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The diaBolical dB
Understanding Logarithmic Scales And The deciBel
LAB
in PDF format
Blame your ears if you are having trouble dealing
with decibels (dB). The dB was originally defined as a measure of relative acoustic power
as perceived by the human ear, and the ear has a logarithmic response. The original unit
of measure was defined as the Bel after Alexander Graham Bell. In practice the deci-Bel ,
1/10 of a Bel, is used as defined in the following equation:
Based on this definition some common power ratios are:
| P2/P1 |
dB |
| 2:1 |
3 |
| 4:1 |
6 |
| 10:1 |
10 |
| 100:1 |
20 |
| 1:2 |
-3 |
| 1:4 |
-6 |
| 1:10 |
-10 |
| 1:100 |
-20 |
The logarithmic
scale provides the best view of wide dynamic range measurements. As an example consider
the FFT analysis of the waveform in figure 1. The lower trace is the power spectrum,
displayed using a logarithmic scale. It covers an amplitude range of 10,0 00:1 or 40 dB in
power. The dB scale overlays a linear grid on the logarithmic scale. This grid makes it
easy to see data separated by common multiplicative factors. For example a 2:1 steps show
up as 3 dB increments, 10:1 steps are 10 dB increments.
If you're given the relative power levels in dB you can calculate the ratio using:
Figure 1
In many applications specific reference levels of power are used. In LeCroy
oscilloscopes and most rf spectrum analyzers the power measurements are referenced to 1
milliwatt. The power spectrum display, in figure 1, has a vertical axis calibrated in
dBm,
that is dB relative to 1 milliwatt. The reference cursor, reading the spectral amplitude
at the center of the display, reads 1.78 dBm.
The absolute power can be calculated as:
Voltage ratios can also be expressed in dB. If you express power in the form of V2/R
with R the same for both measurements, then the definition of dB becomes:
Commonly used voltage ratios are:
| V2/V1 |
dB |
| 2:1 |
6 |
| 4:1 |
12 |
| 10:1 |
20 |
| 100:1 |
40 |
| 1:2 |
-6 |
| 1:4 |
-12 |
| 1:10 |
-20 |
| 1:100 |
-40 |
Given a voltage ratio in dB you can calculate the ratio of the voltages
using:
The unit dBV refers to dB relative to 1 Volt. It simply means that V1 in the
voltage ratio equation is replaced by 1 Volt. So that 6 dBV has an absolute value of 2
Volts. Similarly dBV is dB relative to a microvolt.
Relative levels in signal generators are often described in units of dBc, or decibels
relative to the carrier level. For example an arbitrary waveform generator specification
for non-harmonic spurious is < -60dBc. This means that spurious signals are 60 dB below
(1/1000th) the current carrier voltage level.
Many other "specialized" reference levels are in use with the dB scales but
these are the
most commonly encountered when dealing with LeCroy oscilloscopes and signal generators.
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