Operational amplifier circuit with one ac and one dc voltage source

Question

The following circuit contains ideal operational amplifier, Vs voltage is sinusoidal with amplitude of 1Volt and frequency of 1kHz, where VE is a dc voltage of 2Volts. I am trying to use superposition principle to find the output voltage. Also I want to draw a diagram of Vs(t) and Vout(t) versus time. First, suppose we ignore positive and negative power supply of the op-amp(they are not shown on the circuit I was given).

Step 1: Let's ignore dc source and find the output. The equivalent circuit is:

So Vout1(t) = -(R2/R1) * Vs(t) = -Vs(t) (inverting amplifier)
Step 2: Let's ignore ac source and find the output. The equivalent circuit is:
So Vout2 = Vin * (1 + R1/R2) (non-inverting amplifier)
= VE * (R4/(R3 + R4)) * (1 + R1/R2)
= 2 * (2000/(2000 + 2000)) * (1 + 1)
=2Volts

Finally, Vout(t) = Vout1(t) + Vout2 = 2 - Vs(t) Is that method I followed correct?

Also, T = 1/f = 1/1000Hz = 0.001sec

So a graph I created is the following (supposing that Vs(t) is a sinusoidal signal with initial phase 0 degrees):

I know the graph is not very good but I want to know if it's correct. Thanks.

Answer 1

Yes, correct. Superposition can be applied in a variety of situations regarding op. amps. For example, when doing capacitive AC coupling on input. The analysis is divided betwween AC and DC sections. Remember there is a lot of other details in practice (correct biasing, saturation, noise, stability, CMRR, frequency response, etc.) for proper working.