P 6.4-18 The circuit shown in Figure P 6.4-18 has one input, vs, and one output, io. Express the gain of the circuit, i_o/v_s, in terms of the resistances R₁, R₂, R₃, and R_o. (This circuit contains a pair of resistors having resistance R₁ and another pair having resistance R₂.) Design the circuit so that i_o = 0.02 v_s.

Figure P 6.4-18

Adding Annotations

We can see immediately that

So we need to find So now we write out some node equations. We have already used op-amp rules to identify similar voltages. This is why you see two and two . Recall also that you cannot do a node equation immediately on the op-amp output as that is an unknown current source or sink.

First let’s deal with the supernode

and

Now do node

We have two nodes so the upper one is

Lower one gives us

The node equation can be rearranged to give:

From the two super node equations

and

Which can be rewritten

Or using the other super node equation

Now plug these equations for , , and into the two equations and we have

Plugging into first one

Plugging into second one

Since we have two equations both equal to we can set them equal and we have

Now collect like terms

So solving for

Now substitute for

Now solve for

So the gain is given by

Now we want g = 0.02

Many possible answers, note: is not specified in gain so it can be anything as well.

If we make then we just need

To be safe with op-amps, make them all of the order of kΩ

One possible answer is

Other answers are possible!

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This page last updated on March 16, 2019