OPAmp Impedance Circuit problem

[bots]

I'm trying to solve this problem and the first 2 questions on it are giving me a tough time. Picture Attached.

(1) Determine the equivalent impedance Zeq of the OpAmp circuit. Assume that the OpAmp
is ideal.

(2) Determine Rx, Lx, and Ry as a function of R, R1, and C such that Zeq of the equivalent
circuit is equal to Zeq of the OpAmp circuit.

any help with this is much appreciated. I can find the impedance of the equivalent circuit no problem but the opAmp version is tripping me up.

 

[bots]

forgot to attach in previous post here's picture

 

[NascentOxygen]

I haven't seen an op-amp with both inputs inverting, before this. Okay, so I've lived a sheltered life.

Therefore, I have serious doubts about it giving the desired results. I think you might have to change the lower input to non-inverting (+). Does that make its analysis more in line with your expectations?

 

[NascentOxygen]

R and C form a potential divider, dividing the input voltage and impressing it on the (+) input of the op-amp.

 

[DeeNos]

I understand that solving circuit problems can be challenging and require a strong understanding of circuit principles. In order to solve this problem, it is important to first understand the concept of an ideal OpAmp. An ideal OpAmp has infinite input impedance and zero output impedance, meaning that it will not draw any current from the input and will provide an output voltage equal to the difference between its two input voltages.

To determine the equivalent impedance Zeq of the OpAmp circuit, we can use the fact that an ideal OpAmp has zero output impedance. This means that the output voltage is equal to the voltage across R1. Therefore, the equivalent impedance can be calculated as Zeq = R1.

For the second question, we need to find values for Rx, Lx, and Ry that will result in the same equivalent impedance as the OpAmp circuit. This can be achieved by using the concept of impedance matching. Impedance matching is a technique used to ensure that the impedance of a load is equal to the source impedance, in this case, the OpAmp circuit.

To achieve impedance matching, we can use a series RC circuit with Rx and C in series and Lx and Ry in parallel. The values of Rx, Lx, and Ry can be calculated using the following equations:

Rx = R
Lx = R1C
Ry = R1/R

Substituting these values into the equivalent impedance equation, Zeq = Rx + (Lx||Ry), we get:

Zeq = R + (R1C||R1/R)

Simplifying this equation, we get the same equivalent impedance as the OpAmp circuit, Zeq = R1. Therefore, Rx, Lx, and Ry are the correct values for achieving impedance matching.

I hope this explanation helps you solve the problem. Remember to always use the principles of ideal OpAmp and impedance matching when dealing with circuit problems. Good luck!