Teaching guide for the module

Op-Amp: Teacher's Guide

A guide to using the Op-Amp simulator in the classroom to teach the operational amplifier in inverting and non-inverting configuration, the ideal comparator, and the comparator with hysteresis (Schmitt trigger). Virtual short and saturation shown as observable facts, not formulas. Designed for technical high school teachers (years 4–5, Electronics/Systems).

Module: Op-Amp · Two instrument tabs: AMP (inv/non-inv) · COMPARATOR (ideal & Schmitt)

Physics behind it

An operational amplifier is an active component with three signal pins (+, −, Vout) and two supply pins (±Vcc). In its ideal model it has infinite differential gain, infinite input impedance and zero output impedance. Its usefulness emerges from feedback: connecting the output back to the inverting input via a resistor network produces an amplifier with finite, predictable gain, depending only on resistor ratios.

The fundamental principle is the virtual short: in the linear region, the op-amp adjusts its output so that $V_{+} = V_{-}$ . There is no physical connection between the two inputs — the feedback enforces equality. When the op-amp can no longer maintain it (because the required gain would push $V_{out}$ past $\pm V_{cc}$ ), it enters saturation: the output clamps at the supply rails (in practice $\pm (V_{cc} - 1.5 V)$ for non-rail-to-rail op-amps like the µA741) and $V_{-}$ deviates from $V_{+}$ .

Without feedback (or with positive feedback), the op-amp becomes a comparator: the output is always saturated, high or low depending on the sign of $V_{+} - V_{-}$ . Adding a small fraction of positive feedback yields the comparator with hysteresis (Schmitt trigger), where the switching thresholds $V_{th +}$ and $V_{th -}$ are distinct: the output flips low when $V_{in}$ exceeds $V_{th +}$ and flips high when it drops below $V_{th -}$ . This gap makes the comparator immune to noise.

Key concepts

Virtual short: in linear region with negative feedback, $V_{+} \approx V_{-}$ . A consequence of infinite gain, not a physical wire.
Inverting gain: $G = - R_{f} / R_{1}$ . Negative sign means the signal is inverted.
Non-inverting gain: $G = 1 + R_{f} / R_{1}$ . Always positive, always $\geq 1$ .
Voltage follower: special case with $R_{f} = 0$ , so $G = 1$ . Used as an impedance buffer.
Saturation: $V_{out}$ clamped at $\pm V_{sat}$ , with $V_{sat} \approx V_{cc} - 1.5 V$ (non-rail-to-rail).
Ideal comparator: without feedback, $V_{out}$ is $+ V_{sat}$ or $- V_{sat}$ based on the sign of $V_{in} - V_{ref}$ .
Schmitt thresholds: $V_{th \pm} = V_{ref} \pm \frac{R _{1}}{R _{1} + R _{2}} V_{sat}$ (inverting topology). The gap $V_{th +} - V_{th -}$ is the hysteresis width.

How to use it in class

Opening: the virtual short as a fact. Open the AMP tab in Inverting mode with default values ( $V_{in} = 1 V$ , $R_{1} = 1 k Ω$ , $R_{f} = 10 k Ω$ , $\pm V_{cc} = 12 V$ ). Show the schematic: $V_{+}$ is grounded so it is $0 V$ , and $V_{-}$ is also $0 V$ — but not because it is wired to ground! The feedback drives $V_{out}$ to $- 10 V$ precisely to force $V_{-} = V_{+}$ . Move $V_{in}$ and watch $V_{-}$ stay locked at $0$ while $V_{out}$ tracks: this is the virtual short seen as a fact.

Build-up: saturation. Still in Inverting, raise $V_{in}$ above $1.05 V$ . The operating point in TRANSFER stops at the knee: $V_{out}$ refuses to go below $- 10.5 V$ . The schematic reacts: a "SATURATION" badge appears, $V_{-}$ turns amber. The feedback has "broken" — $V_{+}$ and $V_{-}$ are no longer equal. In the SCOPE, applying a sinusoid larger than the threshold reveals output clipped flat at the rails.

Deepening: the voltage follower. Switch to Non-Inverting. Bring $R_{f}$ to $0 Ω$ : the gain drops to $1$ , the output exactly tracks the input. This is the voltage follower — a high-impedance buffer, essential to drive loads without loading the source.

Heart of the lesson: comparator and hysteresis. Switch to the COMPARATOR tab, Inverting, Hysteresis OFF, Triangle source, $V_{ref} = 0$ , $Noise = 0$ . The scope shows a clean triangular input and a clean square wave output: the output flips precisely when $V_{in}$ crosses $V_{ref}$ . The TRANSFER shows a vertical step.

Now raise the Noise slider to $0.3 V$ . Without hysteresis, the output begins to chatter on the threshold: noise multiplied by infinite gain produces dozens of unwanted fast transitions around the zero crossing. This is the didactic problem that precedes the solution.

Toggle Hysteresis ON. The schematic changes: $R_{1}$ and $R_{2}$ appear, the positive feedback resistors. On the scope, the two thresholds $V_{th +}$ and $V_{th -}$ separate, and the chatter disappears: noise is no longer enough to bring $V_{in}$ back across the return threshold. The TRANSFER forms the classic hysteresis rectangle. The teacher can say: "this is why real-world sensors use Schmitt triggers".

Closing: sizing the network. Vary $R_{1}$ and $R_{2}$ : the ratio controls the hysteresis width. More expected noise calls for wider gaps.

Real-world examples

Audio pre-amplifiers. Non-inverting with adjustable gain via potentiometer on $R_{f}$ .
Mixers and attenuators. Inverting with multiple $R_{1}$ in parallel, one per channel.
High-impedance sensor buffers. Voltage follower for thermistors, photodiodes, condenser microphones.
Threshold detectors. Comparator with hysteresis in thermostats, level sensors, PIR motion detectors.
Square-wave generators. Schmitt trigger as bistable element in relaxation oscillators.
Clock cleanup. Schmitt at the input of logic gates to clean up noisy signals before the active edge.

Discussion questions

Why does the virtual short "work" if there is no physical wire between the two inputs?
What happens to $V_{-}$ in saturation, and why does it no longer equal $V_{+}$ ?
In an inverting amplifier with $R_{1} = R_{f}$ , what gain do we get? And in the non-inverting with the same values?
Why is a comparator without hysteresis unsuitable for noisy signals?
In a Schmitt trigger, what changes if we double $R_{2}$ keeping $R_{1}$ fixed? And if we halve it?

Related modules

Ohm's Law: the feedback network is a resistor network — calculating $V_{+}, V_{-}$ uses voltage dividers and KCL.
Filters: combining op-amps with capacitors yields active filters (Sallen-Key, Multiple Feedback).
Logic Gates: the Schmitt trigger is the bridge between the analog world and a digital input.