Question

Design a circuit having an output given by

$-V_{\text{o}}=3V_1+5V_2-6V_3$

Short answer

The design of the circuit is

Step-by-step solution

Step 1. Given information

The given output of the circuit is given by,

$\begin{array}{l}-V_o=3V_1+5V_2-6V_3\\ V_o=-3V_1-5V_2+6V_3\end{array}$

step 2. Explanation

From the equation it can be observed that there are two negative inputs and one positive input. Therefore, there is a requirement of two op-Amps.

The circuit for the requirement is as given in the figure below.

Write the expression for the voltage generated at op-amp 2.

$\begin{array}{c}{V}_x=-10\times \left(\frac{V_3}{10}\right)\\ =-V_3\end{array}$

The generated voltage from $V_1,V_2\text{\hspace{0.17em}and\hspace{0.17em}}{V}_x$at op-amp 1 is .

$\begin{array}{c}{V}_o=-30\times \left(\frac{V_x}{5}+\frac{V_2}{6}+\frac{V_1}{10}\right)\\ =6V_3-5V_2-3V_1\end{array}$