Question

The op-amps are ideal. Inputs: $V_{S1}=3+0.10\sin(300t)\,\text{V}$ and $V_{S2}=-2+0.11\sin(300t)\,\text{V}$. Find the {average} value of $V_0$ (rounded to two decimals).

Hint:

A midpoint of two equal resistors always gives the average of the end-node voltages—independent of other branches connected between those end nodes.

Answer 1

Correct Answer: 0.49

The buffers drive the top and bottom nodes of the resistor ladder to $V_{S1}$ and $V_{S2}$. The right branch is two equal resistors in series, so the mid-tap gives the average of the end potentials: \[ V_0(t)=\frac{V_{S1}+V_{S2}}{2}. \] Hence the time-average is \[ \overline{V_0}=\frac{\overline{V_{S1}}+\overline{V_{S2}}}{2} =\frac{3+(-2)}{2}=\frac{1}{2}=0.50~\text{V}, \] since the averages of the sinusoidal parts are zero.