Summing amplifier with one op amp

Question

I want to design amplifier that do the following summation

$$V_o = 2V_1 +3V_2 +5V_3 $$

the difficult arose when design with one op-amp and all voltages are referenced to the ground .

I tried with making non inverting amplifier with gain = 7 (any gain more than 5), then putting three resistor in the non inverting input (R1 for \$V_1\$ and R2 for \$V_2\$ and R3 for \$V_3\$) making superposition three times i have three equation.

But i can't solve them; it's very difficult for me. Does anyone have an idea?

Answer 1

You can start by determining the input resistors in terms of an arbitrary parallel resistance R3||R4||R5. Once you have the ratios, determine the gain to get the absolute factors 2, 3, 5. You don't want a resistor to ground from the non-inverting input because that would just increase the required gain, and make the circuit more sensitive to Vos, TCVos, noise etc. In this case, the minimum (and thus optimal) gain is 10.

Once you have that, you should balance the impedances seen by the inverting and non-inverting terminals, and then there will be an arbitrary scaling factor for the entire network. There are thus many solutions. Below is one that happens to end up with the resistors having reasonable integer values.

^{simulate this circuit – Schematic created using CircuitLab}