Special Edition, Part 5.
Welcome to day five of our great exploration of the dB. We’re getting close to defining the difference between -10 dBV and +4 dBu. Hang in there. Please make sure you are acquainted with the previous four issues of inSync before tackling this material.
Yesterday we closed with a look at dBu. The dBV is very similar. In fact the only important difference is just that is has a different reference voltage level. The two references aren’t really designed to be intermingled, which is the crux of the problem we so often run in to. Because we buy gear that references each type of level we do intermingle them in practice. We’ll get back to all this. For now we shall just look at how the dBV works.
dBV
Finally we have an easy one. It works exactly the same way as the dBu, but we’ll quickly go over the math to illustrate (hold the groans please). 0 dBV was conveniently established with a reference level of 1 volt. That means 1 volt equals 0 dBV. If you’ve been following the math you will see that voltages of less than 1 volt will give us dBV levels in negative numbers, while voltages greater than 1 volt will yield dBV values greater than 0. It works out that our -10 dBV equipment produces a voltage of .316 volts. Here’s the math:
20log (.316/1) = -10 dBV
Look back at the mixing board example from yesterday. If your -10 gear could somehow muster up that same 15.5 volts that your +4 gear can (which it typically cannot), the corresponding dBV value would be +23.8 dBV. The math looks like this:
20log (15.5/1) = +23.8 dBV
Got it? In dBu land that same 15.5 volts is +26 dBu. Strange, but that’s what happens when you have two different references.
Be careful jumping to conclusions
So that means there’s a 2.2 dB difference between +4 and -10 (26 – 23.8 = 2.2)? No. All we’ve shown is that there is a 2.2 dB difference between a voltage that is compared to two different references (in this case .775 & 1 volt) into the same load. Put more simply, there is a 2.2 dB difference between the “reference” voltages for dBu and dBV. Using the 20 log formula it’s easy to show the 2.2 difference between the voltage referenced in dBV versus dBu:
20log(1/0.775) = 2.2 dB
So 2.2 is not the answer for the difference between +4 dBu and -10 dBV. It’s the answer for the difference between their reference voltages. +4 and -10 clearly are not zero, so you can see why we need to go a bit further. If you plugged the actual voltage levels for +4 dBu and -10 dBV into our formula what would you get?
20log (1.23/0.316) = 11.8044 dB
Let’s call it 11.8 for short. Voila! That’s it! The difference between +4 dBu and -10 dBV is 11.8 dB. You can now amaze your friends with your command of our audio language.
It can’t be that easy
But it is that easy. And hopefully it actually makes some sense now that we’ve provided a lot of the background. But there is more to the story. What does this 11.8 dB difference really mean? In short, it means there is an 11.8 dB difference between the zero reference or nominal signal level of equipment rated at +4 dBu versus -10 dBV. There are many ways this affects us, but before we go too much further we need to close a few holes we left behind along the way.
This is not your father’s impedance
We have shown how these references fit into a historical context, specifically the 600 ohm world of the telecommunications industry. In modern equipment designs, there is no concern over 600 ohms because the actual input impedances are much higher. As stated before, they are so high that for all practical purposes the power transfer can be ignored given the typical voltages involved. Further, when the load impedance stays the same, two voltages can be accurately compared without even knowing what the impedance is. So in modern audio equipment we just look at voltage differences. There are exceptions, but in terms of the line level gear we deal with, almost everything is referenced to a voltage; it’s just that it may be a dBu reference or a dBV reference. In fact the dBV came into existence as a standard way of looking at only voltage into very high impedances (1000 ohms or higher, typically more like 10,000 ohms). This is where our second homework question from two days ago is relevant. You remember, the one about raising the impedance of a load from 600 ohms to 10,000 ohms and what that does to power transfer. Coincidentally, putting 1 volt of electricity across a load of 1000 ohms will cause enough current flow to produce 1 milliwatt of power (0dBm).
P = E2/R
P = 12/1000
P = 0.001 watts
How handy, and actually it isn’t a coincidence, however it’s not that important because we aren’t too concerned with power transfer these days as input impedances are generally thousands of ohms. But…
He said “but.” Heh, Heh…
A complication arises when you connect your gear to something that does have a 600 ohm input impedance. It’s not too common to find such a device these days, but 20 or 30 years ago it wasn’t hard at all, and this made things quite confusing. If you were to plug a device rated at 0 dBV (1 volt) nominal output into a device rated at 0 dBm (1 milliwatt @ 600 ohms, or .775 volts) less current will be required by the lower .775 volt device to produce the same power (1 milliwatt) at it’s input. Most devices these days can’t easily produce this much output power (remember they are designed to be driven into loads much higher than even 1000 ohms), but if one could what would happen?
Hang on
The device with the 600 ohm input is designed to register “zero” on its dBm metering when it is hit with an input of .775 volts because at 600 ohms this is 0 dBm (the all important power transfer level “required” by the device to properly drive it). If we had a device with a 0 dBV nominal output it would reach “zero” on its meter at 1 volt. Hitting the receiving device with a 1 volt signal is going to cause its meter to show +2.2 dB. This is the quandary caused by the two different standards. There really is no easy way to reconcile them. 2.2 dB is close enough that it’s not that big of a deal and you can probably just live with it, assuming the upstream device can really deliver this much current into the 600 ohm load. If it can’t, then it is going to go into distortion before it even gets to its 1 volt output. Meters aren’t always going to tell you this so you have to listen and be aware of what you are doing.
dBv?
The discrepancy described above between equipment rated at 0 dBV and 0 dBm is actually what caused the dBu standard to come into existence. The Bell Labs guys wanted a way to differentiate between equipment that was true 600 ohm 0 dBm equipment and equipment with higher input impedances that might still be interfaced with equipment rated in dBm. The dBu was adopted and used the .775 volt reference that arises from a 600 ohm load, but it really ignored impedance. Actually, when it first came out it was known as the dBv (little “v”), but people began to use the little “v” and the upper case “V” interchangeably. This obviously caused a lot of confusion and is probably one of the many reasons why this whole topic is so misunderstood to this day. Anyway, they changed the little “v” to a “u” and that was that. So the dBv and dBu are actually the same thing, but dBu is the proper term. It is widely believed that the “u” stands for “unterminated,” because the dBu reference isn’t concerned with the termination impedance.
2.2 dB and you
Because of these two “standards” you know right away that there is a built in 2.2 dB discrepancy between anything rated dBV versus dBu. At a practical level, this means that a 1 volt signal applied to a device rated in dBV will register 2.2 dB lower on its meters than a device calibrated to dBu. We rarely observe this phenomenon, however, because most of the time we are interfacing equipment rated at -10 dBV zero reference with equipment rated at +4 dBu, in which case the levels are much further off than a mere 2.2 dB. How much? 11.8 dB.
Okay, that’s it for today. Tomorrow we are going to wrap this thing up with a look at what all this means at a practical level.