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.

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?

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.