Bode diagram slope contribution: In a log magnitude plot, a single pole factor (1 + s/ω) in the transfer function contributes a slope of how many decibels per octave at high frequency?

Introduction / Context:Bode diagrams are frequency response plots showing system behavior on a logarithmic scale. The slope of the magnitude plot indicates how quickly the response falls with frequency. A single pole introduces a characteristic slope change.

Given Data / Assumptions:

• We are analyzing a single pole contribution to a Bode magnitude plot.
• Frequency scaling is in octaves (doubling of frequency).

Concept / Approach:

A single pole contributes –20 dB per decade beyond its corner frequency. Since one decade = 10× frequency and one octave = 2× frequency, the per-octave slope must be converted accordingly.

Step-by-Step Solution:

Verification / Alternative check:

Textbook Bode plot rules confirm: each pole beyond the break frequency introduces a –20 dB/decade slope or equivalently –6 dB/octave.

Why Other Options Are Wrong:

• –20 dB/octave: too steep; this is per decade, not octave.
• –10 dB/octave: incorrect conversion.
• –2 dB/octave: too shallow.
• –40 dB/octave: corresponds to two poles, not one.

Common Pitfalls:

• Confusing decade with octave.
• Mixing the effect of a single pole with that of multiple poles.

Final Answer:

–6 dB per octave.