Electronics 1 — Filters & Op-Amps
Decibels — the language of gain
ELI5: signal chains multiply gains stage after stage, but multiplying big numbers is annoying — so engineers switch to decibels, where multiplying becomes adding. dB = 20·log₁₀(V_out/V_in): +6 dB ≈ ×2, and −3 dB ≈ ×0.707, the famous "half-power point."
a ×10 voltage amplifier
= = 20 dB
✓ pass −3 dB really is ×1/√2
Real-world hook: decibels measure audio volume, Wi-Fi signal strength, and antenna gain — anywhere quantities span a huge range.