Analog Formula Reference, Glossary & Self-Assessment

A compact reference for the whole course. The key formulas grouped by topic (circuits, devices, amplifiers, op-amps, filters, feedback/stability, oscillators, power, noise and converters), a glossary of essential analog terms, a self-assessment path by level, and a Python 'formula self-check' that evaluates the core formulas with standard values so you can test your own hand calculations.

After working through the course, you need a quick place to look up a formula, recall a definition or test yourself. This lesson collects the essentials and points back to the detailed lessons.

Use the self-check: compute each value by hand first, then compare with the verified Python output below.

An analogy

This lesson is the toolbox lid: every tool (formula) is outlined in its place so you can grab the right one quickly — the lessons are where you learned how to use each tool.

Glossary A–F

Essential terms:

Glossary G–R

More terms:

Glossary S–Z

And the rest:

Self-assessment path

Beginner check: compute dB conversions, divider outputs, RC corners, diode operating points. Intermediate: bias and analyse a CE stage, design op-amp gain stages and a Sallen-Key filter, size a 555 timer. Advanced: estimate bandwidth with Miller, phase margin with capacitive loads, noise budgets, ADC front-end settling. Professional: produce an error budget, a level diagram, a compensated two-stage op-amp and a verified capstone report. Each lesson's problem and quiz form the assessment bank.

Formulas

Worked example: dB to ratio

Given: −6 dB (voltage)

Find: Ratio.

Answer: 0.501

Worked example: Op-amp bandwidth

Given: GBW 10 MHz, gain 20

Find: Bandwidth.

Answer: 500 kHz

Worked example: Thermal voltage

Given: T = 350 K

Find: V_T.

Answer: ≈ 30.2 mV

Where to find each topic

  Foundations ........ signals/dB, circuit analysis, passives, transients
  Devices ............ semiconductor physics, diodes, special diodes, opto, rectifiers, wave-shaping
  Transistors ........ BJT, biasing, BJT amps, FETs, FET amps, small-signal/Miller, frequency response
  Op-amps ............ diff pairs, mirrors, op-amp basics/circuits/applications, comparators
  Signal processing .. filters, feedback, stability, oscillators, 555/waveforms
  Power .............. power amps, thermal, linear/switching regulators, references
  Precision .......... noise, distortion, signal conditioning, error budgets
  Mixed-signal & ICs . ADC front end, DAC, switches/SC, OTA design, PLL/comms
  Practice ........... measurement, debugging, PCB/EMI, SPICE, components, control
  Projects ........... applications, patterns/labs, capstones

The course is organised as a path from foundations to professional practice; each line lists the lessons that go deeper into the formulas summarised here.

Formula self-check

import math
# Formula self-check: evaluate a handful of core analog formulas with standard example values
checks = {
    "RC corner 1k/100n (Hz)": 1 / (2 * math.pi * 1e3 * 100e-9),
    "gm at 1 mA (mA/V)": 1e-3 / 0.02585 * 1e3,
    "non-inverting gain Rf 9k Rg 1k": 1 + 9e3 / 1e3,
    "LC resonance 10uH/100nF (kHz)": 1 / (2 * math.pi * math.sqrt(10e-6 * 100e-9)) / 1e3,
    "thermal noise 1k (nV/rtHz)": math.sqrt(4 * 1.380649e-23 * 300 * 1e3) * 1e9,
    "12-bit ideal SNR (dB)": 6.02 * 12 + 1.76,
    "buck duty 12->5 V": 5 / 12,
    "555 astable 10k/10k/10n (Hz)": 1.44 / ((10e3 + 20e3) * 10e-9),
    "full-power BW 0.5 V/us, 5 V pk (kHz)": 0.5e6 / (2 * math.pi * 5) / 1e3,
    "-3 dB as voltage ratio": 10 ** (-3 / 20),
}
for k, v in checks.items():
    print(f"{k:38s} {v:10.4g}")
# RC corner 1k/100n (Hz)                       1592
# gm at 1 mA (mA/V)                           38.68
# non-inverting gain Rf 9k Rg 1k                 10
# LC resonance 10uH/100nF (kHz)               159.2
# thermal noise 1k (nV/rtHz)                   4.07
# 12-bit ideal SNR (dB)                          74
# buck duty 12->5 V                          0.4167
# 555 astable 10k/10k/10n (Hz)                 4800
# full-power BW 0.5 V/us, 5 V pk (kHz)        15.92
# -3 dB as voltage ratio                     0.7079

Work each value out by hand first: 1.59 kHz, 38.7 mA/V, gain 10, 159 kHz, 4.07 nV/√Hz, 74 dB, D = 0.417, 4.8 kHz, 15.9 kHz and 0.708. If your answer differs, revisit the corresponding lesson.

Common mistakes

Applications

Key takeaways

Going further