• عربي

Need Help?

Subscribe to Circuit

###### \${selected_topic_name}
• Notes

$\begin{array}{l}{\text { The op amp in the circuit shown is ideal. }} \\ {\text { a) Calculate } v_{o} \text { if } v_{a}=1 \mathrm{V} \text { and } v_{b}=0 \mathrm{V}} \\ {\text { b) Repeat (a) for } v_{a}=1 \mathrm{V} \text { and } v_{b}=2 \mathrm{V}} \\ {\text { c) If } v_{a}=1.5 \mathrm{V}, \text { specify the range of } v_{b}} \\ {\text { that avoids amplifier saturation. }}\end{array}$

$V^{+}=V^{-}$

$V_{b}=V_{1} \longrightarrow (1)$

$i_{1}=0, \quad i_{2}=0$

KCL

$\sum I=0 \Rightarrow i_{1}-i_{2}=0$

$i_{1}=i_{2}$

$i_{1}=\frac{فرق الجهد}{المقاومة}=\frac{V_a-V_1}{25}=\frac{V_a-V_b}{25} \longrightarrow (2)$

$i_{2}=\frac{فرق الجهد}{المقاومة}=\frac{V_{1}-V_{0}}{100} \longrightarrow (3)$

$i_{1}=i_{2} \Rightarrow \frac{V_{b}-V_{0}}{100}=\frac{V_a-V_b}{25}$

(a) $V_{0}=? ?, V_a=1, V_b=0$

$\frac{0-V_{b}}{100}=\frac{1-0}{25}$

$V_{0}=-4 volt$

$-10<V_{0}<10$

liner mode

(b) $V_{a}=1, V_{b}=2, V_{0}=? ?$

$V_0=6 V$
liner mode

(c) $V_{a}=1.5 V,$
range of $V_b=??$

Liner mode $-V_{c c} \leq V_{0} \leq V_{c}$

$\frac{V_{b}-V_{0}}{100}=\frac{V_a-V_b}{25}\Rightarrow 100*\frac{V_b-V_0}{100}=\frac{1.5-V_b}{25}*100$

$V_{b}-V_{0}=4\left[1.5-V_{b}\right] \Rightarrow V_{0}=V_{b}-6+4 V_{b}$

$V_{0}=5 V_{b}-6 \rightarrow -V_{cc} \leq 5V_b-6 \leq V_{cc}$

$6-10 \leq 5V_ b-6 \leq 10+6$

$\frac{-4}{5} \leq \frac{5 V_{b}}{5} \leq \frac{16}{5}$

$-0.8 \leq V_ b \leq 3.2 V$

to avoid  saturation