Recently, we posted an article titled "What is dB (Decibel)?" (Document 1) on the technical documentation page of Ono Sokki website. In this column, we will provide supplementary information regarding frequently asked questions from FFT analyzer users.
What does "dBV" mean as the unit for the vertical axis (Y-axis) in an FFT analyzer, and what does it mean when the value is negative?
A decibel is the logarithm of the ratio of two physical quantities. Normally, a decibel is a relative value of two quantities, but if a reference value is defined as a specific physical quantity, it can be converted into a decibel value (absolute level value) that can be expressed as an absolute physical quantity.
"dBV" is the absolute level value of a voltage signal (in volts) with an RMS value of 1V as the reference value. For example, 10dBV corresponds to a signal with an RMS value of 3.16V (=) (see Figure 1). The formulas for converting between voltage value V and decibel value X (dBV) are given in equations (4-4) and (4-5) of Document 1, which are reproduced here.
X=20log(V) .................................（1）
.................................（2）
The initial setting for the vertical axis in the power spectrum display on an FFT analyzer is logarithmic (i.e., the display unit is dBV), but by changing it to linear (i.e., the display unit is not logarithmic, but V), the voltage value (RMS value) can be read directly.
Top panel: Time waveform
Middle section: Spectrum (dBV)
Bottom panel: Spectrum (V)
-
Figure 1. Spectrum of a sinusoidal waveform (when the dB value is positive)
As can be seen in equation (1), X (dBV) is positive when the number inside the logarithmic parentheses (i.e., the argument) is 1 or greater, and negative when it is less than 1. A negative decibel value X means that the linear value (argument value) is a voltage (effective value) less than 1, and does not mean that it is a negative voltage. For example, -10 dBV is a signal with an effective value of 0.316 V (=1/) (see Figure 2).
Top panel: Time waveform
Middle section: Spectrum (dBV)
Bottom panel: Spectrum (V)
FFT analyzers have the ability to read the vertical axis of the spectrum using any physical quantity, not just the default voltage (V). The same conversion method applies in this case as well. For example, the signal from an acceleration sensor has units of m/ s², so its decibel value should be read in dBm/ s². A decibel value of -30 dBm/ s² corresponds to an acceleration value of 0.0316 m/ s².
【Note】
- The definition of a decibel is actually the logarithm of the ratio of powers, not the ratio of voltages. Since power is proportional to the square of the voltage, the decibel values for both are the same (see "3.1 Definition of Decibels" in Document 1).
- As the name suggests, the power spectrum calculated by an FFT analyzer calculates power values in the frequency band, resulting in a value with dimensions of EU (representing an arbitrary physical unit) squared. The conversion to decibels is calculated as 10 log(power value).
------------------------------------------
The following link will take you to our company's website.
Ono Ono Sokki Technical Document: "What is dB (Decibel)?"
Ono Sokki Everyday Measurements: Pascals and Decibels
(Excerpt from the email newsletter issued on July 25, 2011)
