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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).

initial circuit

Step 1: Let's ignore dc source and find the output. The equivalent circuit is: 2nd circuit

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: 3rd circuit
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):

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

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    \$\begingroup\$ The graph looks correct. \$\endgroup\$
    – Andy aka
    May 27 '14 at 19:01
  • \$\begingroup\$ OK, what about the rest of the solution? For example is the expression of Vout(t) = 2 - Vs(t) I found correct? \$\endgroup\$
    – mgus
    May 27 '14 at 19:30
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    \$\begingroup\$ This is what you asked "I want to know if it's correct". I said yes it is. What's the drama about the rest of the solution AND surely, if I think the graph is correct and it peaks at +3 volts and troughs at +1V this must imply something dude? Maybe you are expecting a pat on the back or a medal? \$\endgroup\$
    – Andy aka
    May 27 '14 at 20:07
  • \$\begingroup\$ Easy, please. I am not expecting any medal and I don't think I disrespected you. I just wanted an answer for the solution as a whole. \$\endgroup\$
    – mgus
    May 27 '14 at 21:39
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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.

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