P 6.6-2 Design a circuit to implement the equation

The output of the circuit should correspond to z.

First write the equation so we have output on one side and inputs on the other.

There are many possible circuits one could use. Let’s consider a final summing amplifier to add

So we can first use a summing amplifier on the part in the parenthesis, this will make that negative after the first summing amp, but then it will become positive when we use a second summing amplifier that joins this to a pair of inverting amplifiers to provide the simple multiplication required for this term. So we shall make each part separately and then combine them.

First the summing for the term in the parenthesis.

The voltage output V1 will be

We will need to have

For the second term we use

The voltage output V2 will be

We will need to have

When we combine these two we would have

The voltage output V1 will be

Plugging in previous expressions

The full circuit look likes

So comparing the equations

And

Choosing

We need

Next

So make

And

Finally make

Our final circuit looks like

Now as a final check, let’s make

Then our equation

So we show the circuit with voltages and everything checks out!

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This page last updated on March 18, 2019