Electronics 1 — Filters & Op-Amps

The RC low-pass filter

continues from lesson 1 — values defined earlier in the course stay live here

One resistor, one capacitor — the simplest useful circuit in electronics. Low frequencies pass; highs are shorted away by the cap. The boundary is the cutoff: f_c = 1/(2π·R·C), where the output is down exactly 3 dB:

R_{f} := 1000 ohm

= 1000 ohm

C_{f} := 1e-6 F

= 0.000001 F 1 µF

f_{c} = \frac{1}{2 \cdot \pi \cdot R_{f} \cdot C_{f}}

= 159.15 Hz cutoff ≈ 159 Hz

1 / sqrt(1 + (x / 159.2)^2)

filter response |H| vs frequency (Hz) — 0.707 at the cutoff, sliding down after

✓ pass

\mathrm{abs}\left(\frac{1}{\sqrt{1 + 1}} - 0.7071\right) < 0.001

AT the cutoff: exactly 1/√2 — the −3 dB point

Swap the R and C positions and the same math gives a high-pass — this pair is the tone knob on every guitar amp.