Answered: R L(1-T)R "Vi TR Vo

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

3 R value resistors are connected in the opamp circuit in the figure. One of the resistors is variable and T is used to express the resistor value that the potentiometer is divided at any moment. Derive the expression that gives the output voltage Vo.

Expert Solution

Step 1

Output of an inverting amplifier is given by $v_{out} = - \frac{R_{F}}{R_{1}} v_{in}$

Output of a non-inverting amplifier is given by $v_{out} = (1 + \frac{R_{F}}{R_{1}}) v_{in}$

where, $R_{F}$ is the feedback resistor connected from the output to the inverting input of the Op-amp.

This given circuit is also know as a Switch-hitter.

Step 2

The wiper of a potentiometer is the channel through which the signal is taken to the non-inverting input of the Op-amp.

The potentiometer resistance from the wiper to the ground is given by $TR$

Now, by using the voltage division rule, voltage at the non-inverting op-amp input is given by: $V_{+} = {TV}_{i}$

Redrawing the circuit and showing separately the sources driving the two input terminals of the Op-amp-

By Superposition theorem-

Output due to signal present at only non-inverting input, is given by-
$\begin{array}{rcl} V_{0} & = & (1 + \frac{R}{R}) V_{+} \\ = & 2 V_{+} \\ = & 2 {TV}_{i} \end{array}$

And output due to signal present at just inverting input, is given by-
$V_{0} = - \frac{R}{R} V_{i} = - V_{i}$

So, by superposition of the two sources, output voltage is given by-
$V_{0} = 2 {TV}_{i} - V_{i} V_{0} = (2 T - 1) V_{i}$

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