Op-Amp w/ Inductor: vO & vS Relationship

[tbrownie]

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 K = -1 / R*C. The problem is, the capacitor has been replaced by an inductor.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

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

 

[berkeman]

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 K = -1 / R*C. The problem is, the capacitor has been replaced by an inductor.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

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...

 

[Zryn]

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)?

 

[DeeNos]

Hello,

Thank you for reaching out with your question. I can provide some guidance on how to approach this problem.

First, it is important to understand the basic properties of inductors and how they behave in a circuit. An inductor is a passive electronic component that stores energy in the form of a magnetic field. When a current flows through an inductor, the magnetic field around it increases, and when the current decreases, the magnetic field collapses and releases the stored energy.

In an Op-Amp circuit, the inductor can be represented in the "s domain" as a reactance, similar to how a capacitor is represented. The "s domain" is a mathematical tool used to analyze and understand the behavior of circuits with reactive components.

To find the relationship between vO and vS in this circuit, you will need to use the concept of impedance, which is the overall opposition to the flow of current in a circuit. In the "s domain," impedance is represented by the symbol Z and is a combination of both resistance and reactance.

In an Op-Amp circuit with an inductor, the output voltage (vO) is equal to the input voltage (vS) multiplied by the ratio of the inductor's reactance (XL) to the impedance of the entire circuit (Z). This can be expressed as vO = vS * (XL / Z).

To find the value of Z, you will need to use the formula for impedance in a series circuit, which is Z = √(R^2 + (XL)^2), where R is the resistance in the circuit and XL is the inductor's reactance.

In summary, to find the relationship between vO and vS in an Op-Amp circuit with an inductor, you will need to use the concept of impedance and the "s domain" representation of the inductor. I hope this helps you solve the problem on your homework set. If you have any further questions, please do not hesitate to ask.

Best of luck with your studies!

Sincerely,