Decibels Demystified, Part 2

Aug 1, 2001 12:00 PM, By Scott Wilkinson

In the past two issues, I've presented the underlying ideas necessary to understand decibels. Now that those concepts have been discussed, it's time to dig into information that is more practical and that relates directly to audio equipment.

There are several standard reference values to which power and voltage are compared using decibels (see the table “The Decibel Zoo”). Unfortunately, that leads to much confusion. Remember that all voltage in audio equipment is based on alternating current and measured using the root mean square (RMS) method.

As mentioned last month, power-referenced decibels are used for circuits that draw a significant amount of current from the voltage source. In the following equations, the amount of power being used as a reference is represented by P₀, and the amount of power being measured is P₁. If the measured power is equal to the reference power (P₁ = P₀), the difference is 0 dB. In other words, 0 dB is the reference level. (Recall from last month, if a = 10^b, then b = log a.)

The Decibel Zoo

Decibel Type	Standard Reference (0 dB)
dBm	1 mW
dBu	0.775 VRMS
dBV	1 VRMS

10 log (P₁/P₀) = 10 log 1
= 10 × 0
= 0 dB

If the measured power is twice the reference value (P₁ = 2P₀), the difference is about 3 dB.

10 log (P₁/P₀) = 10 log (2P₀/P₀)
= 10 log 2
= 10 × 0.301
= 3.01 dB

If the measured power is ten times the reference value (P₁ = 10P₀), the difference is 10 dB.

10 log (P₁/P₀) = 10 log (10P₀/P₀)
= 10 log 10
= 10 × 1
= 10 dB

The most common power-referenced decibels are denoted dBm, and the reference power value (P₀) is 1 milliwatt (mW), or 0.001W. In other words,

0 dBm = 1 mW

That type of decibel is handy when talking about small but significant power values such as those that exist in most professional audio equipment. In fact, dBm is typically used to specify the nominal signal level in professional gear.

HIGH-VOLTAGE DECIBELS

Voltage-referenced decibels are used when a circuit draws negligible current from the voltage source (that is, when the impedance is high and the load is small). That applies to most consumer and semipro gear, including synthesizers. The reference level is still 0 dB; however, if the measured voltage is twice the reference value (V₁ = 2V₀), the difference is 6 dB, not 3 dB as in power-referenced decibels.

20 log (V₁/V₀) = 20 log (2V₀/V₀)
= 20 log 2
= 20 × 0.301
= 6.02 dB

If the measured voltage is ten times the reference value (V₁ = 10V₀), the difference is 20 dB.

20 log (V₁/V₀) = 20 log (10V₀/V₀)
= 20 log 10
= 20 × 1
= 20 dB

One common voltage-referenced decibel is denoted dBu. The u stands for unloaded and refers to the very small load that high-impedance circuits present to the voltage source. The reference voltage for dBu is 0.775V. In other words,

0 dBu = 0.775V

Perhaps the most common voltage-referenced decibel is denoted dBV, for which the reference voltage is 1V. In other words,

0 dBV = 1V

That type of decibel is generally used to measure the signal level in consumer and semipro gear. (See the table “dBV Versus dBm/dBu” to compare decibel types.)

You might occasionally come across a similar decibel designation, dBv, which is completely equivalent to dBu. Don't let the v fool you; it is not the same as that in dBV. The dBv decibel is not used much today.