Wireless 101
M09 · L04
Module 9 · Lesson 4

Will It Work, and How Far?

Nothing here is new — that is the point. A link budget spends everything Modules 5 to 9 built, and answers the only question a radio project really asks.

01 / 11
Wireless 101
M09 · L04
One line of addition

Why M2-L4 Taught You Logarithms

Received power, in dBm
P_{rx} = P_{tx} + G_{tx} - L_{tx} - PL - L_{misc} + G_{rx}

Every term is a decibel, so the whole budget is arithmetic. Exactly one term carries a reference letter — the dBm — which is the sanity check that catches most sign errors.

02 / 11
Wireless 101
M09 · L04
The other end of the sum

Sensitivity Is Four Numbers

Sensitivity, from M9-L1
S = -174 + 10\log_{10} B + \mathrm{NF} + \mathrm{SNR}_{req}

20 MHz, NF 6 dB, 20 dB for 64-QAM: −174 + 73.01 + 6 + 20 = −75.0 dBm. M9-L1 ran it at NF 5 and got −76 — one decibel apart, exactly the noise figure ✓

03 / 11
Wireless 101
M09 · L04
Four mechanisms, four rows

Never Write “Margin: 20 dB”

  • Fade — Rayleigh, ~20 dB for 1% outage (M8-L3)
  • Shadowing — zσ, 1.28 × 8 = 10.2 dB at 90% (M8-L4)
  • Interference — 3 dB means I = N (M9-L3)
  • Implementation & ageing — 1 to 3 dB, not random

One lump hides which risk you covered. Root-sum-square only for independent log-normal terms: √(8²+6²) = 10 dB gives 12.8 dB, not 17.9.

04 / 11
Wireless 101
M09 · L04
Worked: 2.4 GHz WiFi

Seventeen Metres

  • 20 − 0.5 + 2 + 2 − 3 − 2 = 18.5 dBm before path loss
  • Margins 8 + 5.1 + 3 = 16.1 dB
  • Allowed PL = 18.5 + 75.0 − 16.1 = 77.4 dB
  • 77.4 = 40.05 + 30 log(d) → d = 17.6 m for 64-QAM
  • At the lowest rate, SNR 5 dB: 55.6 m — 3.16× further

The “range of WiFi” is always the range of the slowest modulation.

05 / 11
Wireless 101
M09 · L04
Try it — B = 20 MHz, n = 3.0

The Budget Waterfall

TX pwr 20 dBm
Gain +4 dBi
NF 6 dB
SNR req 20 dB
Margin 16 dB
sens −75.0 dBm allow 83.0 dB range 27.0 m margin@30m 14.6 dB 30 m link fails
Interactive: close a link budget term by term and read off the range — AI-generated
06 / 11
Wireless 101
M09 · L04
Worked: 900 MHz cellular

The Budget Done Twice

  • Uplink sens: −174 + 60.33 + 2 + 0 = −111.7 dBm
  • Uplink: 23 − 3 + 17 − 2 = 35.0 dBm before path loss
  • Margins 10 + 10.2 + 3 = 23.2 dB → allowed 123.5 dB
  • Downlink sens −106.7 dBm, EIRP 61 dBm → allowed 141.5 dB

Same channel, same margins, same panel — and 18 dB apart. Everything symmetric cancels, so only two lines can be responsible.

07 / 11
Wireless 101
M09 · L04
The most useful insight here

The Uplink Always Loses

46 − 23 = 23 dB of transmit power to the downlink; the base station’s better noise figure hands 5 dB back. 23 − 5 = 18.0 dB ✓

Uplink
0.83 km
Downlink
2.68 km
Area ratio
10.5×

Size the cell on the downlink and about 90% of its area cannot answer. A handset runs on a battery, and no tower engineering repeals that.

08 / 11
Wireless 101
M09 · L04
Reading the spreadsheet

The Two Classic Double-Counts

Combining two log-normal margins
\sigma_{tot} = \sqrt{\sigma_1^2 + \sigma_2^2} \;\Rightarrow\; M = z\,\sigma_{tot}
  • Feeder loss is a budget row or inside NF — never both
  • An interference margin plus a required SINR charges twice
  • Sanity: −95 dBm for 64-QAM in 20 MHz needs NF + SNR = 6 dB. Impossible
09 / 11
Wireless 101
Knowledge Check

Check what stuck

Four questions from this lesson. Answer to see why — the explanation appears whether you were right or wrong. Nothing is scored or saved.

Question 1 of 0
Score 0/0

10 / 11
Wireless 101
M09 · L04
Recap

What you learned

  • Prx = Ptx + G − L − PL, and margin = Prx − sensitivity
  • Sensitivity = −174 + 10log B + NF + SNRreq
  • Four margins, four mechanisms — never one lump
  • WiFi: 77.4 dB allowed → 17.6 m at 64-QAM
  • Cellular is uplink-limited by 18 dB — a 10.5× area ratio
Module 9 complete — up next
Module 10: Access →
All lessons Read article
11 / 11