# dBV, dBu, and dBm

I’ve always have a little trouble remembering the relationship between dBm and the more common signal measurements of dBu and dBV.  The other day I was looking at a transfer function, and I was given results in dBm - the impetus for this post.

First, I should make sure we’re all on the same page.  What is a decibel (dB)?  The decibel is a relative measurement.  For voltage we calculate dB as 20log10(Voltage/Reference), where the reference can be absolute (like with dBu and dBV) or relative (plain old dB).  For an amplifier that outputs a signal twice as large as the input, 20log10(2/1) = 6 .02 dB.  If we ran a signal through this amplifier twice, our output is 4 times as large as the input, or 20log10(4/1) = 12.04dB.  This is the value of a dB scale - we can add gain values in dB instead of multiplying them: 22=4, while 6.02+6.02=12.04.

Before going on I should point out that dBm is not an appropriate measure for a transfer function.  Straight dB is the way to go, as a linear transfer function should produce an output relative to the input - not relative to an absolute value like dBm, dBu, or dBV.  Let’s say I put 0.5 volts into a system, and I get 0.25 volts back out: 20*log10(0.25/0.5) = -6 dB.

So then dBV, dBu, and dBm are all absolute measurements and each has a defined reference value:

• dBV - 1 Volt
• dBu - 0.775 Volts
• dBm - 1 Milliwatt

dBV is straight ahead and simple to work with - this is the measure I use most frequently.  The dBV value of any voltage is 20*log10(V/1), so 1 Volt is 0 dBV, 2 Volts is 6 dBV, and 0.5 Volts is -6 dBV.

Let’s skip to dBm for a second.  This has a reference of 1 milliwatt, a unit of power.  Power is related to voltage by the equation P = VV/R, where R is the resistance the power is dissipated through.  For instance, if I drive 1 Volt into 1000 Ohms of resistance, 1V1V/1000Ohms = 0.001 Watts = 1 mW.  If I increase the voltage by 6 dB (a factor of 2) to 2 Volts, now I’m dissipating 2V2V/1000Ohms = 4 mW.  This is important - doubling the voltage does not lead to a doubling of power, since the power is related to the square of the voltage.  We actually have to use a different formula for dB of power, 10log10(Power/Reference).  With this formula, if we put in our 4mW and 1mW from above, we still get 6 dB of gain.  Math works!

Back to dBu.  dBu is referenced to 0.775 Volts - an odd number to use as a reference.  However, if you calculate the power dissipating by 0dBu through 600Ohms (a long-standing common value for transmission lines), you wind up with exactly 1mW of power, 0dBm.  So 0dBu = 0dBm, if and only if the load is 600 Ohms.  At any other load impedance this relationship changes.

So back to that transfer function in dBm.  In order to get a relative dB measurement I needed two things: the source voltage and the load impedance.  Knowing the load impedance allows you to calculate the voltage output from the system: V = sqrt(PR).  This is still an absolute measurement, so you need to know what the input signal was to calculate the dB out: 20log10(Output/Input).

# Pro Tools – Shortcut of the Week (2009.06.01)

Pro Tools is a strong multi-track editing program, but unless you’re willing to drop some change on a custom keyboard, it can be tough to learn all the keyboard shortcuts.  I’m featuring one a week in an attempt to highlight the tricks I find most useful.

Zoomer Tool:  Command+1

Trimmer Tool:  Command+2

Selector Tool:  Command+3

Grabber Tool:  Command+4

Scrubber Tool:  Command+5

Pencil Tool:  Command+6

Smart Tool:  Command+7

Seven shortcuts!?!  While normally I think that this would be too many to digest in one shot, it wouldn’t make any sense to list these separately.  These tools are lined up across the toolbar in the order above, with the exception of the Smart Tool.  I think it would be harder to remember the shortcuts above if you didn’t see them in one place.

The Smart Tool is actually sitting under the Trimmer/Selector/Grabber tools, but I think it’s easy enough to remember that as command+7 - we read left to right, top to bottom.

So why bother with these shortcuts?  Why not just use the Smart Tool all the time?  I’m just making the transition away from the Smart Tool myself.  The Smart Tool is easy - no need to remember which tool does what, but it also doesn’t have much depth.  Among other behaviors, command-clicking changes functions with each tool.  This means more control with fewer wrist movements, and that’s the main purpose of shortcuts, right?