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Calculate { v }_{ 0 }/{ v }_{ i } in the op amp circuit in Fig. 5.87.

Step-by-step

The first stage is a summer. Let  { V }_{ 1 } be the output of the first stage.

v_{1}=-\frac{10}{5} v_{i}-\frac{10}{4} v_{0} \quad \longrightarrow \quad v_{1}=-2 v_{i}-2.5 v_{0}     (1)

 

By voltage division,

v_{1}=\frac{10}{10+2} v_{0}=\frac{5}{6} v_{0}         (2)

 

Combining (1) and (2),

\frac{5}{6} v_{0}=-2 v_{1}-2.5 v_{0} \quad \longrightarrow \quad \frac{10}{3} v_{0}=-2 v_{i}

 

\frac{v_{0}}{v_{i}}=-6 /10=\underline{-0.6}

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