Crystal Instruments Coco-80 - Db and Linear Magnitude

CoCo-80 User Manual
105
dB and Linear Magnitude
Most often, amplitude or power spectra are shown in the logarithmic unit decibels
(dB). Using this unit of measure, it is easy to view wide dynamic ranges; that is, it
is easy to see small signal components in the presence of large ones. The decibel is
a unit of ratio and is computed as:
dB = 10log
10
(PowerP
ref
)
where Power is the measured power and P
ref
is the reference power. For amplitude
ratios, the formula is:
dB = 20log
10
(AmplA
ref
)
where Ampl is the measured amplitude and A
ref
is the reference amplitude.
When using amplitude or power as the amplitude-squared of the same signal, the
resulting decibel level is exactly the same. Multiplying the decibel ratio by two is
equivalent to squaring the ratio. Therefore, you obtain the same decibel level and
display regardless of whether you use the amplitude or power spectrum.
As shown in the preceding equations for power and amplitude, you must supply a
reference for a measure in decibels. This reference then corresponds to the 0 dB
level. Different conventions are used for different types of signals. A common
convention is to use the reference 1 Vrms for amplitude or 1 Vrms squared for
power, yielding a unit in dBV or dBVrms. In this case, 1 Vrms corresponds to 0 dB.
Another common form of dB is dBm, which corresponds to a reference of 1 mW
into a load of 50 for radio frequencies where 0 dB is 0.22 Vrms, or 600 for
audio frequencies where 0 dB is 0.78 Vrms.
The picture below shows a sine wave with 1 V amplitude displayed in dB. Because
the reference is 1 Vpk , it shows the peak value of this sine wave as 0 dB.
Figure 116. Show a 1Vpk sine signal in frequency domain with dB scaling.