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$$
\begin{array}{l}{\text { a) Find } v_{o} \text { in the circuit shown if } v_{\mathrm{a}}=0.1 \mathrm{V}} \\ {\text { and } v_{\mathrm{b}}=0.25 \mathrm{V} \text { . }} \\ {\text { b) If } v_{\mathrm{b}}=0.25 \mathrm{V}, \text { how large can } v_{\mathrm{a}} \text { be before }} \\ {\text { the op amp saturates? }} \\ {\text { c) If } v_{\mathrm{a}}=0.10 \mathrm{V}, \text { how large can } v_{\mathrm{b}} \text { be before }} \\ {\text { the op amp saturates? }}\end{array}
$$

$$
V_{0}=-\left[\frac{R_{f}}{R_{1}} V_{a}+\frac{R_{f}}{R_{2}} V_{b}\right]
$$

$$
R_f=250 K \Omega \quad R_{1}=5 k \Omega \quad \mathrm{R_i}=25 k \Omega
$$

$$
V_0=-[\frac{250}{5} \mathrm{V_a}+\frac{250}{25} \mathrm{V_b}]
$$

$$
V_{0}=-50 V_{a}-10 V_ b \longrightarrow (1)
$$

(a) $$
V_{0}=? ?\quad V_{a}=0.1, V_{b}=0.25
$$

$$
V_0=-50 * 0.1-10 * 0.25=-7.5 v
$$        liner mode

(b) $$
V_{b}=\frac{1}{4} \quad V_{a}=? ?
$$

to avoid  saturation

$$
-10 \leq V_{0} \leq 15
$$

$$
-10 \leq-50V_a-10V_ b \leq 15
$$

$$
-10 \leq-50 V_ a-2.5 \leq 15
$$

$$
-7.5 \leq -50V_a \leq 17.5
$$

$$
-0.35 \leq V_a \leq0 .15
$$

(c) $$
V_{a}=0.1 \quad V_ b=? ?
$$

$$
-2 \leq V_b \leq 0.5
$$
    volt

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