2.4 GHz link with 4.2 km span, tree intrusion, and an EIRP cap
A 2.4 GHz point-to-point link must connect a grain silo to an office building 4.2 km away. The path is clear line of sight except for a row of trees about 900 m from the silo whose tops stand 4 m above the straight line between the two antenna heights. Planned hardware at both ends is identical: 20 dBm conducted transmit power, 8 dBi grid antenna, 0.5 dB connector and pigtail loss per end. Receiver sensitivity is -85 dBm at 20 MHz channel width and -82 dBm at 40 MHz. The link is specified for 99.9 percent availability, which local design practice converts to a required fade margin of 15 dB, and that figure already includes a 6 dB allowance for vegetation. The regulator caps EIRP at 36 dBm. Rain is negligible at 2.4 GHz. The installer has spare 14 dBi antennas available and the option of adding 1.5 m of mast at either end.
1. Compute the free-space path loss, the received level and the fade margin at both channel widths, and check EIRP compliance.
Read the worked answer
Path loss. FSPL(dB) = 32.45 + 20log10(f in MHz) + 20log10(d in km) = 32.45 + 20log10(2400) + 20log10(4.2) = 32.45 + 67.60 + 12.46 = 112.5 dB.
EIRP per end. 20 dBm + 8 dBi - 0.5 dB = 27.5 dBm, which is 8.5 dB below the 36 dBm cap, so the planned hardware is compliant.
Received level. Link budget: 20 + 8 - 0.5 - 112.5 + 8 - 0.5 = -77.5 dBm.
Fade margin.
- At 20 MHz: -77.5 - (-85) = 7.5 dB against a required 15 dB, a shortfall of 7.5 dB.
- At 40 MHz: sensitivity worsens by 3 dB to -82 dBm, so margin is 4.5 dB, a shortfall of 10.5 dB.
The link as designed does not meet the availability specification at either width, and 40 MHz is strictly worse because the wider channel admits more noise for no capacity benefit here. Note also that the 6 dB vegetation allowance is already inside the 15 dB requirement; the tree row will be assessed against Fresnel clearance next, because the allowance only holds for a modest obstruction.
2. Check the first Fresnel zone against the tree row and decide whether the tree clearance is acceptable, and whether a 1.5 m mast extension fixes it.
Read the worked answer
Fresnel radius at a point: r = 17.32 x sqrt(d1 x d2 / (f(GHz) x D(km))) with distances in km.
- At the tree row, 900 m from the silo: d1 = 0.9, d2 = 3.3, so r = 17.32 x sqrt(0.9 x 3.3 / (2.4 x 4.2)) = 17.32 x sqrt(2.97 / 10.08) = 17.32 x 0.543 = 9.4 m.
- Rule-of-thumb clearance needed is 60 percent of the first zone: 0.6 x 9.4 = 5.6 m.
- For comparison, at the midpoint: r = 17.32 x sqrt(2.1 x 2.1 / 10.08) = 11.5 m, so about 6.9 m of clearance is wanted there.
The tree tops are only 4 m above the line, so the obstruction is inside the first Fresnel zone and the path is not properly clear. Loss will exceed the 6 dB vegetation allowance already baked into the 15 dB margin, and reflection off the canopy will add fading.
Does 1.5 m of mast fix it? A mast at one end raises the line most at that end and least at the far end. Raising the silo end by 1.5 m raises the line at the 900 m point by roughly 1.5 x 3.3/4.2 = 1.2 m, giving about 5.2 m against the 5.6 m needed - close but still short, and it assumes the tree row does not grow. Clearance should be designed with growth headroom. So the mast helps but does not by itself make the path compliant.
3. Recommend a final design that meets the 15 dB margin within the EIRP cap, with justification for each choice.
Read the worked answer
Antenna gain is the lever to use. Fit the spare 14 dBi grids at both ends:
- EIRP = 20 + 14 - 0.5 = 33.5 dBm, still under the 36 dBm cap with 2.5 dB to spare.
- Received level = 20 + 14 - 0.5 - 112.5 + 14 - 0.5 = -64.5 dBm.
- Margin at 20 MHz = -64.5 - (-85) = 20.5 dB, which covers the 15 dB requirement and leaves about 5.5 dB of headroom.
Gain at both ends is the right choice because it improves the received level without raising conducted power, so the regulatory limit is respected. If the cap had been tighter, reducing transmit power to stay legal would have cost margin directly, since lowering TX lowers the received level as well as the EIRP - a trade-off worth stating explicitly.
Channel width: 20 MHz. The 40 MHz setting costs 3 dB of sensitivity for throughput this link does not need, and it occupies more of an unlicensed band that is already crowded.
Shape the path as well as the budget. Use the 1.5 m mast to gain partial clearance on the tree row, and set antenna heights to maximise clearance within the structural limits of the silo - the extra 5.5 dB of margin is partly there to absorb the residual canopy loss. Verify by a link test that records RSSI, SNR and error rate over at least 24 hours including the hottest and windiest hours.
Before installation: confirm mast loading and wind rating, keep both ends on the same polarisation, and do a spectrum scan to choose the quietest 20 MHz channel.