- #1
phiby
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Since the deci in decibels means 10, why is decibels of Magnitude in the Bode plot calculated as 20log instead of 10log?
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SUMMARY
The Bode plot calculates decibels of magnitude using the formula 20log instead of 10log due to the relationship between power and amplitude. Power is proportional to the square of the amplitude, necessitating an additional factor of 2 in the logarithmic conversion. This results in the formula: 10 · log(P/P0) = 10 · log(A²/A0²) = 20 · log(A/A0). Understanding this relationship is crucial for accurately interpreting Bode plots in control systems and signal processing.
PREREQUISITES- Understanding of logarithmic functions and their properties
- Basic knowledge of power and amplitude in signal processing
- Familiarity with Bode plots and their applications in control systems
- Concept of decibels and their use in measuring gain
- Study the derivation of the Bode plot and its significance in control theory
- Learn about the relationship between power and amplitude in signal processing
- Explore the application of decibels in various engineering fields
- Investigate other types of plots used in control systems, such as Nyquist and Nichols plots
Electrical engineers, control system designers, and anyone involved in signal processing who seeks to deepen their understanding of Bode plots and the mathematical principles behind them.
- #2
I like Serena
Science Advisor
Homework Helper
MHB
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Hi phiby! 
The Bode plot shows the power gain in dB.
Power is correlated to the square of the amplitude.
Since amplitude is used as input, you get an extra factor 2.
In formula form:
[tex]P \propto A^2[/tex]
[tex]10 \cdot \log {P \over P_0} = 10 \cdot \log {A^2 \over A_0^2} = 20 \cdot \log {A \over A_0}[/tex]
The Bode plot shows the power gain in dB.
Power is correlated to the square of the amplitude.
Since amplitude is used as input, you get an extra factor 2.
In formula form:
[tex]P \propto A^2[/tex]
[tex]10 \cdot \log {P \over P_0} = 10 \cdot \log {A^2 \over A_0^2} = 20 \cdot \log {A \over A_0}[/tex]
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