Design Steps

The output voltage v for the ideal case (R_s = 0 and R_m = ) is

(10.4)

where a is the divider ratio

(10.5)

The output voltage v` for the practical case is

(10.6)

where

(10.7)

Substituting the values of R₁ and R_p from Equation (10.7) in Equation (10.6)

(10.8)

We may define the error as

(10.9)

Substituting, we get

(10.10)

Our design objective is to minimize the error e by selecting R₂. We may use calculus and fix de/dR₂ = 0 in order to find the value of R₂. Accordingly, we have

(10.11)

From equation (10.7), we may find

(10.12)