Understanding the Relationship Between Voltage Gain and Power Gain in dB

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SUMMARY

The relationship between voltage gain and power gain in decibels (dB) is defined by the formulas 20 Log(v2/v1) for voltage gain and 10 Log(p2/p1) for power gain. Voltage gain must be squared to convert it to power gain, which is why the logarithmic expression for voltage gain includes a factor of 2. This conversion assumes that the voltages are measured across the same impedance, ensuring comparability between gains. Understanding this relationship is crucial for accurate gain calculations in electrical engineering.

PREREQUISITES
  • Basic understanding of logarithmic functions
  • Familiarity with electrical concepts such as voltage and power
  • Knowledge of impedance in electrical circuits
  • Experience with decibel (dB) calculations
NEXT STEPS
  • Study the derivation of dB formulas for voltage and power gains
  • Explore the implications of impedance on voltage and power measurements
  • Learn about the applications of dB in audio engineering and telecommunications
  • Investigate the differences between linear and logarithmic scales in signal processing
USEFUL FOR

Electrical engineers, audio engineers, and students studying electronics who need to understand gain calculations and their implications in circuit design and analysis.

likephysics
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Why is voltage gain in db given by

20 Log (v2/v1)

but power gain is straight forward : 10 Log (p2/p1).
 
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Remember that Log(x2) = 2·Log(x)

Bob S
 
The gain in dB is power gain. When you are expressing the voltage gain, the gain must be squared in order to convert it to power gain so that when gains are compared they in fact are comparable. (This assumes the voltages are across the same impedance.) Squaring the voltages is the same as adding a factor of 2 ahead of the Log as Bob S shows above.
 

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