Logarithmic magnitude plot of a constant-gain system: In Bode plot analysis, what is the log magnitude curve corresponding to a constant gain K?
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AA horizontal straight line
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BA horizontal straight line with magnitude 20 log K decibels
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CAn inclined line having slope K
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DAn inclined line having slope –K
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ENone of the above
Answer
Correct Answer: A horizontal straight line with magnitude 20 log K decibels
Explanation
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:
Write gain in decibels: 20 log K.Plot magnitude vs. log frequency: horizontal line at that level.No slope is present because there is no dependence on frequency.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.