Digital Signal Processing Reference
In-Depth Information
In the digital world, the concept of resistance and power do
not exist. A given signal has specific amplitude, expressed in
a digital numerical system (such as signed fractional or integer for
example).
Understanding that dB increases using the two measurement
methods is important. Let's look at doubling of the amplitude
ratio and doubling of the power ratio:
6.02 dB
voltage
¼
6.02 dB
digital value
¼
20
log (2 / 1)
3.01 dB
power
¼
log (2 / 1)
This is why shifting a digital signal left one bit (multiplying by
2) will cause a 6 dB signal power increase, and why so often the
term 6 dB/bit is used in conjunction with ADCs, DACs or digital
systems in general.
By the same reasoning, doubling in power to an RF engineer
means a 3 dB increase. This will impact upon the entire system:
coding gain, as used with error correcting code methods, is based
upon power. All signals at antenna interfaces are defined in terms
of power, and the decibels used will be power ratios.
In both systems, ratios of equal power or voltage are 0 dB. For
example, a unity gain amplifier has a gain of 0 dB.
0dB
power
¼
10
log (1 / 1)
A loss would be expressed as a negative dB. For example
a circuit whose output is equal to ½ the input power:
10
3.01 dB
power
¼
10
log (1 / 2)
