Core Lesson Content
From Holding a Point to Moving a Signal
Lesson 3 ended with a transistor parked at a Q-point β a DC state. Amplification is what happens when you let a small AC signal wiggle the operating point around that Q: a few millivolts at the base become volts at the collector. This lesson follows that idea up the abstraction ladder:
- The discrete stage: a single common-emitter amplifier β how gain arises, what sets it, and why impedance matters when stages connect.
- The integrated leap: the operational amplifier β dozens of matched transistors packaged as one near-ideal gain block, tamed by feedback.
- The six classic configurations every technician meets: inverting, non-inverting, follower, comparator, integrator, differentiator.
Try It Live
The Common-Emitter Small-Signal Amplifier
Take the voltage-divider-biased CE circuit from Lesson 3 and add three capacitors β that's the complete classic amplifier:
- Input coupling capacitor: passes the AC signal into the base while blocking the source from disturbing the DC bias.
- Output coupling capacitor: delivers only the amplified AC to the load, stripping off the collector's DC level.
- Emitter bypass capacitor: for DC it's invisible (the emitter resistor still stabilizes the Q-point); for AC it's a short circuit, grounding the emitter so the full signal appears across the base-emitter junction β maximizing gain.
The Signal's Journey
A small positive swing at the base increases VBE, which increases IC (exponentially sensitive β Lesson 1's diode curve at work), which increases the drop across RC, which pulls the collector voltage down. Input up β output down: the CE stage inherently inverts (180Β° phase shift), exactly like the inverting op-amp configuration you'll meet in Tab 5.
Voltage Gain and Impedance Analysis
Where CE Gain Comes From
For AC, the transistor's emitter presents a tiny internal resistance:
Worked example: a CE stage biased at IE = 1 mA with RC = 3.6 kΞ©: r'e = 25 mV / 1 mA = 25 Ξ©, so AV β β3600/25 = β144. A 10 mV input becomes a 1.44 V inverted output. Notice the gain rides on IE β which drifts with temperature β one of several reasons designers migrated to op-amps.
With the bypass capacitor removed, the emitter resistor enters the AC path: AV β βRC/(r'e + RE) β much lower gain, but far more stable and predictable. Gain traded for stability: your first taste of feedback (RE is feedback).
Impedance: Why Stages Load Each Other
| Property | Typical CE Stage | Consequence |
|---|---|---|
| Input impedance | β1β5 kΞ© (bias divider β₯ Ξ²Β·r'e) | Loads down high-impedance sources β a weak sensor loses most of its signal at the door |
| Output impedance | βRC (kΞ© range) | Gain collapses when a heavy (low-Z) load is connected: the load parallels RC |
Cascade two CE stages and the second stage's input impedance loads the first stage's output β realized gain is always less than the product of the unloaded gains. Managing this loading is half of discrete amplifier design, and it's precisely the problem op-amps erase: near-infinite input Z, near-zero output Z.
Meet the Op-Amp
An operational amplifier is a complete multi-stage amplifier on one chip β a differential input pair, gain stages, and a push-pull output driver. From outside, it's five pins that matter: two inputs, one output, two supply rails. It amplifies the difference between its inputs:
The Ideal Op-Amp (and how close reality gets)
| Property | Ideal | Real (LM741 / LM358 class) |
|---|---|---|
| Open-loop gain | Infinite | 100,000 β 1,000,000 |
| Input impedance | Infinite (no input current) | MΞ©βTΞ© (nA of bias current) |
| Output impedance | Zero | Tens of ohms |
| Output swing | Unlimited | Within 1β2 V of the rails (Β±Vsat) |
| Speed | Instant | Slew-rate limited (0.5 V/Β΅s for a 741) |
A gain of 100,000 sounds wonderful and is nearly useless raw: a 150 Β΅V difference between the inputs already slams the output into a rail. The insight that makes op-amps practical is to throw most of that gain away deliberately through negative feedback β covered in the next two tabs and formalized in Tab 9.
The Inverting Amplifier and Virtual Ground
Ground the + input. Feed the signal through Rin to the β input, and connect Rf from the output back to the β input. Now apply the golden rules:
- Rule 2: the output drives Vβ to equal Vβ = 0 V. The β input sits at ground potential without being connected to ground β the virtual ground.
- Input current is therefore I = Vin/Rin (the full input voltage appears across Rin).
- Rule 1: none of that current can enter the op-amp β it must all continue through Rf, forcing Vout = βIΒ·Rf.
Everything a technician needs is in that equation: gain is set by two resistors you can read off the board, the minus sign means the output is inverted, and the input impedance is simply Rin (the source looks into a resistor that ends at a virtual ground).
Non-Inverting Amplifier and the Voltage Follower
Non-Inverting: Gain Without Loading
Drive the + input directly with the signal. Rf and Rin form a voltage divider from the output to ground, with its midpoint feeding the β input. Golden rule 2 forces that midpoint to equal Vin, so the output must rise to:
- Input impedance is essentially infinite β the signal touches only the op-amp's + input, which draws no current. The perfect home for high-impedance sensors.
- Minimum gain is 1: with the divider in place the output can never be smaller than the input. Need attenuation with inversion? That's the inverting amp's job (Rf < Rin).
The Voltage Follower: Gain of Exactly One, On Purpose
Delete both resistors and wire the output straight to the β input: 100% feedback, AV = 1. Why build an amplifier that doesn't amplify? Impedance transformation. Enormous input Z, near-zero output Z β it's Lesson 3's emitter follower perfected. Place it between a weak source (pH probe, high-value divider, sample-and-hold capacitor) and anything that needs current.
The Comparator: An Op-Amp With No Leash
Remove all feedback and the op-amp's full open-loop gain runs wild β which is exactly what you want for making decisions. With a reference voltage on one input and a signal on the other:
The output lives at the rails, snapping between them as the signal crosses the reference. Analog in, digital-style decision out β the bridge between this course's analog half and its digital half.
Where You'll Meet Comparators
- Threshold alarms: over-temperature, low-battery, light/dark switches (a thermistor or photodiode from Lesson 2 sets one input).
- Zero-crossing detectors: firing the TRIAC phase-control circuits from Lesson 3 in sync with the AC line.
- Waveform squaring: turning any periodic signal into a clean logic-compatible square wave.
The Integrator and the Differentiator
Swap one resistor of the inverting amplifier for a capacitor and the circuit stops multiplying and starts doing calculus β in real time, on real voltages.
Integrator: Capacitor in the Feedback Path
The virtual ground still fixes the input current at Vin/Rin; that current now charges Cf, so the output ramps at a rate proportional to the input level. Consequences you can see on a scope:
- Square wave in β triangle wave out (constant input = constant-slope ramp, flipping with each half-cycle).
- DC in β runaway ramp β the circuit integrates forever until it hits a rail, which is why practical integrators add a large bleed resistor across Cf.
- Applications: ramp/sweep generators, triangle-wave oscillators, active filters, and the front half of analog PID controllers.
Differentiator: Capacitor at the Input
Current only flows through an input capacitor when the input is changing, so the output reports the input's slope:
- Triangle in β square out (constant slopes become constant levels).
- Square in β sharp spikes at each edge β instant edge detection.
- Applications: rate-of-change alarms (how fast is the temperature rising?), edge detectors, FM demodulation. Practical versions add a small series resistor to tame high-frequency noise, which differentiation amplifies aggressively.
Feedback Fundamentals: The Big Idea
Every circuit in this lesson is one idea wearing six costumes: take an absurd amount of raw gain and spend it buying precision.
What Negative Feedback Buys
- Gain set by parts you choose: AOL varies chip-to-chip and with temperature; Rf/Rin is a ratio of 1% resistors. Closed-loop gain inherits the resistors' precision, not the chip's chaos.
- Bandwidth: gain Γ bandwidth β constant (the GBP, ~1 MHz for a 741). Configure less gain, receive more bandwidth β a trade you control.
- Lower distortion, stable impedances: feedback continuously corrects the output against the input, flattening nonlinearities that plague open-loop stages like the CE amplifier.
One Table to Rule the Six Configurations
| Circuit | Feedback | Gain | Signature Behavior | Classic Use |
|---|---|---|---|---|
| Inverting | Negative (Rf) | βRf/Rin | Virtual ground; Zin = Rin | Scaling, mixing, signal inversion |
| Non-inverting | Negative (divider) | 1 + Rf/Rin | Huge Zin; gain β₯ 1 | Sensor amplification |
| Follower | Negative (100%) | exactly 1 | Impedance transformer | Buffering weak sources |
| Comparator | None | AOL (rails) | Digital decision output | Thresholds, zero-cross |
| Integrator | Negative (Cf) | β1/(RCΒ·s) | Square β triangle; accumulates | Ramps, filters, PID |
| Differentiator | Negative (Cin path) | βRCΒ·s | Triangle β square; edges β spikes | Rate alarms, edge detect |