Friday, May 17, 2024

Decibel (dB) Calculator

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This calculator will convert voltage or power gains into decibels. Enter one of the three values and the calculator will output the other two.

Inputs

Voltage Gain (Vout/Vin):
Power Gain (Pout/Pin):
Decibels (dB):

This Decibel (DB) Calculator convert a voltage or power gain into decibels. This can be useful to express gains on a logarithmic scale and can also make arithmetic easier, as decibels can be added instead of multiplied. For instance, it can be applied to represent the gain of a linear system across frequencies in a Bode plot, facilitating clearer analysis and understanding.

Bode plot showing the gain in dB versus frequency

Convert Voltage or Power Gain to Decibels

To convert voltage or power gains to decibels, you can use the below formula:

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Voltage or Power Gain to Decibels Conversion Formula

Where:

  • NdB = The power or voltage gain expressed in decibels
  • AV = The voltage gain of the system
  • AP = The power gain of the system

Further, the voltage and power gains of the system can be expressed as:

Voltage Gain and Power Gain

Where:

  • VOUT = The system output voltage level
  • VIN = The system input voltage level
  • POUT = The system output power level
  • PIN = The system input power level

Technically, decibels are a measurement unit for a power ratio. However, because the power is proportional to the square of the voltage, we can express the power gain as a function of the voltage ratio (AV) as shown above.

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