# Decibels Explained

Exploration
Published February 1994

Most of us accept that our VU meters are calibrated in decibels, or dBs, but even the most experienced engineer can start to fumble when asked to explain exactly what they are, and how they are related to the likes of dBu, dBm, dBv and dBV. The name decibel means a tenth of a bel, the bel part being named after that well‑known inventor of telephones, Alexander Graham Bell (hence the capital B in dB). The first hurdle is to grasp that the dB doesn't have to relate to any fixed level of signal; it is simply a convenient way of expressing the ratio between two signal levels. I say convenient because the nature of the decibel makes it logarithmic, and it just so happens that our ears are also logarithmic in the way they perceive sound level.

The method of calculating dBs for both voltage and power ratios is shown in the accompanying box. We can pick any power or voltage to be our 0dB level and then express all other values relative to that. For example, the record level meter on a tape machine is always set so that the optimum recording level is shown as 0dB, regardless of what that means in terms of magnetic flux at the record head. If a signal is lower than optimum, it is read as minus so many dBs, whereas if the signal is too high, it is shown as plus so many dBs. Some of the more common ratios are shown in the table below.

From the table, it can be seen that a voltage amplifier having a gain of 60dB amplifies the input signal 1000 times. The same is true of specifications such as dynamic range: A 100dB dynamic range means that the largest signal a circuit can handle is 100,000 times bigger than the smallest signal it can handle.

## The dBm

While dBs express only general ratios, the dBm is a fixed value where 0dBm equates to 1 milliwatt of power. This is of little direct relevance in the world of modern audio, but was vitally important in the pioneering days of telephone when small amounts of electrical power needed to be transmitted over long distances. In the world of telephones and 600 ohm line impedances, 0 dBm tended to mean a signal of 0.775 Volts applied to a load of 600 ohms — or 1mW.

Today, the term dBm is often abused to signify a signal level of 0.775 Volts, but unless the load impedance is exactly 600 ohms, this is incorrect. Because exact load impedances are less of an issue in modern audio systems, the new term dBu (u meaning unloaded) was introduced to signify a voltage level of 0.775 Volts, regardless of the load impedance. In other words, while the dBm is a measure of power, the dBu is a measure only of voltage. The term dBv (lower case v) also means the same thing as dBu, though the term dBu is more commonly used.

So far so good, but a reference voltage level of 0.775 Volts is pretty clumsy — 1 Volt would be far easier to manage. And that's where the recently introduced dBV (note the upper case V) comes in. This simply signifies a signal level of 1V without regard to the load impedance.

## Standard Levels

Most audio equipment is specified as working at either 'Plus 4' or 'Minus 10', but what does that mean in practice? 'Plus 4' means +4dBu, an operating level adopted in pro audio due to historic rather than purely logical reasons, and corresponding to an RMS signal level of 1.23 Volts. This is a fairly convenient figure for use with modern op‑amp circuitry as it leaves a sensible amount of headroom before the circuitry runs into clipping.

The so‑called 'Minus 10' level was introduced along with semi‑pro recording gear and is largely a Japanese concept. Correctly stated, this is ‑10dBV which corresponds to 0.316 Volts — roughly a third of a volt. Again this is reasonable for use with op‑amp circuitry, but many purists feel the +4dBu system provides a better balance between noise and headroom.

Some musical instruments, such as electronic keyboards, have an even lower, ‑20dBV output level allowing them to be used with domestic hi‑fi equipment. Because of this, some effects units also have matching ‑20dBV low level inputs corresponding to a signal level of only 0.1 Volt RMS. Such equipment can cause problems because a lot of mixer gain is required to bring the signal up to a manageable level, the unwanted side‑effect being noise. For this reason, it may be wise to use purpose‑built keyboard preamps or DI boxes rather than relying purely on the mixer line input to provide all the gain.

## Tech Talk

When comparing two power levels, the number of dBs difference may be calculated by the equation:

Number of dBs = 10 log (P1/P2) where P1 and P2 are the two powers being compared and where the log is to the base 10.

If you don't understand how logs work, don't worry because nobody actually works out dB levels in this way — well hardly anyone. However, there are some useful figures that you should remember, the most common being that 3dB represents a doubling in power. It follows then that a 10 Watt amplifier can produce 3dB more power than a 5 Watt amplifier. Similarly, a 20 Watt amplifier can produce 3dB more power than a 10 Watt amplifier. So, how much more powerful is a 20 Watt amplifier than a 5 Watt amplifier? Simple, just add two lots of 3dB, which gives you 6dB.

Because of the mathematical relationship between power and voltage, the calculations are slightly different when it comes to working out voltage ratios in dBs. Here the equation is:

Number of dBs = 20 log (P1/P2) where P1 and P2 are the two powers being compared and where the log is to the base 10.

Note that we now have a 20 in the equation instead of a 10 which means the answer is twice what it would be for a ratio of powers. In other words, double the voltage and the level goes up by 6dB; halve the voltage and the level goes down by 6dB.

 Amplifier Power (Watts) Level in dB (Relative to 1 Watt = 0dB) Signal Voltage Level in dB (Relative to 1V = 0dB) 1 0dB 2 6dB 10 10dB 4 12dB 100 20dB 8 18dB 200 23dB 10 20dB 400 26dB 100 40dB 800 29dB 1000 60dB 1000 30dB 10,000 80dB 2000 33dB 100,000 100dB