2.3 RF Units and the Rule of 10s and 3s

Why WLAN people speak decibels

Watts are honest SI units. They are also clumsy for Harborline's radios, which hop from 200 mW at an AP transmitter to nanowatts at a client in the far aisle. Decibels compress that span. CWNA-109 Domain 1.2 wants you fluent in watt and milliwatt, dB as a ratio, dBm as absolute power referenced to 1 mW, dBi as antenna gain versus isotropic, and the rule of 10s and 3s that converts dBm to mW without a calculator.

Independent CWNA-109 math practice by OpenExamPrep stays on those units here. EIRP, SNR, and RSSI wait for the next chapter so you do not mix a cable power with a received indicator.

Watt and milliwatt

The watt (W) is the SI unit of power: one joule per second.

WLAN conducted powers are usually more convenient in milliwatts (mW):

1 W = 1000 mW

1 mW = 0.001 W

Tiny received powers use microwatts (µW) and nanowatts (nW):

1 mW = 1000 µW

1 µW = 0.001 mW = 10^−6 W

Harborline's indoor AP might be set near 100 mW (0.1 W) conducted on a chain before antenna math. A client at the coverage edge might be receiving on the order of 0.0000001 mW. You will not add those on a linear napkin; you will add decibels.

Keep the prefixes honest. 23 on a screen is not 23 milliwatts if the unit is dBm, and 1 W is not 1 mW. Write the unit every time you copy a number onto a whiteboard.

Decibel (dB): a ratio, never a standalone power

dB compares two powers:

dB = 10 log₁₀ (P₂ / P₁)

Because it is a ratio, the AP is 20 dB is incomplete. Twenty dB relative to what? Cable loss of 3 dB means the output is about half the input. Antenna gain of 6 dBi is a different reference (isotropic), taught below as a dBi figure, not a naked dB of power in a cable.

Useful anchors you should recite:

You add decibels; you multiply linear power. A +10 dB amplifier after a −3 dB jumper is +7 dB net, which is a bit more than a 5× linear gain, not 10 minus 3 milliwatts.

dB is also used for return loss (previous section) and for gains/losses in a link budget. Still a ratio. If a stem gives only dB and no reference, look for the missing milliwatt, watt, or isotropic comparison.

dBm: absolute power versus 1 milliwatt

dBm is decibels relative to 1 mW:

dBm = 10 log₁₀ (P / 1 mW)

Now you have an absolute power. 0 dBm is not zero power; it is 1 mW.

Adding dB (a ratio) to dBm (an absolute) yields dBm. Example: 20 dBm into a −3 dB jumper → 17 dBm at the antenna feed.

You cannot add dBm to dBm and call it dBm of a combined power without converting to milliwatts first. Two 20 dBm transmitters are not 40 dBm. Exam trap.

Negative dBm is still real power, just below 1 mW. −30 dBm is not a sign error; it is 1 µW.

dBi: antenna gain versus isotropic

An isotropic radiator is a theoretical point source that spreads energy equally in every direction. No physical WLAN antenna is isotropic; the idea is a reference.

dBi is antenna gain in decibels relative to isotropic. A 5 dBi indoor antenna means that, in its favored directions, the field is 5 dB stronger than the same watts would produce from an isotropic source, and weaker in other directions. That is passive gain: no extra watts created. You already distinguished that from amplification; here you lock the unit name.

Do not confuse:

You cannot convert dBi to milliwatts by itself. Gain has no milliwatts until you know the conducted power going into the antenna. This chapter does not compute EIRP (conducted dBm + antenna dBi − cable dB). Remember the ingredients exist; apply them next chapter.

Rule of 10s and 3s

The rule of 10s and 3s converts between dBm and mW using only doubling and decade jumps.

Start from the identity:

0 dBm = 1 mW

Then:

• +10 dB → multiply mW by 10
• −10 dB → divide mW by 10
• +3 dB → multiply mW by 2
• −3 dB → divide mW by 2

You can chain them. 6 dB is two 3 dB steps (×4). 9 dB is three doublings (×8). 7 dB is not a pure 3-and-10 combo; estimate or use a calculator. Exam items prefer the neat marks: 0, 3, 10, 13, 17, 20, 23, 27, 30 and the negative mirrors.

To go mW → dBm, reverse the arrows: find a nearby landmark (1, 10, 100, 1000 mW) and count 10s and 3s. 50 mW is half of 100 mW → 20 dBm − 3 dB = 17 dBm. 25 mW is half of 50 mW → 14 dBm. 4 mW is 1 mW ×2 ×2 → 6 dBm.

Worked conversions the exam expects

0 dBm = 1 mW
By definition. This is the home square on the board.

10 dBm = 10 mW
0 dBm = 1 mW, +10 dB → ×10 → 10 mW.

20 dBm = 100 mW
0 dBm = 1 mW, +10 → 10 mW, +10 → 100 mW.
Or 10 dBm = 10 mW, +10 → 100 mW.

23 dBm = 200 mW
20 dBm = 100 mW, +3 dB → ×2 → 200 mW.
Harborline's radio at 23 dBm conducted is 0.2 W, not 23 mW. Confusing the unit suffix is a classic miss.

−30 dBm = 1 µW
0 dBm = 1 mW
−10 dB → 0.1 mW
−10 dB → 0.01 mW
−10 dB → 0.001 mW = 1 µW.

Additional drills Amira uses on a whiteboard:

• 13 dBm: 10 dBm = 10 mW, +3 → 20 mW
• 17 dBm: 20 dBm = 100 mW, −3 → 50 mW
• 27 dBm: 30 dBm = 1000 mW, −3 → 500 mW
• −20 dBm: 0 dBm = 1 mW, −10 twice → 0.01 mW = 10 µW
• −10 dBm: one decade down from 1 mW → 0.1 mW = 100 µW
• 6 dBm: 0 dBm = 1 mW, +3 twice → 4 mW
• 30 dBm: three +10 steps from 1 mW → 1000 mW = 1 W

If a stem gives 23 dBm and four linear choices, walk 20 dBm = 100 mW then double. Do not average 20 and 30.

Table of common WLAN power levels

These are typical orders of magnitude for study, not a regulatory table and not EIRP. Conducted chain settings vary by vendor, band, and country.

Client received levels in a working BSS are often tens of dB below 0 dBm; that is RSSI/SNR territory next chapter. Do not call −70 dBm a transmit setting, and do not convert it in this section as if it were EIRP.

Harborline scenario: the 23 dBm ticket

A technician sets an AP to 23 dBm and emails Amira that the radio is now 23 milliwatts, so it is quieter than the old 100 mW AP. That technician mixed dBm with mW. 23 dBm is 200 mW, twice 20 dBm's 100 mW. The change was louder, not quieter. Amira walks the rule of 10s and 3s on a whiteboard: 0 dBm = 1 mW, two +10 steps to 100 mW, then +3 to 200 mW. The ticket is corrected before the neighbor tenant files an interference complaint.

A second mistake on the same ticket: adding the AP's 5 dBi antenna as if it were +5 dBm already labeled as a milliwatt result. Antenna gain is dBi, a different reference. Stop at conducted dBm until the next chapter.

A third mistake: adding two 20 dBm chains on paper to get 40 dBm. Convert to milliwatts if you must combine linear power; 100 mW + 100 mW is 200 mW, which is 23 dBm, not 40 dBm.

Unit traps

1. Reading 23 dBm as 23 mW (it is 200 mW).
2. Treating dB as an absolute power.
3. Adding two dBm values as if they were dB ratios.
4. Using dBi and dBm interchangeably, or converting dBi to mW alone.
5. Forgetting 0 dBm = 1 mW, so negative dBm is still real power, just below 1 mW.
6. Bringing EIRP, SNR, or RSSI into a units-only question.