Question

In the context of Bode magnitude plots, \(40 \, {dB/decade}\) is the same as:

• A. \(12 \, {dB/octave}\)
• B. \(6 \, {dB/octave}\)
• C. \(20 \, {dB/octave}\)
• D. \(10 \, {dB/octave}\)

Hint:

In Bode plot analysis, use the conversion factor \(1 \, {decade} \approx 3.32 \, {octaves}\) to easily switch between dB/decade and dB/octave values.

Answer 1

The Correct Option is A

Step 1: Establish the relationship between a decade and an octave.
A decade represents a tenfold increase in frequency, while an octave represents a doubling of frequency. The relationship between the two is: \[ 1 \, {decade} = \frac{\log_{10}(10)}{\log_{10}(2)} \approx 3.32 \, {octaves}. \] Step 2: Convert \(40 \, {dB/decade}\) to dB/octave.
Since \(40 \, {dB/decade}\) is distributed over \(3.32 \, {octaves}\), the dB per octave is calculated as: \[ \frac{40 \, {dB}}{3.32 \, {octaves}} \approx 12 \, {dB/octave}. \] Final Answer: \[ \boxed{{(1) \(12 \, {dB/octave}\)}} \]