Decibel & S-Readings (2024)

Serge Stroobandt, ON4AA

Copyright 2015–2021, licensed under Creative Commons BY-NC-SA

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\(\log_{10}{x}=\dots\quad\) means: “To what power do Ineed to raise 10, in order to obtain x?”

\[\log_{10}{x}=y\quad\Leftrightarrow\quad 10^y=x\]

Thedecibel (dB) is alogarithmic unit used to express theratio of two values of aphysical quantity.¹ For power ratios thedecibel unit is defined as follows:

\[L_{dB}=10\cdot\log_{10}{\frac{P_{out}}{P_{in}}}\]

For intensity ratios thedecibel unit is defined as follows:

\[G_{dB}=20\cdot\log_{10}{\frac{A_{out}}{A_{in}}}\]

dBm is alogarithmic unit of power level, expressed in decibel (dB) and referenced to apower level of one milliwatt (mW).²

Inthis table, theterm noise floor refers to thecalculated thermal noise, also known as theJohnson–Nyquist noise.³

Many amateur radio and shortwave broadcast receivers feature asignal strength meter (S‑meter).⁴ In1981, theInternational Amateur Radio Union (IARU) Region1 agreed on atechnical recommendation for S‑meter calibration of HF and VHF/UHFtransceivers.^5,6

IARURegion1 TechnicalRecommendationR.1 defines S9 for theHF bands to be areceiver input power of -73dBm. This is alevel of 50µV at thereceiver’s antenna input assuming theinput impedance of thereceiver is 50Ω.

Therecommendation defines adifference of one S-unit corresponds to adifference of 6dB, equivalent to avoltage ratio of two, or apower ratio of four. Signals stronger than S9 are given with anadditional dB rating, thus “S9+20dB”, or, verbally, “20 decibel over S9”, or simply “20 over 9” or even thesimpler “20 over.”

Thenoise floor for a\(B=2700\)Hz wide SSB signal at \(T=300\)K is:³

\(P=k_B\cdot T\cdot B=k_B\cdot300\cdot2700=11.8\cdot10^{-18}\,\text{W}=11.8\text{aW}=-139.5\,\text{dBm}\)

where \(k_B=1.3806488\cdot10^{-23}\,\text{J/K}\) is Boltzmann’s constant.

Thesame IARU Region1 recommendation defines S9 for VHF/UHF to be areceiver input power of -93dBm. This is theequivalent of 5µV in 50Ω. Again, one S-unit corresponds to adifference of 6dB, equivalent to avoltage ratio of two, or apower ratio of four.

Thenoise floor for a10kHz wide FM signal at 300K is:³

\(P=k_B\cdot T\cdot B=k_B\cdot300\cdot10^{4}=41\cdot10^{-18}\,\text{W}=41\text{aW}=-134\,\text{dBm}\)

where \(k_B=1.3806488\cdot10^{-23}\,\text{J/K}\) is Boltzmann’s constant.