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## Homework Statement

Given the availability of resistors of value 1 kΩ and 10 kΩ only, design a circuit based on the non-inverting configuration to realize a gain of +10 V/V.

## Homework Equations

## The Attempt at a Solution

So I was doing some of those good old design problems, and I came across this one.

I know the gain of the standard non-inverting configuration is given by ##\frac{v_o}{v_i} = 1 + \frac{R_2}{R_1}##. So I want to design the circuit such that:

$$10 = 1 + \frac{R_2}{R_1} \Rightarrow \frac{R_2}{R_1} = 9$$

I'm limited to only the ##1k## and ##10k## resistors provided, and this provides a design problem. Usually, we would like the input impedance to be a large as possible to retain as much of the signal in accordance with ##V = IR##. Similarly, we would like the output impedance to be as small as possible. Looking at the equation:

$$\frac{R_2}{R_1} = 9$$

It doesn't take long to realize I must choose ##R_1 << R_2##, which of course is the exact opposite of what a good amplifier should have. Ideally I want to choose ##R_1 >> R_2##, but I can't figure out the ideal resistor values.

Is this just a bad amplifier design?