Electronics 1 — Filters & Op-Amps

Decibels — the language of gain

Signal chains multiply gains; engineers prefer adding. dB = 20·log₁₀(V_out/V_in) turns multiplication into addition: +6 dB ≈ ×2, −3 dB ≈ ×0.707 (the famous "half-power point"):

G_{ratio} = 10

a ×10 voltage amplifier

G_{dB} = \frac{20 \cdot \mathrm{log}\left(G_{ratio}\right)}{\mathrm{log}\left(10\right)}

20

= 20 dB

✓ pass

\mathrm{abs}\left(\frac{20 \cdot \mathrm{log}\left(0.7071\right)}{\mathrm{log}\left(10\right)} - -3.01\right) < 0.01

−3 dB really is 1/√2