Op-Amp w/ Inductor: vO & vS Relationship

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SUMMARY

This discussion focuses on the relationship between output voltage (vO) and input voltage (vS) in an operational amplifier (Op-Amp) circuit where an inductor replaces a capacitor. The key equation derived is vO = -L/R * dVs(t)/dt, utilizing the "virtual ground" property of the Op-Amp's inverting input. Participants emphasize the importance of understanding the "s domain," which refers to the Laplace domain, for analyzing circuits with inductors and capacitors. The discussion highlights the need for clarity on how inductors are represented in the context of Op-Amp circuits.

PREREQUISITES
  • Understanding of Operational Amplifier fundamentals
  • Basic knowledge of inductors and their behavior in circuits
  • Familiarity with the concept of the "s domain" in Laplace transforms
  • Ability to derive transfer functions for circuit analysis
NEXT STEPS
  • Study the Laplace transform and its application in circuit analysis
  • Learn about the reactance of inductors and capacitors in the s domain
  • Explore the concept of virtual ground in Op-Amp circuits
  • Practice deriving transfer functions for various Op-Amp configurations
USEFUL FOR

Electrical engineering students, particularly those in introductory ECE courses, as well as educators and professionals seeking to understand the dynamics of Op-Amps with inductive components.

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 K = -1 / R*C. The problem is, the capacitor has been replaced by an inductor.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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