Decibels and gain chains

Levels & units — a level in any unit, converted to all the others. Power units and voltage units are tied by the impedance (P = V²/Z): dBm needs it (50 Ω for RF, 75 Ω for video, 600 Ω in old audio); dBu is a voltage (0.775 V rms, which puts 1 mW into 600 Ω) whatever the load; dBV is referenced to 1 V rms. Peak and peak-to-peak assume a sine wave.
Ratios — power ratio 10^(dB/10), voltage ratio 10^(dB/20): +3 dB doubles the power, +6 dB doubles the voltage.
Gain & noise chain — stages from the input, each with its gain and noise figure (a passive loss has a noise figure equal to its loss) and optionally its input IP3. The cascade uses Friis' formula F = F₁ + (F₂ − 1)/G₁ + (F₃ − 1)/(G₁G₂) + … and, for linearity, 1/IIP3 = 1/IIP3₁ + G₁/IIP3₂ + G₁G₂/IIP3₃ + … in linear units. With a bandwidth it gives the noise floor −174 dBm/Hz + 10·log₁₀(B) + NF, the sensitivity at your required SNR, and the spurious-free dynamic range ⅔·(IIP3 − floor).

For RF power, antennas, path loss, and link budgets, see the RF tool.

Share link copies a URL that opens this tool with your current settings — every value it remembers between visits, packed into ?s=. Opening a link replaces your saved settings for this tool.

Linking to an example

Companion to the logarithmic scales in chapter 12 of Mathematics, Reconnected. Settings have short parameters, and the tab comes from the # part of the address, for example /tools/decibels/?db=25#ratios or ?level=-10&unit=dBV#levels. The gain chain’s stages travel only in Share link's compressed ?s=.

Tab Parameter Meaning Example

Tab	Parameter	Meaning	Example
`#levels`	`level`, `unit`, `z`	a level, its unit (`dBm`, `dBW`, `dBV`, `dBu`, `dBmV`, `dBuV`, `W`, `Vrms`, …) and the impedance in Ω (write `+` as `%2B`)	`level=-60&unit=dBm&z=50`
`#ratios`	`db`	decibels to power and voltage ratios	`db=25`
`#ratios`	`power`, `voltage`	a power or voltage ratio, converted to decibels (opens this tab)	`power=2`
`#chain`	`bw`, `snr`	bandwidth in Hz and required SNR in dB	`bw=200k&snr=10`
	`example`	one of the presets below (it also picks the tab); other parameters override it	`example=ch12-double-power`

#levels

level, unit, z

a level, its unit (dBm, dBW, dBV, dBu, dBmV, dBuV, W, Vrms, …) and the impedance in Ω (write + as %2B)

level=-60&unit=dBm&z=50

#ratios

db

decibels to power and voltage ratios

db=25

#ratios

power, voltage

a power or voltage ratio, converted to decibels (opens this tab)

power=2

#chain

bw, snr

bandwidth in Hz and required SNR in dB

bw=200k&snr=10

example

one of the presets below (it also picks the tab); other parameters override it

example=ch12-double-power

Presets:

ch12-85-vs-60-db — 85 dB against 60 dB: 25 dB is 10^2.5 ≈ 316 times the intensity
ch12-double-power — Doubling the power adds 10 log₁₀ 2 ≈ 3.01 dB
ch12-ten-times — 10 dB is ten times the power
ch12-wifi-dbm — A Wi-Fi signal of −60 dBm in watts and volts (50 Ω)

Sharing

Linking to an example