Consider the Schmitt trigger in Figure 15.31(a). (a) Derive the expressions for the switching point and crossover

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Consider the Schmitt trigger in Figure 15.31(a).

(a) Derive the expressions for the switching point and crossover voltages, as given in Equations (15.78) and (15.79).

(b) Let \(V_{H}=12 \mathrm{~V}, V_{L}=-12 \mathrm{~V}\), and \(R_{2}=20 \mathrm{k} \Omega\). Determine \(R_{1}\) and \(V_{\mathrm{REF}}\) such that \(V_{T H}=-1 \mathrm{~V}\) and \(V_{T L}=-2 \mathrm{~V}\).

Figure 15.31(a):-

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