vS.
  • Another participant proposes a potential relationship: vO = -L/R * dVs(t)/dt, but does not confirm its correctness.
  • A request is made for a circuit diagram and derivation of the proposed equation, indicating a desire for clarification on the analysis process.
  • One participant explains that the 's-domain' refers to the Laplace domain and discusses the concept of reactance in relation to capacitors, suggesting that the analysis should consider the transfer function of the circuit.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the correct relationship between vO and vS in the context of an inductor in an operational amplifier circuit. Multiple viewpoints and approaches are presented, but no consensus is reached on the solution or methodology.

Contextual Notes

There is a lack of clarity regarding the application of the 's domain' in this specific scenario, and participants have not fully defined the assumptions or parameters necessary for deriving the relationship between vO and vS.

tbrownie
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Alright, so I have a problem on my homework set that features an Operational Amplifier. It's very similar to a "Integrator" Circuit which means the gain would be.. K = -1 / R*C. The problem is, the capacitor has been replaced by an inductor. I'm trying to find the relationship between vO and vS but there is nothing in my book or notes detailing what to do with an inductor in an Op-Amp. I've been searching around for help, and was told to think about how capacitors and inductors are represented in the "s domain." I don't even know what the "s domain" is, this is just a basic ECE 201 class. We just started learning about capacitors, inductors, and Op-Amps. Am I missing something?
 
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Would the answer be... -L/R * dVs(t)/dt?
 
tbrownie said:
Alright, so I have a problem on my homework set that features an Operational Amplifier. It's very similar to a "Integrator" Circuit which means the gain would be.. K = -1 / R*C. The problem is, the capacitor has been replaced by an inductor. I'm trying to find the relationship between vO and vS but there is nothing in my book or notes detailing what to do with an inductor in an Op-Amp. I've been searching around for help, and was told to think about how capacitors and inductors are represented in the "s domain." I don't even know what the "s domain" is, this is just a basic ECE 201 class. We just started learning about capacitors, inductors, and Op-Amps. Am I missing something?

tbrownie said:
Would the answer be... -L/R * dVs(t)/dt?

Can you show the circuit and how you derived that equation? I think you are on the right track. You just use the "virtual ground" property of the "-" input of the opamp to write the current and voltage equation there...
 
The 's-domain' is the Laplace domain.

Normally when you analyze a resistive Op-Amp circuit you look at the resistances and figure out the transfer function (circuit gain).

Capacitors don't have a resistance per se, they have a reactance. Do you know what the formula is for the reactance of a capacitor, and then what this looks like in the Laplace domain (hint: it will have an 's' variable in it somewhere)?
 

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