Schmitt Trigger Example

Problem

Design the Schmitt trigger circuit (a) to achieve the transition shown in (b). The current through any resistor should not exceed 1mA

Describing the system

Looking at the hysteresis voltages, we have:

$$\begin{array}{r}{V}_{re{f}_1}=2.1\\ V_{re{f}_0}=1.2\end{array}$$

When $V_{out}=0$, we have this equivalent circuit:

This is described by:

$$V_{re{f}_0}=3.3\frac{R_2\parallel R_3}{R_1+R_2\parallel R_3}$$

When $V_{out}=\text{“1"}=3.3V$, we have:

This is governed by:

$$V_{re{f}_1}=3.3\frac{R_2}{R_1\parallel R_3+R_2}=2.1$$

Solving the system

For now, we have 2 equations and three unknowns. We find a third clue from “the current through any resistor should not exceed $1\text{ mA}$“. Solving just in terms of ratios:

$$R_1=R_2=0.75R_3$$

A quick choice would be: $R_1=R_2=7.5\text{ k}\Omega$ and $R_3=10\text{ k}\Omega$. A rigorous solution would require us to ensure that in the top case, we have:

$$\begin{array}{r}{R}_1+R_2\parallel R_3\le 3.3\text{ k}\Omega \end{array}$$

And that in the bottom case we have:

$$R_1\parallel R_3+R_2\ge 3.3\text{ k}\Omega$$

This gives $R_{3min}\le 2.8\text{ k}\Omega$.