The Engineer's Guide to Decibels: dB, dBm, dBi, and dBW

Why Decibels?

Decibels compress enormous ranges onto a manageable scale. A microphone might produce 1 μV; a power amplifier might output 100V. That's a 10⁸ ratio — impossible to plot on a linear scale. In decibels, it's just 160 dB.

Decibels also make multiplication into addition. A signal through three stages with gains of 10, 100, and 10 has total gain 10 × 100 × 10 = 10,000. In dB: 20 + 40 + 20 = 80 dB. Simple addition.

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The Fundamental Definition

The factor of 20 (not 10) for voltage comes from the power-voltage relationship $P = V^2/R$:

Essential Conversions to Memorise

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Absolute Decibel Units

Plain "dB" is always a ratio. To express an absolute level, you need a reference. Different references are used in different fields:

dBm — Power relative to 1 milliwatt

Common in RF engineering and wireless systems:

• 0 dBm = 1 mW
• 10 dBm = 10 mW
• 30 dBm = 1 W (typical WiFi transmit power)
• −50 dBm = 10 nW (typical received WiFi signal)
• −100 dBm = 10 pW (noise floor in a 1 MHz bandwidth)

Use the dBm to Watts converter to convert between dBm and milliwatts.

dBW — Power relative to 1 watt

dBW = dBm − 30. Used for high-power transmitters and satellite links.

dBV — Voltage relative to 1 volt

Common in audio. Consumer line level is −10 dBV (316 mV RMS). Professional line level is +4 dBu ≈ 1.23V RMS.

dBu — Voltage relative to 0.775V

dBu = 20·log₁₀(V / 0.775V). The 0.775V reference is the voltage that produces 1 mW in a 600Ω impedance (the old telephone standard). Professional audio uses +4 dBu as nominal level.

dBFS — Relative to Full Scale (digital audio)

In digital systems, 0 dBFS is maximum amplitude. All signals are at or below 0 dBFS. Peaks above 0 dBFS clip.

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Antenna Gain: dBi and dBd

dBi — Gain relative to isotropic antenna

An isotropic antenna radiates equally in all directions. Real antennas concentrate power in certain directions:

• Isotropic: 0 dBi
• Half-wave dipole: 2.15 dBi
• Patch antenna: 5–8 dBi
• Parabolic dish (1m, 5 GHz): ~35 dBi
• Yagi (10 elements): ~14 dBi

dBd — Gain relative to dipole

dBd = dBi − 2.15. Used in amateur radio. A "10 dBd" antenna = 12.15 dBi.

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Using dB in Link Budgets

A link budget calculates whether a wireless system can work by adding gains and subtracting losses:

Example for a 2.4 GHz WiFi link at 100m:

• TX power: +20 dBm
• TX antenna gain: +3 dBi
• Free-space path loss at 100m: −80 dB (use the Free-Space Path Loss calculator)
• RX antenna gain: +3 dBi
• RX sensitivity: −80 dBm

$P_{rx} = 20 + 3 - 80 + 3 = -54$ dBm. Margin = $-54 - (-80) = 26$ dB. The link works with 26 dB to spare.

Use the RF Link Budget calculator for full link budget calculations.

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Common Pitfalls

Mixing Power and Voltage dB

This is the most common mistake. When in doubt:

• Is it a power quantity? Use 10·log₁₀
• Is it a voltage or field strength? Use 20·log₁₀

Noise figure is in dB (power ratio). Voltage amplifier gain is in dB (20·log). You can add/subtract them only if they represent power at the same impedance.

dBm Is Not dBV

dBm → dBV requires knowing the impedance. In 50Ω: 0 dBm = 224 mV RMS = −13 dBV.

For 50Ω: dBV = dBm − 13. For 600Ω (audio): dBV = dBm − 2.2 ≈ dBu.

Forgetting That dB Represents Ratios

"My amplifier has 20 dB of gain." ✓ (ratio, valid) "The signal is 20 dB." ✗ (20 dB compared to what?)

Always specify the reference when stating absolute levels: 20 dBm, −60 dBV, +4 dBu.

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Summary Reference Card