P 6.4-19 The circuit shown in Figure P 6.4-19 has one input, v_s, and one output, v_o. The circuit contains one unspecified resistance, R.

(a) Express the gain of the circuit, v_o/v_s, in terms of the resistance R.

(b) Determine the range of values of the gain that can be obtained by specifying a value for the resistance R.

(c) Design the circuit so that v_o = – 3 v_s.

Figure P 6.4-19

Annotating the figure

From op-amp rules we have noted voltage nodes by their values and we can also point out that . Again remember you cannot do node equations on nodes directly on the output of an op-amp since those are unknown current sources or sinks.

(a) Express the gain of the circuit, v_o/v_s, in terms of the resistance R.

Even though we know , here is the node equation

simplify

Now do the node equation by the 40 kΩ resistor.

Solve for

Plug this into previous equation

Now solve for

So the gain is

(b) Determine the range of values of the gain that can be obtained by specifying a value for the resistance R.

So assume can be anything positive so

So gain can be

(c) Design the circuit so that v_o = – 3 v_s.

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This page last updated on March 16, 2019