It is usually preferable to obtain all the required gain in the first stage, leaving the sccond stage to perform the task of taking the difference between tbe outputs of the first stage and thereby rejecting the common-mode signal. In other words, the second stage is usually designed for a gain of 1 . Adopting this approach, we select all the second-stage resistors to be equal to a practically convenient value, say $10 \mathrm{k} \Omega$. The problem then reduces to designing the first stage to realize a gain adjustable over the range of 2 to 1000 . Implementing $2 R_1$ as the series combinatiou of a fixed resistor $R_{1 /}$ and the variable resistor $R_1$, obtained using the $100-\mathrm{k} \Omega$ pot, we can write

$$
1+\frac{2 R_2}{R_{1 f}+R_{1 y}}=2 \text { to } 1000
$$


Thus,

$$
1+\frac{2 R_2}{R_{1 f}}=1000
$$

and

$$
1+\frac{2 R_2}{R_{1 f}+100 \mathrm{k} \Omega}=2
$$


These two equations yield $R_{1 f}=100.2 \Omega$ and $R_2=50.050 \mathrm{k} \Omega$. Other practical values may be selected; for instance, $R_{1 j}=100 \Omega$ and $R_2=49.9 \mathrm{k} \Omega$ (both values are available as standard $1 \%$-tolerance metal-film resistors; see Appendix G) results in a gain covering approximately the required range.