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The op amp in the circuit of Fig. P5.32 is ideal. a) Plot v versus a when Rf = 4R-[ and
Chapter 5, Problem 5.32(choose chapter or problem)
The op amp in the circuit of Fig. P5.32 is ideal.
(a) Plot \(v_o\) versus \(\alpha\) when \(R_f=4 R_1\) and \(v_g=2 \mathrm{~V}\). Use increments of 0.1 and note by hypothesis that \(0 \leq \alpha \leq 1.0\).
(b) Write an equation for the straight line you plotted in (a). How are the slope and intercept of the line related to \(v_g\) and the ratio \(R_f / R_1\) ?
(c) Using the results from (b), choose values for \(v_g\) and the ratio \(R_f / R_1\) such that \(v_o=-6 \alpha+4\).
Questions & Answers
QUESTION:
The op amp in the circuit of Fig. P5.32 is ideal.
(a) Plot \(v_o\) versus \(\alpha\) when \(R_f=4 R_1\) and \(v_g=2 \mathrm{~V}\). Use increments of 0.1 and note by hypothesis that \(0 \leq \alpha \leq 1.0\).
(b) Write an equation for the straight line you plotted in (a). How are the slope and intercept of the line related to \(v_g\) and the ratio \(R_f / R_1\) ?
(c) Using the results from (b), choose values for \(v_g\) and the ratio \(R_f / R_1\) such that \(v_o=-6 \alpha+4\).
Step 1 of 5
We have given an op amp in the circuit shown in figure below
a) First we write a node-voltage equation
\(\frac{v_{\mathrm{n}}-v_{\mathrm{g}}}{R_{1}}+\frac{v_{\mathrm{n}}-v_{0}}{R_{\mathrm{f}}}=0\)
Next we multiply with \(R_{\mathrm{f}}\)
\(\left(v_{\mathrm{n}}-v_{\mathrm{g}}\right) \frac{R_{\mathrm{f}}}{R_{1}}+v_{\mathrm{n}}-v_{0}=0\)
\(v_{0}=v_{\mathrm{n}}\left(\frac{R_{\mathrm{f}}}{R_{\mathrm{g}}}+1\right)-v_{\mathrm{g}} \frac{R_{\mathrm{f}}}{R_{1}}\)