## The Decibel

September 14, 2013 in Tech Talk, The Basics by Sam Davisson Honestly, I wasn’t sure what direction this was going to go when I started writing and I’ve spent most of the last week trying to decide what should be next. I was thinking linearly, like a book. But in reviewing and responding to comments on the Power and Grounding post, I realized that perhaps the best approach would be to tackle misconceptions as they arose and then precede from there.

In order to do that, I found that I needed to set the definition of what is probably the most confusing or perhaps better expressed as confused term in the industry.

The Decibel

The decibel (dB) is a logarithmic unit used to express the ratio between two values of a physical quantity (usually measured in units of power or intensity). In AV the decibel is commonly used as a measure of gain or attenuation, the ratio of input and output powers of a system, or of individual factors that contribute to such ratios. The number of decibels is ten times the logarithm to base 10 of the ratio of the two power quantities.

The decibel is used for a wide variety of measurements in science and engineering. In AV we use it for the gains of amplifiers, attenuation of signals, signal-to-noise ratios and sound pressure levels. The decibel offers a number of advantages, such as the ability to conveniently represent very large or small numbers, and the ability to carry out multiplication of ratios by simple addition and subtraction. On the other hand the decibel confusing and cumbersome.

A change in power by a factor of 10 represents a 10dB change in level. Whereas a change in power by a factor of 2 represents a 3dB change (remember the relationship is logrithmic and not linear). To keep things even more confusing a change in voltage by 10 is equivalent to a change in power by a factor of 100 or a 20dB change. Therefore a change in voltage by a fator of 2 represents a 6dB change.

Confused yet? The thing to remember is that the decibel is usually qualified with a suffix to indicate which reference quantity or frequency weighting function has been used. Common suffixes in the AV world are:

Volages

• dBV – RMS voltage relative to 1 volt, regardless of impedance (the apparent ac resistance of a circuit containing capacitance and/or inductance in addition to pure resistance)
• dBu or dBv – Originally this was always expressed dBv but changed to dBu to avoid confusion with dBV. The v comes from volt whereas the u comes from unloaded. dBu can be used regardless of impedance, but is derived from a 600 Ω load dissipating 1mW (0dBm)
• dBmV – voltage relative to 1 millivolt across 75 Ω. Obviously this is typically used in analog video systems
• dBuV – voltage relative to 1 microvolt. Widely used in television and aerial amplifier specifications. 60 dBμV = 0 dBmV.

Accoustics

• dB (SPL) – sound pressure level referenced to the nominal threshold of human hearing (0dB SPL)
• dB(A), dB(B) and dB(C) – These symbols are often used to indicate the use of different weighting filters, used to approximate the human ear’s response to sound. The measurement is still in dB(SPL). These measurements usually refer to noise and the effects on humans and animals. They are in widespread use with regard to noise control issues, regulations and environmental standards. According to ANSI standards, the preferred usage is to write LA = x dB. Nevertheless, the units dBA and dB(A) are still commonly used as a shorthand for A-weighted measurements.

Audio Electroncis

• dBm – power relative to 1 milliwatt. In audio, dBm is typically referenced relative to a 600 ohm impedance. This measurement has pretty much been retired in line level audio as the typical impedance of a an input on a piece of equipment is greater than 10 kΩ aka Hi Z.
• dBFS – the amplitude of a signal compared with the maximum which a device can handle before clipping occurs. Full-scale may be defined as the power level of a full-scale sinusoid or alternatively a full-scale square wave. A signal measured with reference to a full-scale sine-wave will appear 3dB weaker when referenced to a full-scale square wave, thus: 0 dBFS(ref=fullscale sine wave) = -3 dBFS(ref=fullscale square wave).

The point behind this is that simply stating that something is 74dB is pointless without the suffix referencing what that measurement is relative to. 74dB is not the same as 74dB SPL or 74dBV.