# Operational amplifier circuit with one ac and one dc voltage source

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.

• The graph looks correct. May 27 '14 at 19:01
• OK, what about the rest of the solution? For example is the expression of Vout(t) = 2 - Vs(t) I found correct?
– mgus
May 27 '14 at 19:30
• 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? May 27 '14 at 20:07
• 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.
– mgus
May 27 '14 at 21:39