P 6.5-5 Design the operational amplifier circuit in Figure P 6.5-3 so that vout = 5 · v1 – 2 · v2

 

Let’s try a basic difference amplifier.  The circuit is

The voltage output is given by

 

Trying to simplify use

The output reduces to

 

This will not work as the coefficients need to be same and we are trying to create

 

 

So using the more complex relationship, make   This means we replace  with

 

 

Which creates relation

 

But we really don’t want to deal with negative resistances, so try a new circuit.  Let’s consider a basic summing amplifier

The voltage output is given by

 

 

This will allow us to produce different coefficients, but they are both negative, so if we add an inverting amplifier to one input we can swap the sign.  So an inverting amplifier looks like

The voltage output is given by

 

Since we want

 

And the summing amplifier makes things negative, we will put inverting amplifier on the first voltage and have the circuit below:

Now the voltage output is given by first consider the summing amp still gives us

 

But now  is  which is given by

 

So combining we get

 

And so we must have

 

 

Many possible choices can fulfill these conditions, so there are many possible answers, again keep the values in the kΩ range to keep op-amps acting like ideal op-amps.  One choice is given by

 

 

As you can see if we make

 

We correctly get a

 

One possible answer is

Other answers are possible!

As well as other circuits!!

 

 

Please send any comments or questions about this page to ddonovan@nmu.edu

This page last updated on March 17, 2019