EE 2115-03 - Lec 29 - 2026_11_04
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Overview
Hiren Trada reviews comparator behavior and explains how positive feedback creates a hysteretic comparator with separate high-to-low and low-to-high thresholds, reducing unwanted switching from noise near a set point. The lecture derives feedback thresholds using a resistor divider and voltage division, covers nonzero references and single- versus dual-supply designs, then outlines the open-book Midterm 2 scope.
Key takeaways
- A hysteretic comparator switches at two thresholds rather than one: the example switches high-to-low at +0.24 V and low-to-high at -0.24 V, holding its state between them.
- Positive feedback makes a comparator's switching behavior depend on its prior output state, which prevents small input disturbances near the set point from causing repeated toggling.
- For a divider with R1 at the comparator input node and R2 between that node and Vout, the feedback fraction is R1/(R1 + R2); a smaller R1 relative to R2 produces a narrower hysteresis window.
- Threshold calculations must use the output rail that existed before the transition: VDD for high-to-low and VSS for low-to-high; when VSS = 0 V, its contribution to the latter equation is zero.
- Hysteresis width is the difference between the two transition voltages, while the set point is their midpoint; the 4 V set-point example uses a 2 V width to produce 3 V and 5 V thresholds.
- The stated Midterm 2 scope is basic comparators and hysteretic comparators, a combined Zener-diode problem, and introductory inverting/non-inverting op-amp gain, with no difference or summing amplifier analysis.
Chapters
- For a non-inverting comparator with a 0 V reference, the output goes high when Vin rises above 0 V and low when Vin falls below it.
- An inverting comparator reverses that response: Vin above the reference drives the output low, while Vin below it drives the output high.
- A thermostat set to 70°F can switch unnecessarily if refrigerator air or heat from a cooking range briefly changes its local temperature.
- Hysteresis adds a tolerance window around the set point so small disturbances do not repeatedly trigger a system.
- With comparator feedback, the output depends on the current input and the output's present or prior state.
- For the inverting hysteretic comparator example, an output that starts high switches high-to-low when rising Vin reaches +0.24 V.
- After the output is low, falling Vin must reach -0.24 V to cause the low-to-high transition.
- Between -0.24 V and +0.24 V, the output retains its state; the labels H-to-L and L-to-H identify the direction of each transition.
- A resistor divider feeds back a fraction of Vout: R1 is the lower resistor connected to the comparator input node, and R2 connects that node to the output.
- The feedback fraction is R1/(R1 + R2), so making R1 small relative to R2 keeps the hysteresis window narrow.
- For a dual supply of +5 V and -5 V, the rails are VDD = +5 V and VSS = -5 V; the example uses R2 = 100 kΩ and R1 = 5.1 kΩ.
- When resistor values are unspecified, Trada recommends choosing an upper resistor around 100 kΩ to 200 kΩ and calculating the other value for the desired thresholds.
- A nonzero reference voltage shifts the comparator's set point; the reference node's circuit position and polarity determine its contribution to the divider voltage.
- Superposition separates the feedback node voltage into a Vout contribution weighted by R1/(R1 + R2) and a Vreference contribution weighted by R2/(R1 + R2).
- For a high-to-low transition, use the prior high output value VDD; for a low-to-high transition, use the prior low value VSS.
- In a 0 V to 10 V single-supply circuit, VSS is 0 V, so the Vout term vanishes in the low-to-high threshold equation; a negative VSS would make that term nonzero.
- The hysteresis width is the voltage difference between the high-to-low and low-to-high transition points, and the set point is halfway between them.
- The design example uses a 0 V to 10 V supply to create a 4 V set point and a 2 V hysteresis width, giving thresholds of 3 V and 5 V.
- Design proceeds by substituting the desired set point and width into the threshold equations, then solving for the resistor value not already specified.
- Midterm 2 is open book and open notes, with lecture slides, notes, homework, and digital devices allowed; the exam is expected to last 50 minutes.
- The stated content includes Zener diodes in a combined problem, comparators including hysteretic comparators, and basic op-amp inverting and non-inverting configurations.
- Op-amp coverage includes closed-loop gain and the voltage follower as a unity-gain non-inverting amplifier; difference and summing amplifiers are excluded.
- Trada is considering making the practice exam available on Canvas from Friday through Sunday so students with Friday conflicts can take it at a convenient time.
Transcript excerpt
0:00 So uh today's uh we're continuing with our uh review of uh the topics for midterm 2. Uh I've been struggling with this technology since I came in like 15 minutes more than 15 minutes were um gone in the first section trying to get it to work and then like 10 minutes later it dropped Ethernet. So I was like trying to fix it. But luckily uh today uh is not going to take long. So uh what we are looking at is the hysteric comparator and then just a little bit about uh the opamp um and then I'll just explain what's going to be on the midterm. All right, let's see. Five three.
1:05 Okay. So first let's look at a regular comparator right a regular non-inverting comparator where the reference point um is at the inverting terminal inputs going into the non-inverting so V+ so if your reference point is at zero and your input is going into V+ as the input increases crosses zero goes greater than zero output goes high So in a non-inverting comparator as VN increases above the reference point output goes high then crosses zero and VN goes lower than the reference
1:53 point. Let's do it on this side. As Vin goes negative below zero, it's going below the reference point. So now output goes low. So that's non-inverting. Right? That's the characteristic of a non-inverting comparator. Inverting comparator is the exact opposite. As Vin goes above the reference point, output goes low. So if your reference point again if your reference point is at 0 volts Vin is increasing VN goes above the reference point output goes low and
2:41 that's what we see here. And as Vin um drops from positive crosses zero and goes negative which means goes negative here output goes
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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.