# Decibel & S-meter

## dBm as a power level

dBm (sometimes dBmW or decibel-milliwatts) is unit of level used to indicate that a power ratio is expressed in decibels (dB) with reference to one milliwatt (mW). It is used in radio, microwave and fiber-optical communication networks as a convenient measure of absolute power because of its capability to express both very large and very small values in a short form compared to dBW, which is referenced to one watt (1,000 mW).

Since it is referenced to the watt, it is an absolute unit, used when measuring absolute power. By comparison, the decibel (dB) is a dimensionless unit, used for quantifying the ratio between two values, such as signal-to-noise ratio. The dBm is also dimensionless but since it compares to a fixed reference value the dBm rating is an absolute one.

A power level of 0 dBm corresponds to a power of 1 milliwatt. A 10 dB increase in level is equivalent to a 10-fold increase in power. A 3 dB increase in level is approximately equivalent to doubling the power, which means that a level of 3 dBm corresponds roughly to a power of 2 mW. Similarly, for each 3 dB decrease in level, the power is reduced by about one half, making −3 dBm correspond to a power of about 0.5 mW.

dBm as a power level | ||
---|---|---|

dBm | P out | Typical for |

60 | 1kW | typical radiated RF power of a microwave oven |

50 | 100W | typical maximum output RF power from a ham radio HF transceiver |

40 | 10W | |

37 | 5W | typical maximum output RF power from a handheld ham radio VHF/UHF transceiver |

33 | 2W | maximum output from a GSM 850/900 mobile phone |

30 | 1W | DCS or GSM 1 800/1 900 MHz mobile phone |

20 | 100mW | EIRP for a IEEE 802.11b/g 20 MHz-wide channel in the 2.4 GHz ISM band (5 mW/MHz) |

10 | 10mW | |

0 | 1mW | Bluetooth class 3 radio with 1 m range |

-10 | 100µW | IEEE 802.11 maximal signal strength |

-60 | 1nW | power received per m2 of a magnitude +3.5 star |

-73 | 50pW | S9 signal strength on S-meter |

-100 | 100fW | IEEE 802.11b/g minimal signal strength |

-101 | 83fW | noise floor of a IEEE 802.11b/g 20 MHz channel at 300 K |

-134 | 41aW | noise floor of a 10 kHz wide FM signal at 300 K |

-140 | 12aW | noise floor of a 2.7 kHz wide SSB signal at 300 K |

## HF S-meter

Many amateur radio and shortwave broadcast receivers feature a signal strength meter (S‑meter). In 1981, the International Amateur Radio Union (IARU) Region 1 agreed on a technical recommendation for S‑meter calibration of HF and VHF/UHF transceivers.

IARU Region 1 Technical Recommendation R.1 defines S9 for the HF bands to be a receiver input power of -73 dBm. This is a level of 50 µV at the receiver’s antenna input assuming the input impedance of the receiver is 50 Ω.

The recommendation defines a difference of one S-unit corresponds to a difference of 6 dB, equivalent to a voltage ratio of two, or a power ratio of four. Signals stronger than S9 are given with an additional dB rating, thus “S9 + 20 dB”, or, verbally, “20 decibel over S9”, or simply “20 over 9” or even the simpler “20 over”.

Conversion between power and HF S-units | |||
---|---|---|---|

S-reading | P out @ 50Ω | V out @ 50Ω | (V out / 1µV) @ 50Ω |

S9 + 40 dB | -33 dBm | 5 mV | 74 dBµV |

S9 + 30 dB | -43 dBm | 1.6 mV | 64 dBµV |

S9 + 20 dB | -53 dBm | 0.5 mV | 54 dBµV |

S9 + 10 dB | -63 dBm | 0.16 mV | 44 dBµV |

S9 | -73 dBm | 50 µV | 34 dBµV |

S8 | -79 dBm | 25 µV | 28 dBµV |

S7 | -85 dBm | 12.6 µV | 22 dBµV |

S6 | -91 dBm | 6.3 µV | 16 dBµV |

S5 | -97 dBm | 3.2 µV | 10 dBµV |

S4 | -103 dBm | 1.6 µV | 4 dBµV |

S3 | -109 dBm | 800 nV | -2 dBµV |

S2 | -115 dBm | 400 nV | -8 dBµV |

S1 | -121 dBm | 200 nV | -14 dBµV |

The noise floor for a 𝐵=2700 Hz wide SSB signal at 𝑇=300 K is −139.5dBm

## VHF/UHF S-meter

The same IARU Region 1 recommendation defines S9 for VHF/UHF to be a receiver input power of -93 dBm. This is the equivalent of 5 µV in 50 Ω. Again, one S-unit corresponds to a difference of 6 dB, equivalent to a voltage ratio of two, or a power ratio of four.

Conversion between power and VHF/UHF S-units | |||
---|---|---|---|

S-reading | P out @ 50Ω | V out @ 50Ω | (V out / 1µV) @ 50Ω |

S9 + 40 dB | -53 dBm | 0.5 mV | 54 dBµV |

S9 + 30 dB | -63 dBm | 0.16 mV | 44 dBµV |

S9 + 20 dB | -73 dBm | 50 µV | 34 dBµV |

S9 + 10 dB | -83 dBm | 16 µV | 24 dBµV |

S9 | -93 dBm | 5 µV | 14 dBµV |

S8 | -99 dBm | 2.5 µV | 8 dBµV |

S7 | -105 dBm | 1.26 µV | 2 dBµV |

S6 | -111 dBm | 630 nV | -4 dBµV |

S5 | -117 dBm | 320 nV | -10 dBµV |

S4 | -123 dBm | 160 nV | -16 dBµV |

S3 | -129 dBm | 80 nV | -22 dBµV |

S2 | -135 dBm | 40 nV | -28 dBµV |

S1 | -141 dBm | 20 nV | -34 dBµV |

The noise floor for a 10 kHz wide FM signal at 300 K is −134dBm

The term noise floor refers to the calculated thermal noise, also known as the Johnson–Nyquist noise.

P = k_{b}*T*B

Where k_{b} = 1.3806488*10^{-23} J/K (Boltzmann's constant)

Johnson–Nyquist noise (thermal noise, Johnson noise, or Nyquist noise) is the electronic noise generated by the thermal agitation of the charge carriers (usually the electrons) inside an electrical conductor at equilibrium, which happens regardless of any applied voltage. Thermal noise is present in all electrical circuits, and in sensitive electronic equipment such as radio receivers can drown out weak signals, and can be the limiting factor on sensitivity of an electrical measuring instrument. Thermal noise increases with temperature. Some sensitive electronic equipment such as radio telescope receivers are cooled to cryogenic temperatures to reduce thermal noise in their circuits. The generic, statistical physical derivation of this noise is called the fluctuation-dissipation theorem, where generalized impedance or generalized susceptibility is used to characterize the medium.

Thermal noise in an ideal resistor is approximately white, meaning that the power spectral density is nearly constant throughout the frequency spectrum. When limited to a finite bandwidth, thermal noise has a nearly Gaussian amplitude distribution.

## Discussion