Tyco 579-769 V = I ⋅ R, P = V ⋅, Basic Audio Math, Decibel = 10 log⎜, P = I2 ⋅ R, dB = 10log

Basic Audio Math

Ohm’s Law and the Decibel

Audio engineers use “Decibels” (dB) to express ratios between levels, such as power, Volts, Amps, and Sound Pressure Levels (SPL). The decibel is not an absolute measure like Volts and Amps, rather it is used to make comparisons between two numbers. The decibel is defined as the logarithm of two power levels, shown below in the equation as P1 and P0:

⎛ P1	⎞
Decibel = 10 log⎜	⎟
⎝ P0	⎠

Equation 2-1. The Decibel

P0 is the reference power and P1 is the power level used for comparison. The logarithm is used in the decibel in order to make comparisons of power over a very wide range. This is very useful in audio applications as the ear responds logarithmically to changes in SPL.

You can also use the decibel for voltage comparisons. From Ohm’s Law we know that:

V = I ⋅ R

Equation 2-2. Ohm’s Law

The electrical power equation:

Where:

•V = Volts

•I = Amps

•R = Resistance

P = V ⋅ I	P =	V2	P = I2 ⋅ R
		R

Equation 2-3. Power Relationships

Use the following equation to determine the decibel difference between two voltage measurements powering the same load resistance:

	⎡		(V )2	⎤
	⎢		1	⎥
			R
dB = 10log	⎢			⎥
		(V0 )2
	⎢			⎥
	⎢			⎥
			R
	⎣			⎦

⎛ V ⎞ which can be simplified to : dB = 20log ⎜ 1 ⎟ ⎜⎝ V0 ⎟⎠

Equation 2-4. dB and Voltages

The decibel is often used to make comparisons between two different numbers, neither of which is at an absolute reference level. For instance, if we take two voltage measurements along the length of a speaker circuit, the power lost to the wiring can be calculated directly. If the voltage at the amplifier driving a speaker circuit is 25 V (V0) and the voltage at the last speaker on the circuit is 15 V (V1) the power loss due to the wiring is 4.4 dB.

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