# Summing op-amp exercise

Open this schematic of a summing amplifier.

**Develop an expression for $\bm{v_o}$ in terms of $\bm{v_{ina}}$, $\bm{v_{inb}}$ and the resistor values.**

## show answer

From the video: The gain expression for a summing amplifier is,

$v_o = - \left (\dfrac{\text{Rf}}{\text{Ra}} \,v_{ina} + \dfrac{\text{Rf}}{\text{Rb}} \,v_{inb} \right )$

Fill in the resistor values,

$v_o = - \left (\dfrac{\text{20\,\text k}}{10\,\text k} \,v_{ina} + \dfrac{20\,\text k}{20\,\text k} \,v_{inb} \right )$

$v_o = - \left (2 \,v_{ina} + v_{inb} \right )$

**Describe in words what this amplifier does.**

The schematic has a voltage probe on one input.

**Click TRAN to run a transient simulation and see what that input looks like.**

Move the voltage probe to the other input.

**Click TRAN again to see what the other input looks like.**

One input voltage is a square wave. The other is a single step voltage.

**Sketch what you think the output will look like.**

You know the inputs and the amplifier function—what will the output look like?

**Add a voltage probe to the output node. Run another TRAN.**

Does the simulated output match your sketch?

## show answer

Simulation model of a summing amplifier with probes.

### Design challenge

Open a blank schematic.

**Design a summing amplifier that performs this function: $\bm{v_o = -\left ( 4\,v_{ina} + 3\,v_{inb}\right )}$.**

Hint: Pick values for the resistors with the appropriate ratios.

Verify your new amplifier does what you expect.

Change the input waveforms to something else. For example, make one of them a sine wave. Does the output do what you expect?

Make them both sine waves with a different frequency.

Make up a desired output signal in your head. See if you can build it from two inputs.

## Questions

Hi Willy, I think you made a typo on Rf/Rb, you say it’s 10/15 but it should be 20/15 Thanks for the great material, really enjoying it so far!

Pareto - Thanks for letting me know. The typo is fixed. I also modified Rb from 15k to 20k (makes for a prettier whole-integer result).