Thinking in Decibels
Antenna gain, path loss, signal-to-noise ratio — from here on, almost every number in this course arrives in dB. Fifteen slides and you will never have to guess again.
The Numbers Get Absurd
Your phone transmits about 0.2 watts. It can still decode a signal of 0.0000000000001 watts. Write a link budget in watts and you spend the whole calculation counting zeros.
Logs Turn × into +
A radio link is a chain of multiplications: amplifier ×4, cable ÷1.6, free space ÷10¹⁰. Take the logarithm of the whole chain and every multiplication becomes an addition. That is the entire reason decibels exist.
A dB Is a Ratio
Hold on to this one sentence. A decibel never tells you how much power there is — only how much more, or less, than something else. There is a division sign inside the formula, and it never goes away.
Ratio → Decibels
Why 20 log for Voltage
Power goes as amplitude squared, and the log of a square is twice the log. So the factor is not a second convention — it is the same formula with the squaring pulled out front. Double the voltage, quadruple the power: +6 dB either way.
Six Anchors
Learn these six and you can read most dB figures without a calculator, because dB add: ×20 is ×2 then ×10, so 3 + 10 = 13 dB.
- 0 dB — ×1, no change at all
- 3 dB — ×2, double the power
- −3 dB — ÷2, half the power
- 10 dB — ×10
- 20 dB — ×100
- 30 dB — ×1000
3 dB Is Almost Double
Doubling is 3.0103 dB, not 3. Lean on “3 dB = ×2” four times and you get ×16 where the truth is ×15.85 — about 1% off. Perfect for a head check, wrong for a data sheet.
dBm: Add a Reference
If a dB is only a ratio, how does a spec sheet quote an absolute power? It fixes the denominator. Set it to 1 milliwatt and you get dBm — still a ratio, but now to a known quantity, so it pins down a real number.
dBm → Watts
dBW and dBi
Change the reference, change the unit. dBW compares against 1 watt, so dBm = dBW + 30. dBi compares an antenna against an isotropic radiator — an imaginary antenna that sprays power equally in every direction. A plain half-wave dipole beats it by 2.15 dBi.
A Link Budget
Here is the payoff. Transmitter 20 dBm, cable −2 dB, antenna +6 dBi, path −100 dB, receive antenna +3 dBi. Add them up: −73 dBm. In watts that same sum needs five multiplications and eleven decimal places.
Numbers You’ve Already Met
Every dB figure quoted so far in WRL-101 now decodes:
- “3 dB bandwidth” (M2-L1) — where power has halved
- SNR 0–30 dB (M2-L3) — signal from 1× to 1000× the noise
- 18.75 dB (M4-L2) — FM’s 75× noise win, since 20 − 1.25 = 18.75
- 3 dB capture (M4-L3) — twice the power is enough to win
Key Takeaways
- dB exist because cascaded gains multiply — logs make them add
- 10 log for power, 20 log for amplitude — because P ∝ A²
- A dB is a ratio, never a quantity
- dBm, dBW, dBi fix the reference and become absolute
- 0, 3, −3, 10, 20, 30 dB → ×1, ×2, ÷2, ×10, ×100, ×1000
Module 2 Complete!
You’ve mastered Signals & Sine Waves — amplitude, frequency, phase, time and frequency domains, superposition, and the decibel that measures all of them.