Author: Peter Wittenberg

- Introduction to dB

Decibels are a way of expressing power ratios that allows easy calculation and memorization. Most radar power calculations involve multiplication. Using decibels turns the multiplication problem into addition. Decibels provide a compression of numbers so that the decibel values are usually between 0 and 100, and for most rough calculations, it isn't necessary to be any more precise than whole values.

The equation for decibels is always a ratio of two powers, but compressed by taking the base 10 logarithm as

dB = 10·log10(P1/P2)

Note that the powers P1 and P2 must be in the same units. This means that you must compare Watts to Watts, milliwatts to milliwatts, and so on. If the units are not compatible, you must transform them.

A special case of power comparison happens when we look at a piece of hardware, examining the power at the output Pout and comparing it to the power at the input Pin. If we take the ratio of these powers, we can call it the gain of the piece of hardware. In decibel terms,

Gain ( in dB ) = 10·log10(Pout/Pin)

Let's try some problems.

  1. P1 = 100 W and P2 = 1 W. How many decibels is P1 relative to P2?
  2. P1 = 30 W and P2 = 15 W. How many decibels is P1 relative to P2?
  3. P1 = 30 W and P2 = 15 mW. How many decibels is P1 relative to P2?
  4. P1 = 3.2 mW and P2 = 3.2 mW. How many decibels is P1 relative to P2?
  5. For an amplifier, Pout = 5000 W and Pin = 2.5 mW. What is the gain of the amplifier?