dB Made Easy

5 January 2009
(revised 30 Jan 2010)

The essentials of the dB

For a definition and brief history of the decibel, look it up on Wikipedia. There's no point in me repeating their good work. Read that page until your eyes start to roll, then return here for the four things you need to remember about the decibel in order to get by.

The math

You can skip to the next section if you want, but it's not that bad.... A decibel is one-tenth of a bel. A bel is the power that ten must be raised to to give the value in question. Let's take the number 100. 10 to the power of 2 equals 100. (10 x 10 = 100.) So a ratio of 100, expressed in bels, is 2. But since a decibel is ten bels, we multiply that number by 10 to get 20. A ratio of 100 is 20 decibels, or 20 dB.

The four points

  1. Decibel values of 10, 20, 30... represent power ratios of 10, 100, 1000... See the pattern?
  2. Every time you double your power output, the gain increased by another 3 dB.
  3. On most rigs, one S-unit represents a 6 dB gain, or four times the power output.
  4. Decibel values less than ten are greater than their corresponding power factors. Decibel values greater than ten are smaller than their corresponding power factors - sometimes much smaller.

The subscript

As you know, decibels represents a ratio. So, if someone reports that an antenna has a gain of 6 dB, the question is: "relative to what?" In amateur radio, here are the dBx's that you are most likely to encounter:

Symbol Reference
dBi Antenna gain relative to a (fictional) isotropic antenna. Imagine a point source in free space radiating equally in all directions. That's an isotropic antenna. The degree to which an antenna focuses that energy into a specific direction represents dBi gain.
dBd Antenna gain relative to an ideal dipole antenna. This is a more realistic statement of antenna gain in that it is compared to a real antenna. (Note: When comparing antennas, ensure you are not mixing dBi an dBd measurements. 0 dBd = 2.15 dBi.)
dBiC Antenna gain relative to a circularly polarized isotropic antenna.(I've never actually encountered this, but I thought you should know I read the entire Wikipedia article.
dBm Power relative to 1 milliwatt. In radio usage, this is referenced to a 50 ohm load, giving 0.224 volts.
dBW Power relative to 1 watt.
dBu Voltage relative to one microvolt. You may see receiver sensitivity expressed as: 12 dBu at 12dB sinad. This means that at 12 dB below one microvolt (0.25 microvolts), the signal is 20 dB (or eight times, or twoS-units, above the noise floor.

A real-life example

My Kenwood TH-F6A handheld radio has the following power settings when running on batteries:

Some reviews on eHam.net and such have complained that the power settings should be a less logarithmic 5, 2.5 and 1 watt or something similar. But look at the following chart:

Actual TH-F6A
  
Proposed TH-F6A
Setting Watts dB S-Units* Setting Watts dB S-Units*
H 5.0 0 0 H 5 0 0
L 0.5 -10 -2 L 2.5 -3 -0.5
EL 0.05 -20 -3 EL 1 -7 -1
* Rounded slightly * Rounded slightly

In other words, cutting the power output in half doesn't have a huge impact on the receiving end. The receiving this, and many other radios have such seemingly dramatic power variations is because it takes that much to make a difference. If you don't believe me, try a little QRP experiment next time you're working HF. Turn the power on your 100 watt rig down to the minimum (likely 5 watts). Unless band conditions are quite poor, chances are your contact can still hear you despite the significant drop in power. (Changing from 100 watts to five watts is only a drop of two s-units.)

Comments?

I am by no means a decibel, or even a math, expert. Please e-mail me your comments and clarifications.

Last update: 30-Jan-2010 10:59 AM
Web page by: Warren Paulson