# MEASURING AUDIO

Measuring audio involves determining which yardstick you want to use. The same audio signal can be described several ways, and all are correct.
We can take a handful of sound (don’t try this at home) and call it +4 dBu. That same amount of sound can also be labeled:

1.228 Vrms
1.736 Vp
3.472 Vpp
1.781 dBv
4.000 dBr
4.000 dBm
2.510 mW
-4.000 dBrinv

And these are only the analog labels.

Let’s begin by finding out what a dBu is and why we started with four of them.
The sounds you hear are caused by changes in air pressure. According to reference books the smallest change in air pressure you can hear is 20 x 10-6 Pascals (Pa) which is also equal to 0 dBspl. The loudest sound (excluding certain rock concerts) humans can tolerate is 200,000,00 x 10-6 Pa. This is a ratio of 10,000,000:1. This range is too large to work with in everyday measurements.
Some people at Bell Labs created a scale with fewer numbers. They named the units Bels, after Alexander Graham Bell (I bet you always wondered why the B is capitalized). This scale is a measurement of power differences. It’s the logarithm of the ratio of two powers. This is expressed in the equation:

Power (Bels) = log (Power 1/ Power 2)

In the range of discernable sound the result of this equation is usually less than one. Since the people at Bell labs were trying to make the scale easier to use, they added a factor of ten. This is written as the letter ‘d’. We now have the ‘Decibel’ (dB). Remember any decibel scale is a power ratio and can be used for anything from the noise level of an avalanche to the power output of a satellite transmitter. The reason for so many different kinds of decibel scales is that different applications have chosen different standards of reference.

## This leaves us with the ‘u’ in dBu

As soon as we transmit analog audio by means of a wire, we’re dealing with the laws of electricity. A sine wave (tone) signal can be expressed as a voltage level (Vrms). Since a decibel is a ratio, there has to be a reference. To find this magic number we have to go back about sixty years (yes - they had sound back then). All audio equipment had an input impedance of 600 ohms. This impedance value of 600 ohms goes even further back in history. When audio was transmitted over long distances, the length of the wires approaches the electrical wavelength of the signal. Termination of the signal was required to avoid reflective noise in the system. Six hundred ohms was used as a standard.
The measurement device of the time was a swinging needle gauge called a VU (Volume Units) meter. Sixty years ago it was decided that the zero reading on the meter would be equal to a power level of 0.001 watt or 1 milliwatt (mW). Since we know the resistance (600 ohms) and the power level (1 mW) we can calculate the voltage required to zero the meter as 0.774596669 Vrms. In the last sixty years the industry has gotten away from the 600 ohm standard. A rounded figure of 0.775 Vrms is still used as the standard reference.
Finally, using that voltage level as the reference, we have another decibel-style equation.

Voltage expressed in dBu = 20 log (Voltage1/0.775 Vrms)

This used to be called dBv but that was often confused with another measurement (dBV) so it was changed to dBu. TAADAA, we now have dBu.

## Why +4 dBu

This level was chosen as a ‘Standard Operating Level’ because it provides sufficient headroom and is far enough above the noise floor to avoid distortion at the inputs and outputs. This insures that the signal will retain its integrity while traveling between components. In most cases the signal itself will be recorded as 0 dBu on the tape.

This means that a +4dBu signal applied to a deck’s input will display as 0dB VU on the analog meter on the deck. The signal applied to the record head will be at a 0 dBu level. When the tape is played back, the heads will read the 0 dBu information on the tape and play it out at +4 dBu.
This ‘Standard Operating Level’ varies to some extent. There are manufacturers and formats that use different levels for standard input and output. These can vary from 0 dBu to +9 dBu.
Adjusting the meter to read a certain level with a known input is performing a calibration of the unit. Be sure to read and follow the instructions with each unit to set the correct levels.

## NEXT -- Entering the Digital Domain

Digital audio consists of a series of zeros and ones. At the top of the range, the highest level of audio consists of a series of ones. The lowest possible digital signal would consist of all zeros. It doesn’t quite get there as the noise floor limits the Analog to Digital Converter (ADC).

A new scale was needed to which would display these new limits in a logical manner. The largest signal was defined as 0 decibels full scale (dBFs). This is the highest digital audio level available. Anything over this will be clipped. Therefore the digital audio level will always be a negative number.
The low end of the digital stream is a series of zeros.

Does this mean the +4 dBu Standard Operating Level is relegated to the junk pile with 8-track tapes and polyester suits? Not yet.

## Calibration

Calibration is all about setting up the gain controls on a your equipment to get one reference level to line up with another. In the analog world, we would line up the +4dBu voltage with the 0VU point on the equipment, so that signals would not be distorted.

Most engineers discovered that equipment was designed with substantial "headroom" above the 0VU point before distortion would occur, so many real world signals exceed the +4dBu limits. When it comes to digital calibration, the 0dBfs barrier is a hard barrier that cannot be exceeded, so the 0VU point is placed down the scale to provide the headroom needed to account for this. This headroom is also needed so that when signals are added together in mixing, there will be enough room to prevent the signal from exceeding the numerical limits. Mixing two channels requires 6dB of headroom, and mixing four channels requires 12dB of headroom.

Different manufacturers have placed the 0VU point at different places on their digital scale, in order to meet the requirements of their customers. You need to check your equipment specifications to determine where the 0VU point is for your equipment, and establish a calibration that matches. Common values are between -8dBfs and -20dBfs, with professional multi-track recording equipment tending toward the -20 end of the scale. In order to ensure there is plenty of room for signals that exceed 0VU, and for mixing multiple tracks of material, without worry of exceeding the numerical limits of the digital audio system.

I’d like to thank Jeffrey Lomicka of Avid Technology for the ‘Calibration’ portion of the article.

 Jim Alfonse, owner of Tri-Sys Designs, is a Systems Integrator with twenty-five years experience in the Broadcast Industry. He's designed, built and commissioned installations from Satellite News Vehicles to Production Suites to OB vans. Jim has been involved with several equipment manufacturers performing video standards compliance and signal integrity testing. For more articles on various subjects visit www.tri-sysdesigns.com