Last
time we were noting how the humble dB has been used and abused, and how it has
spread like a computer virus throughout engineering circles. It’s now used to measure so many things (other
than audio power) in so many ways (often incorrectly) that much of its meaning can
be lost.
Let
me get back to basics before I confuse anyone (including self) any
further. It is possible to make sense of
this bedlam, by rigidly enforcing two simple rules:
(1) The decibel is
always used to express a ratio of power levels. Quantities that are not powers must be made
proportional to power. Since power is
proportional to the square of voltage for a fixed
impedance, output and input voltages may be squared before calculating
their ratio. Most people just remember
to multiply the log of the linear quantities (e.g. Volts) by 20 instead of 10,
which can accomplish the same thing in fewer steps, but you must remember this only
works if the impedance remains the same throughout. If the impedance changes, you must
work out the output and input power some other way (like figuring out the
resistance at each point and calculating the powers from there), before logging
and multiplying by 10.
(2) The units used
to measure the input and output power levels must be the same, so they will
cancel out. Example measurements could
be in watts, volts, cubits, or pints of beer.
As a result decibels themselves have no dimension as such, and so technically
speaking they are not units. The dB (without
any suffix attached) is used to measure power ratios, so it can measure gain or
loss, but there is no reference to either the input or output level, just the
ratio. The statement “I set the level to 0 dB” is meaningless.
Make
these two simple rules into your dB religion, and you’ll find you won’t have
nearly as much trouble working with decibels.
An
additional note concerning dB’s and audio: because modern audio systems
don’t worry much about impedance matching (all sources are very low impedance, and
all inputs are very high impedance, so “open-circuit” conditions prevail),
there has been a transition from using dB with power references (“dBm”) towards
voltage references (“dBu”). A few months
ago in this very space, I was referring to older transmission practices in
broadcast, and used “dBu.” Laverne
Siemens of Golden West quite properly pounced, and reminded me that in the old
days nobody used the expression “dBu.”
Transformer coupled audio equipment would be specified using dBm, since
impedance was still vitally important then.
Today we use dBu (0 dBu = 0.775 V, the voltage across a 600 ohm load at 0
dBm) extensively, and sometimes carelessly, and pretend that impedance doesn’t
matter. And it doesn’t, really, as long
as it doesn’t change.
But
try always to remember the power origins of the decibel,
and you’ll avoid a lot of confusion, and have guaranteed happy karma.
dB = 10 log(PO/PI)
= 10 log(VO/VI)2*
= 20 log(VO/VI)*
*but only if
the impedance remains the same!