decibels

[last updated: 2026-02-10]
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• Things to Memorize for the Technician exam:
  • 3 dB is a 2x ratio
  • 6 dB is 4x ratio
  • 10 dB is 10x ratio
  • Be careful of the trick question:
    T7C06 asks: what does 4:1 SWR indicate?
    The correct answer is "impedance mismatch".
    But one of the multiple-choice options is "6db"
    And yes, 6dB does indicate a 4x gain,
    but that doesn't apply to SWR. The correct answer is "impedance mismatch".

• Understand the Basics:
  • Decibels are always a measure of power gain (or loss).
        (though they can also be used, with clever math tricks, to express absolute values, or voltage gains. See below.)
    The gain or loss is expressed mathematically as a ratio of two power levels.
    The "dB" is the "unit", like volts or amps. You would state: "x number of dB's"
    Gain_dB = 10 * log₁₀ (power-out/power-in)
    You would state this formula as: "Gain, in dB, equals 10 times the log, to the base 10, of the ratio of power-out to power-in"
    This equation is included for reference or if you want to do actual calculations,
    but it's not required knowledge for any exam question.
  • Decibels are most often used to characterize the gain of an antenna where gain = (power-out / power-in)
  • They are also used to characterize losses in antenna feedlines.
    In an application dealing with losses, there are two different ways you can express the mathematics.
    Remember that a "loss" is a "negative gain".
    • So one way to express it is the same as before, with gain = (power-out/power-in)
      When you do this calculation, the gain ratio will be less than 1 (power-out is less than power-in),
      so the dB will be negative, indicating the loss.
    • But some places on web and other resources state the loss dB as:
      loss = (power-in / power-out)
      When you do this calculation, the loss ratio will be greater than 1,
      so the dB will be positive,
      but you have to remember to state is as "a loss of x dB"
  • Decibels are logarithmic.
    This means they increase exponentially.
    To see this, know that a dB of 50 indicates an absolute power of 100W,
        (When using dB's to express absolute power, use: dB_m)
    but a dB_m of 53 indicates a power of 200W,
        so an increase in 3 dB indicated an increase of 100W.
    But a dB_m of 56 indicates a power of 400W.
        so an increase in 3 more dB indicates an increase of 200W.

• Other things to know (some of these are required for the General license exam):
  • 1 dB is ~ 20%
  • 20x ratio is 10x (10 dB) x 2x (3 dB) = 13 dB
  • 100x is 20 dB
  • 1000x is 30 dB
  • S-units: 1 S-unit is 6dB
    S levels can be from 1 to 9
    Signals stronger than S9 are stated as "S9 + [some number of] dB"

• dBi is antenna gain
  in reference to an isotropic ideal resonator with uniform propagation in all directions
• dBd is antenna gain in reference to a dipole antenna
• dBi = dBd + 2.15
• dBc is signal strength relative to the strength of the carrier frequency ...
• dBm is absolute power
  as a ratio to 1mW
  for example: for a 100W transmitter,
  dBm = 10 * log(100W / 1mW) = 10 * log(100,000) = 10 * 5 = 50

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