Q4Analog Electronics

Question

(A) Derive the expression for closed loop Inverting Amplifier, Non inverting Amplifier, Differentiator and Integrator with the help of operational amplifier.

Answer 1

The input $V_{in}$ is applied to the inverting (âˆ’) terminal via $R_{1}$ , and $R_{f}$ is the feedback resistor. Using virtual ground concept ( $V_{-} \approx 0$ ):

A_{v} = \frac{V _{o u t}}{V _{in}} = - \frac{R _{f}}{R _{1}}

$V_{in}$ applied to (+) terminal; $R_{1}$ from (âˆ’) to ground, $R_{f}$ as feedback. Virtual short gives $V_{-} = V_{in}$ :

A_{v} = 1 + \frac{R _{f}}{R _{1}}

Replace $R_{f}$ with capacitor C. Current through $R_{1}$ charges C:

V_{o u t} = - \frac{1}{R _{1} C} \int V_{in} d t

Replace $R_{1}$ with capacitor C. Current through C flows through $R_{f}$ :

V_{o u t} = - R_{f} C \frac{d V _{in}}{d t}

Q4Analog Electronics

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