Decibels

Related wiki pages Gain, Radiated Power Measurement

What is a decibel dB?

Some facts

• a decibel is the ratio of two power measurements
• decibels is a logarithmic relationship
• a decibel is 1/10 of a Bel
• decibels have no units
• decibels were created to make sense of the relationships between numbers that are several orders of magnitude different in size. eg 32 000 000 000 000W and 450W
• the formula used to calculate decibels is:

Power difference in dB = <math>10 \log_{10}\frac{P_A}{P_B}</math>

Why use decibels

Using the two numbers above:

<math> P_A = 32 000 000 000 000</math>W and <math> P_B = 450</math>W , then:

<math>10 \log_{10}\frac{32000000000000}{450}</math> <math>\approx</math> 109

Hence we would say that Power A is approximately 109dB greater than Power B

What about voltage comparisons in dB?

the relationship between Power and Voltage is:

<math> Power = \frac{Voltage^2}{Resistance} </math>

Squaring a number will double its logarithm (log), so

Power difference in dB = <math>20 \log_{10}\frac{V_A}{V_B}</math>

What is a reference level?

Reference levels were created because dB is a unitless calculation, unlike calculations such as voltage, power current etc.

In Ham radio, the most common measurements that requires the use of dB are Gain and Radiated Power Measurement. Further information about refeence leves can be found in the linked pages.