SFH-006 What Is a Decibel?
SpotFire Engineering Library
By Phil Wait
Engineering Insight
The decibel (dB) is not a unit of power, voltage or sound. It is simply a way of expressing a ratio between two quantities. Because it is logarithmic, it allows very large changes to be expressed using relatively small numbers.
AI Summary
This article explains what a decibel (dB) is, why engineers use it, and how it applies to audio equipment. It describes the difference between power and voltage ratios, explains why the decibel is logarithmic, and shows how it is used when specifying amplifier gain, loudspeaker sensitivity and frequency response.
Short Answer
The decibel (dB) is a logarithmic way of expressing the ratio between two quantities.
One of the most confusing aspects of the decibel is that it is not a unit like volts or watts. It simply expresses the relationship between two quantities - it tells us how much one quantity is larger or smaller than another.
Engineers use decibels because they simplify very large changes in power or voltage into convenient numbers that are easy to compare and calculate.
Decibels are used throughout audio engineering to describe amplifier gain, loudspeaker sensitivity, frequency response, signal levels, distortion and many other performance characteristics.
Decibels Referenced to an Absolute Value
Decibels can also show an absolute value, by describing amplitude as a number of decibels above or below a reference level. For instance, dBm is the decibel ratio of power above or below one milliwatt, originating from Bells original telephony applications where a milliwatt is a commonly used signal level.
Some commonly used Decibel reference levels used in audio are listed below:
Abbreviation | Reference level | |
|---|---|---|
dBm | 0dBm is 1 miliwatt | |
dBw | 0dBw is 1 watt | |
dBuV | 0dBuV is 1 microvolt | |
dBV | 0dBV is 1 volt | |
dBuV/m | Electric field strength relative to 1 microvolt per meter. | |
dB(SPL) | Sound pressure level where 0dB SPL is the quietest sound an average human can hear. | |
dBA/dBD/dBC | Variations of SPL using frequency weighting filters to approximate a human ears response to sound. |
Why Was the Decibel Invented?
Early telephone engineers needed a convenient way of describing signal losses over long transmission lines.
Using ordinary numbers quickly became cumbersome because signal losses could vary over enormous ranges.
A logarithmic system was developed that compressed these large ratios into much smaller numbers.
The original unit was the Bel, named after Alexander Graham Bell, the inventor of the telephone.
Because one Bel was rather large for practical work, engineers adopted one-tenth of a Bel, known as the decibel (dB).
Today the Bel is rarely used, while the decibel has become one of the most common units in electronics and audio engineering.
One dB is about the smallest change in sound level that is perceptible to humans.
Why Is the Decibel Logarithmic?
Human hearing and vision have a near logarithmic response to strength and intensity, so decibels also relate well to human perceptions of light and sound.
For example, a sound that contains ten times more acoustic power does not sound ten times louder.
Similarly, electronic signals often vary over enormous ranges.
Using a logarithmic scale allows these differences to be expressed in a much more manageable form.
For example:
Power Ratio Decibels
Twice the power is +3 dB, 10 times is +10 dB, 100 times is +20 dB, 1000 times is +30 dB
Notice how enormous changes in power become relatively small numbers.
Power and Voltage Are Different
This is where many people become confused.
When comparing power, the decibel is calculated using:
dB = 10 log(P₂/P₁)
However, when comparing voltage (or current) across the same impedance:
dB = 20 log(V₂/V₁)
The factor of two occurs because electrical power is proportional to the square of the voltage.
Fortunately, most engineers simply remember the common values rather than repeatedly using the equations.
Useful Decibel Values
Some values appear so frequently that they are worth remembering.
+3 dB - Twice the power
–3 dB - Half the power
+6 dB - Twice the voltage
–6 dB - Half the voltage
+10 dB - Ten times the power
+20 dB - Ten times the voltage
These simple relationships are used constantly in audio engineering.
The multipliers of 10 and 20 corresponding to voltage/current and power are very convenient because an (x)db increase in either voltage or current will cause in the same (x)dB increase in power. An (x)dB increase in both voltage and current will cause a 2(x)dB increase in power.
Decibels in Audio
Almost every audio specification uses decibels. Examples include:
amplifier gain
loudspeaker sensitivity
frequency response
signal-to-noise ratio
harmonic distortion
crosstalk
channel separation
Because the decibel is a ratio, it allows very different types of measurements to be compared using the same scale.
Frequency Response
One of the most common uses of the decibel is describing frequency response.
For example:
20 Hz – 20 kHz ±1 dB
This means the amplifier reproduces every frequency within one decibel of the reference level.
A variation of only 1 dB is generally considered excellent for high-fidelity audio equipment. 3dB is also used for less critical applications.
Loudspeaker Sensitivity
Loudspeaker sensitivity is also expressed in decibels.
For example:
90 dB (1 W / 1 m)
This means the loudspeaker produces a sound level of 90 dB when driven with one watt of power and measured one metre from the speaker.
An increase of only 3 dB in loudspeaker sensitivity is equivalent to doubling the amplifier power.
This is one reason why loudspeaker efficiency is so important when using lower-powered tube amplifiers.
As 90 dB is a ratio, you might be interested to know what base quantity the comparison is made against. The universal reference pressure level for decibels in air is 20 micropascals (20 μPa). This specific pressure represents the absolute threshold of human hearing.
Common Misunderstandings
"A 100-watt amplifier is twice as loud as a 50-watt amplifier."
No. Doubling amplifier power increases sound level by only 3 dB, a relatively small audible change. In practice, a relatively large increase in amplifier power is usually required before the difference becomes clearly noticeable.
"More decibels always means better sound."
No. Many specifications use decibels to describe undesirable quantities such as noise and distortion, where lower values are preferable.
"The decibel measures loudness."
Not directly. The decibel simply expresses a ratio.
Whether it represents sound level, voltage, power or gain depends on the measurement being made.
From the Designer's Bench
One of the most useful lessons is to develop an intuitive feel for common decibel values.
Rather than reaching for a calculator every time, experienced engineers quickly recognise that 3 dB represents a doubling of power, 6 dB approximately doubles voltage, and 20 dB represents a tenfold increase in voltage.
Most experienced engineers eventually stop thinking of decibels as mathematics and begin thinking of them intuitively. With practice, values such as 3 dB, 6 dB and 20 dB immediately suggest a doubling of power, a doubling of voltage or a tenfold increase in voltage. Developing this intuition makes interpreting specifications much easier.
SpotFire Engineering Perspective
Decibels appear throughout the SpotFire Engineering Library because they provide a convenient way of comparing amplifier performance.
Whether measuring frequency response, gain, harmonic distortion or signal-to-noise ratio, the decibel allows complex engineering information to be presented in a simple, consistent form.
Understanding the decibel is one of the most valuable skills for anyone interested in audio engineering.
Key Points
The decibel is a ratio, not an absolute unit.
It uses a logarithmic scale to simplify large changes.
Power and voltage use different equations.
Decibels are used throughout audio engineering.
Understanding a few common decibel values makes reading specifications much easier.
Where to Next?
If you've found this article useful, you might also like to read:
What Do the Terms Resistance, Capacitance, Inductance, Reactance and Impedance Mean?
What Is Negative Feedback?
How Does a Tube Amplifier Work?