First-order filters: A basic single-pole RC or RL filter exhibits a magnitude slope (roll-off rate) of approximately 20 dB per decade beyond its cutoff frequency. State whether this is true or false.

Introduction / Context:
Single-pole filters are the simplest building blocks in analog electronics. Understanding their asymptotic roll-off rate is essential for quick Bode plot sketches, noise estimation, and cascade design for higher-order responses.

Given Data / Assumptions:

• Filter is first-order (one reactive element and one resistive element).
• Type is RC or RL (either low-pass or high-pass topology).
• Cutoff (break) frequency is defined where magnitude is 1/√2 of passband (−3 dB point).

Concept / Approach:

A first-order transfer function has the form |H(jω)| = 1 / √(1 + (ω/ωc)^2) for a low-pass (or its dual for high-pass). On a log-magnitude (dB) plot, the asymptotes differ by 20 dB per decade between successive decades of frequency beyond the break point, yielding the well-known slope of 20 dB/dec (≈6 dB/octave).

Step-by-Step Solution:

Verification / Alternative check:

Construct Bode asymptotes: horizontal in the passband, then a straight line with slope ±20 dB/dec starting one decade away from the break, intersecting at the corner. SPICE simulations confirm within a small margin near the corner where the exact response deviates by up to 3 dB.

Why Other Options Are Wrong:

• “False” would imply a different slope for first-order filters; slopes like 40 dB/dec or 60 dB/dec correspond to second- or third-order networks (additional poles).

Common Pitfalls:

Confusing per-octave and per-decade slopes (6 dB/oct vs 20 dB/dec); mixing passband ripple (active filters) with simple RC/RL responses; misidentifying the −3 dB point as the slope rather than the breakpoint.

Final Answer:

True