notor research - What is a dB?

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The abbreviation dB stands for decibel, which was originally used only as a measure of audio power. The B stands for Bell, as in Alexander Graham Bell, the famous inventor of the telephone.

In the wireless biz, a dB is a relative measure of power, indicating the ratio of two power levels. It is calculated as P = 10*log(P1/P2), where P1 and P2 are in watts, and P is given in dB. The logarithmic nature of the calculation leads to the following:

  1. a power ratio of 1 equals 0 dB
  2. a power ratio of 2 equals 3 dB, a power ratio of 0.5 equals -3 dB
  3. a power ratio of 4 equals 6 dB,  a power ratio of 0.25 equals -6 dB
  4. a power ratio of 10 equals 10 dB, a power ratio of 0.1 equals -10 dB
  5. a power ratio which is 10 raised to an integer power (100, 1000, etc) is that integer times 10  in dB
  6. 1 dB change represents an approximately 26% change in power level

The dB is always a measure of relative power. But voltage ratios are often expressed in dB for convenience. Voltage ratios in dB are calculated as V=10*log[(V1/V2)2] or V=20*log(V1/V2). Notice that the voltage ratios have to be squared in order to convert them into power terms. The logarithmic calculation of voltage ratio leads to the following:

  1. a voltage ratio of 1 equals 0 dB
  2. a voltage ratio of 1.414 (the square root of 2) equals 3 dB, 0.707 (the inverse of the square root of two) equals -3 dB
  3.  a voltage ratio of 2 equals 6 dB, a voltage ratio of 0.5 equals -6 dB
  4. a voltage ratio of 4 equals 12 dB, a voltage ratio of 0.25 equals -12 dB
  5. a voltage ratio of 5 equals 14 dB, a voltage ratio of 0.2 equals -14 dB
  6. a voltage ratio of 10 equals 20 dB, a voltage ratio of 0.1 equals -20 dB
  7. a voltage ratio which is 10 raised to an integer power (100, 1000, etc) is that integer times 20 in dB
  8. 1 dB change represents an approximately 12% change in voltage level

Lots of signal levels are represented relative to some standard level:

  1. dBm is a power measurement and means dB relative to 1 milliwatt
  2. dBW is a power measurement and means dB relative to 1 Watt
  3. dBuV, dBmV and dBV are AC voltage measurements and mean dB relative to 1 microvolt, 1 millivolt and 1 Volt AC RMS, respectively. 
  4. dBc is a power measurement and means dB relative to the carrier level - this is used when a signal (the carrier) is modulated by desired or undesired (spurious) signals to describe the level of the modulating signals relative to the carrier signal.

In acoustic terms, the dB is the sound pressure level relative to a 20 uPa (micropascal) nominal reference, which is a generally accepted value for the sensitivity of the human ear at the peak of the ear's audio response. The audio dB level is calculated as 20*log(p2/ref), where ref = 20 uPa.

The peak audio response for humans occurs at approximately 2.5 kHz. The peak is a pretty broad, relatively flat response from about 1 to 6 kHz, as modeled in the widely used A weighted audio response curve.

Note: RMS is an abbreviation of root mean square, and refers to the DC equivalent value of an AC (alternating current) signal. It is important to distinguish between the amplitude of an AC signal (the peak value of the AC signal), the peak to peak value, the average value, and the RMS value. 

Since dB is always a measure of relative power, the RMS value of the signal is always used in calculating voltage relationships in dB. In pulsed signals (often used in radar and communications), the peak power is the power calculated assuming the signal is on all the time, based on the RMS value of the voltage waveform. The term peak then refers to the instantaneous value of power during the on interval.

Speaking wireless means speaking dB. If you get good at it, people actually think you know what your talking about.

 

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Last Revised: February 2, 2017