P 6.5-12 The input to the circuit shown in Figure P 6.5-12a is the voltage . The output is the voltage . The voltage is used to adjust the relationship between the input and the output.

(a) Show that the output of this circuit is related to the input by the equation

Where a and b are constants that depend on

(b) Design the circuit so that its input and output have the relationship specified by the graph shown in Figure P 6.5-12b.

Figure P 6.5-12

Annotating the circuit

(a) Show that the output of this circuit is related to the input by the equation

Where a and b are constants that depend on

There are two unique nodes. The two on the left are electrically connected. So write a node equation for each the left and the right.

Left

Right

This equation leads to

Plug this into other equation

Solve for

So comparing with the equation given

So the coefficients are:

(b) Design the circuit so that its input and output have the relationship specified by the graph shown in Figure P 6.5-12b.

First find the equation of the line. Use the two points (-4, 0) and (0, 5)

So we have So we have the two conditions

There are many solutions. To simplify let’s make the assignment

The two conditions become

Again, keep in the kΩ range, but there are many possible answers.

Let Then and choose

Find a and b

As it should be. Now find b

One possible answer is

Other answers are possible!

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This page last updated on March 17, 2019