Question 9.15: Calculate the value of the output voltage for the amplifier ...
Calculate the value of the output voltage for the amplifier circuit shown in Fig. 9.43.
Assuming infinite amplifier gain, potential at point a is taken as equal to potential at point b.
V_{a}=\frac{R_{3}}{R_{2}+R_{3}} × V_{2}V_{b}=\frac{R_{3}}{R_{2}+R_{3}} × V_{2}
V_{a} -V_{o}= V_{c}
\frac{R_{3}}{R_{2}+R_{3}} V_{2} – V_{o}=\frac{1}{C} \int_{o}^{t} idt
q=\int idt
q = CV_{c}
or, V_{c}=\frac{1}{C} \int idt
V_{o}= \frac{R_{3}}{R_{3}+} \frac{V_{2}}{R_{3}} – \frac{1}{C} \int_{o}^{t} idt (9.24)
Again, i=\frac{V_{1} – V_{b}}{R_{1}}=\frac{1}{R_{1}} \left\lgroup V_{1}-\frac{R_{3}V_{2}}{R_{2}+R_{3}} \right\rgroup (9.25)
From Eqs. (9.24) and (9.25),
V_{o}=\left\lgroup \frac{R_{3}}{R_{2}+R_{3}} \right\rgroup V_{2} – \frac{1}{CR_{1}} \int_{o}^{t}\left\lgroup V_{1}-\frac{R_{3}V_{2}}{R_{2}+R_{3}} \right\rgroup dt.