Special +4/-10 Edition
More than you want to know about how dB’s work – Part 1
Welcome to the 800th edition of inSync. Over the past few years we’ve brought you the news and answered hundreds of technical questions about everything from burning CD’s to synchronizing MIDI to film, to tracking down ground loop hums, to buying gear on the Internet. During that time we’ve received hundreds of other questions that we answered privately via e-mail. But there’s been one burning question through all of this that we’ve never really been able to get to… until now.
What is the actual difference between -10 and +4 and what does it mean at a practical and technical level?
Before we could try to cover it we had to have a small library of words defined in our Word for the Day archives. I’ve been sneaking these words in here and there for literally two years all in anticipation of this glorious day where we finally hit this very confusing and popular topic. So, in honor of our 800th issue of inSync (why 800th? Why not?), we shall now get down to business on this subject. Rather than give a quick answer that doesn’t produce a real understanding of it I have decided to include additional background about this thing we call the dB. There’s a lot of general confusion about the dB and its applications we will be able to clear up along the way, and in the end most of you should have a good practical understanding of what’s going on. The full explanation is going to span over several issues of inSync, and since today is Friday you’ll have to wait in suspense over the weekend until we can dig back in to it next week.
The Set Up
If you’ve managed to get this far and are still reading we shall assume you are one of the many who’ve noticed that most audio equipment seems to come with either or both -10 dBV audio connections or +4 dBu audio connections and that these refer to different signal levels. You may be aware that +4 dBu gear is sometimes considered “pro” and -10 dBV gear is considered semi-pro or consumer. You may also know, possibly by learning it the hard way, that the two levels aren’t very compatible with one another. You can’t just plug a +4 dBu device into a -10 dBV device and expect ideal results. There is a significant difference between the two. But what is it? It’s not “14.”
Due Diligence
Since you are going to have the weekend to consider this topic we recommend you spend a few minutes boning up on some terms and concepts. Before you try to tackle the upcoming sections make sure you have consulted our WFTD archives and checked out the definition for Ohm’s Law, Voltage, Current, Resistance, Impedance, dB, dBm, dBu, and dBV and followed the various linked terms in those records. Don’t worry if you don’t understand everything. Just get acquainted with the terms. You should now understand that the dB ratings we use represent some value compared to some “reference” value. The “reference” for 0 dBu = .775 volts so that means +4 dBu = 1.23 volts. Don’t worry too much if you don’t fully grasp all the math behind this (though it does really help if you do). As you read through this keep in mind that voltage is provided by a supply or source, and generally doesn’t change with different loads (resistance or impedance). The amount of current flow or amperage is what changes with different loads. Changing any of the three (voltage, current, resistance) will change the amount of power or work being done. This is a simplified generalization with exceptions, but it will help you to keep it in mind as you read.
Also of note: It is merely a matter of convention that +4 dBu gear often has balanced connections and -10 dBV gear is often unbalanced. The operating level of gear can be (for the most part) independent of the type of connections it has. For the sake of this discussion we will not concern ourselves with the implications of balancing or anything beyond the nominal operating levels of equipment.
A Word About Logs (no, not lumber)
Logarithmic equations seem to intimidate people fairly easily. But they don’t have to. Logs are a critical part of working with and understanding the dB. You will need to work with logs at a basic level to fully benefit from the explanation that is to follow. A key purpose of the logarithmic function is to make very unwieldy numbers easier to work with and visualize. Here’s a good example. Suppose you take two measurements of sound intensity in different parts of a studio. Without getting too deep into physics and all the background of how these measurements are really made just accept that you end up with numbers that represent sound power (Be careful, this is not the same as sound pressure (SPL)). So we get two numbers: 0.00012301269 and 0.000008909014. Now quickly, what is the difference between the two values? Sure, with calculators a dime a dozen, and even built into watches today, it’s pretty easy to punch in a few numbers and come up with 0.000114103676, assuming your calculator can deal with numbers this long. But for us humans these kinds of numbers are so abstract they really don’t mean anything. We can’t just look at them and draw any conclusions. But way back when scientists were wrestling with them they didn’t even have the benefit of calculators so they came up with a short cut – the log.
The logarithm is just a simple math trick. It lets us put these numbers into a form that makes them easier for us to handle and relates better to the way in which we actually perceive sound. A log is the exponent that shows the power to which a fixed number (the base) must be raised to produce a certain number. For example, 3 to the power of 2 is 9. The log of 9, with a base of 3 equals 2.
Log39 = 2
In science the base is always assumed to be 10 unless otherwise specified. The base 10 log of 100 equals 2. This is just another way of saying 10 to the power of 2 equals 100 and would normally be written as log100 = 2.
Don’t worry if you don’t fully follow all this background about logs. We have calculators today that handle the details for us. So getting back to the long numbers above, the log of the first number is -3.91, and the log of the second number is -5.05. I did a little rounding there, but we’re close enough. You can verify this with any decent calculator that has a log function. Just type in one of the long numbers above and hit the log button. So the difference between -5.05 and -3.91 = 1.14. In some applications it is easier to find the difference between the two numbers and then just find the log of that difference, but to do that you need to divide (not subtract) them. That’s just the way it works. You can accept it or go get your old math books out and learn all the subtleties. In the example we are using that would look like this.
Log ( 0.00012301269
0.000008909014) =1.14
In this example that happens to be 1.14 “Bels,” a term coined by the folks at Bell Labs years ago when they were figuring all this stuff out. In practice they opted to use the decibel, which is 1/10th of a Bel. The decibel is easy to obtain by multiplying the log by 10. This means 10log100 = 20. Applying this to our example above leaves us with a difference of 11.4 decibels.
10Log ( 0.00012301269
0.000008909014) =11.4
The decibel made a lot of the numbers those Bel scientists were crunching even easier to handle. What they left us by doing this is a legacy we will likely never depart from. The decibel is a mainstay of the audio industry. It is abbreviated dB and nowadays there are several different forms of the dB that mean different things. We will cover a few of those.
This is where we break off for this issue. Don’t worry if you don’t understand everything so far. Read through this and the linked words a couple of times, and if possible get your calculator out and punch in the numbers. You’ll find that the second or third time through you will understand it much better. We’ll pick things up on Monday and dive into a few of the forms and background of the dB and what they mean.