Logarithmic magnitude plot of a constant-gain system: In Bode plot analysis, what is the log magnitude curve corresponding to a constant gain K?

Introduction / Context:
Bode plots represent frequency response in logarithmic scale. The magnitude plot uses decibels to make multiplicative relationships additive, simplifying system analysis.

Given Data / Assumptions:

• System transfer function has only a constant gain K, with no frequency-dependent terms.
• Magnitude response is frequency-independent.

Concept / Approach:

Magnitude in decibels is given by 20 log(K). For any frequency, the magnitude remains constant, so the graph is a flat line parallel to the frequency axis.

Step-by-Step Solution:

Verification / Alternative check:

Compare with Bode plots of poles/zeros: poles give –20 dB/decade slopes, zeros give +20 dB/decade slopes. A constant gain has none, so slope = 0.

Why Other Options Are Wrong:

• Horizontal line without specifying decibel magnitude is incomplete.
• Inclined lines occur only with frequency-dependent poles or zeros.

Common Pitfalls:

• Mixing up magnitude scale (linear vs. decibels).

Final Answer:

A horizontal straight line with magnitude 20 log K decibels.