Question

Design a circuit that will produce the following output:

$v_o=2.0{\int }_0^t{v}_{1}dt-6.0(v_2+v_3)$

Short answer

The circuit will contain an integrator whose output signal along with two other input signals is fed to a summing amplifier.

Step-by-step solution

Step 1. Given Information

Given a mathematical function and asked to design a circuit that performs the given function.

Step 2. Explanation

Here, the mathematical function is the result of an integrator circuit whose output signal along with two other input signals is fed to a summing amplifier.

The circuit can be designed as follows;

The output of the integrator circuit is given by;

$v_o\text{'}=\frac{-1}{1\times {10}^6\times 1\times {10}^{-6}}{\int }_0^t{v}_{1}dt=-1.0{\int }_0^t{v}_{1}dt$

The net output of the summing amplifier is given by;

$$\begin{gathered} v_o=-12\left(\frac{v_o\text{'}}{6}+\frac{v_2}{2}+\frac{v_3}{2}\right)=-2v_o\text{'}-6(v_2+v_3) \\ {v}_o=2.0{\int }_0^t{v}_{1}dt-6(v_2+v_3) \end{gathered}$$