In the amplifier circuit shown in Fig. 9.44, show that [latex]V_{o} = V_{2} – V_{1}[/latex] if [latex]R_{1} = R_{2}[/latex].

[latex]V_{a}=\frac{R_{2}}{R_{1}+R_{3}}×V_{2}[/latex] [latex]V_{b}=V_{a}=\frac{R_{2}}{R_{1}+R_{2}}×V_{2}[/latex] (9.26) Again, [latex]\frac{V_{1}-V_{b}}{R_{1}}=\frac{V_{b}-V_{o}}{R_{2}} [/latex] (9.27) From Eqs. (9.26) and (9.27) [latex]\frac{V_{1}}{R_{1}}-\frac{V_{b}}{R_{1}}=\frac{V_{b}}{R_{2}}-\frac{V_{o}}{R_{2}}[/latex] when [latex] R_{1} = R_{2}[/latex] [latex]\frac{V_{1}}{R_{1}}-\frac{V_{b}}{R_{1}}=\frac{V_{b}}{R_{1}}-\frac{V_{o}}{R_{1}}[/latex] or, [latex]V_{o}= V_{1}- 2V_{b}[/latex]. (9.28) Again, [latex]V_{b}=\frac{R_{2}}{R_{1}+R_{2}}×V_{2}=\frac{R_{2}}{2R_{2}}V_{2}=\frac{V_{2}}{2}[/latex] (9.29) From Eqs. (9.28) and (9.29), [latex]V_{o}= V_{1}- 2 × \frac{V_{2}}{2}[/latex] or, [latex]V_{o}= V_{1}-V_{2}[/latex]

Question 9.16: In the amplifier circuit shown in Fig. 9.44, show that Vo = ...

Basic Electrical and Electronics Engineering-II

In the amplifier circuit shown in Fig. 9.44, show that $V_{o} = V_{2} – V_{1}$ if
$R_{1} = R_{2}$ .

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$V_{a}=\frac{R_{2}}{R_{1}+R_{3}}×V_{2}$
$V_{b}=V_{a}=\frac{R_{2}}{R_{1}+R_{2}}×V_{2}$ (9.26)
Again, $\frac{V_{1}-V_{b}}{R_{1}}=\frac{V_{b}-V_{o}}{R_{2}}$ (9.27)
From Eqs. (9.26) and (9.27)
$\frac{V_{1}}{R_{1}}-\frac{V_{b}}{R_{1}}=\frac{V_{b}}{R_{2}}-\frac{V_{o}}{R_{2}}$
when $R_{1} = R_{2}$
$\frac{V_{1}}{R_{1}}-\frac{V_{b}}{R_{1}}=\frac{V_{b}}{R_{1}}-\frac{V_{o}}{R_{1}}$
or, $V_{o}= V_{1}- 2V_{b}$ . (9.28)
Again, $V_{b}=\frac{R_{2}}{R_{1}+R_{2}}×V_{2}=\frac{R_{2}}{2R_{2}}V_{2}=\frac{V_{2}}{2}$ (9.29)
From Eqs. (9.28) and (9.29),
$V_{o}= V_{1}- 2 × \frac{V_{2}}{2}$
or, $V_{o}= V_{1}-V_{2}$