• phiby

#### phiby

Since the deci in decibels means 10, why is decibels of Magnitude in the Bode plot calculated as 20log instead of 10log?

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:

$$P \propto A^2$$
$$10 \cdot \log {P \over P_0} = 10 \cdot \log {A^2 \over A_0^2} = 20 \cdot \log {A \over A_0}$$

## 1. Why is 20log used in Bode plots instead of 10log?

The use of 20log in Bode plots is due to the fact that the magnitude of the transfer function is represented in decibels (dB), which is a logarithmic scale. The decibel scale is based on a power ratio of 10, so using 20log allows for a more accurate representation of the magnitude compared to using 10log.

While it is possible to use 10log in Bode plots, it is not recommended as it does not accurately represent the magnitude of the transfer function. Using 20log is the standard convention in Bode plots and allows for a better understanding of the frequency response of a system.

## 3. How is the decibel scale related to 20log and 10log?

The decibel scale is a logarithmic scale that is used to measure the magnitude of a signal. It is based on a power ratio of 10, and as such, 20log and 10log are used to convert between the decibel scale and linear scale. 20log is used for power ratios, while 10log is used for voltage and current ratios.

## 4. Is it necessary to use decibels in Bode plots?

While it is not necessary to use decibels in Bode plots, it is the standard convention and offers several advantages. Decibels allow for a wider range of values to be represented on a graph, making it easier to compare different magnitudes. Additionally, decibels are useful for representing the relative strength or weakness of a signal.

## 5. Are there any drawbacks to using 20log in Bode plots?

One potential drawback of using 20log in Bode plots is that it can be more difficult to interpret for those who are not familiar with logarithmic scales. This may make it challenging for non-experts to understand the frequency response of a system. Additionally, using decibels can sometimes obscure the actual values of the magnitude, making it less precise compared to using a linear scale.