Terminology: Why critical frequencies are often called the −3 dB points Are the critical (cutoff) frequencies of first-order filters commonly referred to as the −3 dB frequencies?

Introduction / Context:“Critical frequency,” “cutoff frequency,” and “−3 dB frequency” are terms frequently used interchangeably for first-order filters and many normalized second-order prototypes. Understanding why helps in reading datasheets and designing networks.

Given Data / Assumptions:

• First-order RC or RL filters in sinusoidal steady state.
• Cutoff defined where the magnitude falls to 1 / sqrt(2) of the passband value.
• Decibel conversion for voltage ratios: 20 * log10(Vout / Vin).

Concept / Approach:

At the cutoff frequency fc, |H(j2 * pi * fc)| = 1 / sqrt(2) ≈ 0.707 for first-order filters. Converting to decibels, 20 * log10(0.707) ≈ −3.01 dB, hence the shorthand “−3 dB frequency.” This convention extends to many higher-order responses when defining half-power points for bandwidth measurements.

Step-by-Step Solution:

Verification / Alternative check:

Measure a first-order low-pass Bode plot; the intersection of the 0 dB low-frequency asymptote and the −20 dB/decade high-frequency asymptote occurs at fc and is labeled −3 dB, matching the analytic result.

Why Other Options Are Wrong:

• It is not limited to Butterworth or RC; RL and many normalized second-order filters use the same naming for their half-power points.
• Load reactance does not alter the definition of the filter’s own cutoff when referenced to the designed transfer function.

Common Pitfalls:

Confusing −3 dB (voltage) with −3 dB (power) without recognizing that −3 dB in voltage implies half power only when the load impedance is constant across frequency. Nevertheless, the naming convention for cutoff remains −3 dB for first-order sections.

Final Answer:

True