Decibel Formula & Equation

- explanation of the decibel and the formula used to calculate power, current and voltage ratios on a logarithmic scale.

Decibels pages include:

    •  Decibel & formula
    •  Decibel table / chart
    •  Watts / dBm / dBW conversion table
    •  dBm / Watts / voltage conversion table
    •  Decibel calculator
    •  Nepers & neper to dB conversion

The decibel is used within the electronics and associated industries to provide a method of indicating the ratio of a physical quantity - often electrical power, intensity, current, or voltage.

The decibel uses the base ten logarithms, i.e. those commonly used within mathematics.

As it can be seen from the name, a deci-bel is actually a tenth of a Bel - a unit that is seldom used.

The abbreviation for a decibel is dB - the capital "B" is used to denote the Bel as the fundamental unit.

DeciBel applications

The decibel is widely used in many applications. It is used within a wide variety of measurements in the engineering and scientific areas, particularly within electronics, acoustics and also within control theory.

Typically the decibel is used for defining amplifier gains, component losses (e.g. attenuators, feeders, mixers, etc), as well as a host of other measurements such as noise figure, signal to noise ratio, and many others.

In view of its logarithmic scale the decibel is able to conveniently represent very large ratios in terms of manageable numbers as well as providing he ability to carry out multiplication of ratios by simple addition and subtraction.

Decibel formula for power comparisons

The most basic form for decibel calculations is a comparison of power levels.

The decibel formula or equation for power is given below:

Where:
    Ndb is the ratio of the two power expressed in decibels
    P2 is the output power level
    P1 is the input power level

If the value of P2 is greater than P1, then the result is given as a gain, and expressed as a positive value, e.g. +10dB. Where there is a loss, the decibel equation will return a negative value, e.g. -15dB.

Decibel equations for voltage and current

Although the decibel is used primarily as comparison of power levels, decibel current equations or decibel voltage equations may also be used provided that the impedance levels are the same. In this way the voltage or current ratio can be related to the power level ratio.

In the first instance for voltage because power = voltage squared upon the resistance:

Where:
    Ndb is the ratio of the two power expressed in decibels
    V2 is the output voltage level
    V1 is the input voltage level

Similarly because power = current squared upon the resistance, the decibel current equation becomes:

Where:
    Ndb is the ratio of the two power expressed in decibels
    I2 is the output current level
    I1 is the input current level

Voltage & current decibel equations for different impedances

As a decibel is a comparison of two power or intensity levels, when current and voltage are used, the impedances for the measurements must be the same, otherwise this needs to be incorporated into the equations.

Where:
    Ndb is the ratio of the two power expressed in decibels
    V2 is the output voltage level
    V1 is the input voltage level
    Z2 is the output impedance
    Z1 is the input impedance

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