EE 2115-01 - Lec 15 - 2026_09_30

Overview

Hiren Trada explains how positive feedback turns an inverting comparator into a Schmitt trigger, or hysteretic comparator, whose output switches at separate upper and lower thresholds rather than reacting to every input fluctuation. He derives how resistor values and a reference voltage set the hysteresis window, verifies the behavior in LTspice, and works through a single-supply design with a 2 V window, a 4 V set point, and a 10 V supply.

Key takeaways

Positive feedback makes a comparator's threshold depend on its output state, creating separate upper and lower switching limits.
A Schmitt trigger rejects input changes inside its hysteresis window, reducing noise-driven output chatter and rapid on/off cycling.
For the worked single-supply design, a 10 V supply, 100 kΩ R2, and 25 kΩ R1 produce a 2 V window centered at a 4 V set point.
A 3.75 V reference can be generated from the 10 V supply with a divider designed for a 3.75 V Thevenin voltage and 25 kΩ equivalent resistance.
Real comparator behavior includes device-level hysteresis as well as deliberately designed feedback; the LTspice example shows roughly 100 mV intrinsic hysteresis alongside the added window.

Chapters

0:00 Comparator Recap and Inverting-Input Behavior

A comparator compares its inverting (V−) and non-inverting (V+) inputs and drives its output toward a supply rail.
For an inverting comparator, the output goes positive when V− exceeds V+ and goes low when V+ exceeds V−.
Earlier examples use a fixed reference input; practical signals may both vary over time.

5:00 Positive Feedback Sets a Moving Comparator Threshold

The Schmitt-trigger circuit feeds part of its output back to V+ through a 100 kΩ and 5.1 kΩ voltage divider.
The divider returns only a fraction of the output voltage, making the comparator threshold depend on its current output state.
Negative feedback is commonly used to make op-amp amplifiers, while positive feedback is also used in oscillator circuits.

8:00 Hysteresis: Separate Thresholds Prevent Rapid Switching

Hysteresis means a system's output depends on its input and its present or past output state.
A thermostat set near 72°F could otherwise switch cooling rapidly as temperature fluctuates around the set point.
Using distinct turn-on and turn-off temperatures—for example, around 73°F and 71°F—adds tolerance and reduces cycling.

12:00 Upper and Lower Switching Thresholds Form a Hysteresis Loop

With the output high, feedback shifts V+ to about +0.24 V; the input must cross that threshold to switch the output.
As the input moves in the opposite direction, the output does not switch back until the lower threshold, about −0.24 V, is crossed.
The two transition levels are the upper and lower limits; their difference is the hysteresis window, which rejects smaller fluctuations.

17:00 LTspice Shows Schmitt-Trigger Switching and Device Hysteresis

An LTspice comparison shows an ordinary comparator switching repeatedly near its threshold, unlike the hysteretic circuit.
The simulated input is a sine wave, and the hysteretic comparator produces a cleaner rectangular output despite input variation.
The component itself contributes roughly 100 mV of hysteresis; together with designed feedback, the illustrated transitions are approximately −270 mV and +270 mV.

22:00 Hysteresis Suppresses Noise-Induced Output Chatter

A noisy input near a normal comparator's threshold can cause repeated unwanted output transitions.
The example's output toggles up and down as the input fluctuates, analogous to a compressor repeatedly turning on and off.
With a hysteresis window, the input must cross the opposite threshold before the output changes state, preventing chatter from smaller noise.

26:00 Single-Supply Threshold Equations Use VDD and Vreference

With a single supply, the comparator output switches between 0 V and VDD rather than between positive and negative rails.
A resistor network connects Vreference and Vout to V+, so the feedback voltage depends on both sources.
The upper and lower thresholds determine the window width, while Vreference lets the designer position the switching levels around a chosen set point.

34:00 Design Example: 2 V Window Around a 4 V Set Point

The design targets a 2 V hysteresis window centered at 4 V, giving a lower threshold of 3 V and an upper threshold of 5 V.
For VDD = 10 V and R2 = 100 kΩ, the window equation gives R1 = 25 kΩ.
The required reference voltage is 3.75 V; the resistor values and reference are then checked against the intended thresholds.

43:00 Create the 3.75 V Reference from the 10 V Supply

Instead of adding a separate 3.75 V source, a divider from the 10 V supply can generate the reference.
The divider is designed for a 3.75 V Thevenin voltage and a 25 kΩ equivalent resistance, using 66.67 kΩ and 40 kΩ ideal resistor values.
Standard 68 kΩ and 39 kΩ parts are close alternatives; series or parallel combinations can provide closer values when needed.

49:00 Schmitt Trigger Namesake and Upcoming Quiz Schedule

The Schmitt trigger is named for Otto Herbert Schmitt, who developed the circuit as part of his doctoral dissertation.
LTspice can verify that the supply-derived reference and resistor network preserve the intended switching window.
Starting the following week, a short quiz is scheduled every Wednesday, typically under five minutes, except during the week of Midterm 2.

Summary, takeaways, and chapters were generated by AI from the video's transcript and may contain errors. The video belongs to its creator, Hiren Trada.