Silo on the Path: An 18 GHz Hop Loses Its Fresnel Clearance
A regional utility runs a 12.4 km point-to-point link on 18 GHz between a hilltop repeater and a substation. Both ends use 0.6 m parabolic dishes mounted 40 m above local ground on flat farmland, vertical polarization. The link is engineered with 20 dB of fade margin, and the operator's planning tool gives 14 dB of rain attenuation at 0.01% of the worst month for this path length. A grain cooperative now wants to build a silo 6.2 km from the hilltop end, with a roof reaching 34 m above ground. Records already show deep fades on late-summer afternoons, before the silo was proposed, and the original path was cleared using k = 4/3. The planning team asks three things: whether the silo can be accepted, what antenna height change would be needed if it is built, and whether migrating the hop to 23 GHz, where more channel width is available, would be a better answer than raising the antennas.
1. Calculate the first Fresnel zone radius at the silo and assess the clearance for k = 4/3 and k = 2/3. Is the silo acceptable?
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Fresnel radius. d1 = d2 = 6.2 km, D = 12.4 km, f = 18 GHz: F1 = 17.3 x sqrt(d1 d2 / (f D)) = 17.3 x sqrt(38.44 / (18 x 12.4)) = 17.3 x 0.415 = 7.18 m.
Clearance. Both antennas sit at 40 m over flat terrain, so the line of sight at the silo is at 40 m and the geometric clearance is 40 - 34 = 6.0 m (84% of F1). That is misleading, because k changes how much ground appears to bulge into the path: bulge = d1 d2 / (2 k a), a = 6371 km.
- k = 4/3: 38.44 / (2 x 1.333 x 6371) = 2.26 m, so clearance = 3.74 m = 52% of F1, roughly 1-3 dB of diffraction loss.
- k = 2/3: 38.44 / (2 x 0.667 x 6371) = 4.52 m, so clearance = 1.48 m = 21% of F1. That is deep inside the zone; expect 10 dB or more, and this is exactly the sub-refractive summer condition the fade records show.
The usual criterion is at least 60% of F1 at the worst k, i.e. 0.6 x 7.18 = 4.31 m of clearance after the bulge. Only k above about 1.2 meets that.
Verdict: not acceptable. To restore 60% clearance at k = 2/3, the line of sight at the silo must reach 34 + 4.52 + 4.31 = 42.8 m. Raising both dishes to about 43 m (3 m each), or raising one end alone by about 6 m, achieves it; 45 m is preferable to leave margin for the k = 2/3 assumption and survey error.
2. Test the fade budget with and without the height change, and evaluate the 23 GHz migration proposal.
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Without the height change. At k = 2/3 the obstruction alone contributes an order of 10 dB. Adding the 14 dB rain figure and about 1 dB for ageing and alignment gives roughly 25 dB against a 20 dB margin: the hop fails during summer storms and during sub-refractive afternoons, which matches the existing fade log. Even at k = 4/3 (2 dB diffraction) the budget is 17 dB, leaving only 3 dB for multipath and ageing.
With the antennas raised to full 60% clearance, the diffraction term drops to about 0-1 dB, so the budget is 14 + 1 + 1 = 16 dB against 20 dB: about 4 dB of spare margin. That is workable but thin for a 12.4 km hop; 1.2 m dishes (roughly +6 dB) or a space-diversity arrangement would make it comfortable.
23 GHz is not the answer. The Fresnel radius at 23 GHz would be 17.3 x sqrt(38.44 / (23 x 12.4)) = 6.35 m, so the radius shrinks, but the clearance in metres does not change. At k = 2/3 the clearance stays 1.48 m, i.e. 23% of the smaller zone, so the diffraction penalty is essentially unchanged. Rain, however, gets worse: specific attenuation in this band rises steeply with frequency, so the same 0.01% rain rate that gives 14 dB at 18 GHz gives roughly 20-23 dB at 23 GHz. That alone consumes the entire margin.
The extra channel width at 23 GHz is a capacity argument, not a propagation argument. Keep 18 GHz, raise the antennas, and let the planning tool re-run the 0.01% rain calculation if a 23 GHz upgrade is ever considered.
3. The contractor suggests tilting the hilltop dish a few degrees downward so the main beam clears the silo roof. Evaluate this proposal.
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It does not work, and it costs margin. Obstruction is a property of the straight line joining the two antenna phase centres after the earth-bulge correction. Tilting a dish rotates its pattern relative to that line; it does not move the phase centre, so the clearance at the silo is unchanged and the 7.18 m Fresnel zone is still intersected as before. The diffraction loss stays exactly where it was.
What it does cost. The half-power beamwidth of a 0.6 m dish at 18 GHz is about theta = 70 lambda / D = 70 x (0.3 / 18) / 0.6 = 1.9 degrees. Pointing the hilltop antenna 2-3 degrees down therefore puts the far-end antenna several beamwidths off the peak, sacrificing several dB of gain at both ends and degrading the cross-polar discrimination. In a link that has only about 4-6 dB of spare margin, that is a direct availability loss.
What to say instead. The clearance problem must be solved in geometry: raise one or both antennas, or negotiate the silo height. If the dish must be re-pointed for any other reason, do it with a proper alignment survey and confirm the received level against the as-designed value. Also note the reverse risk: an upward tilt during the original alignment could explain part of the recorded fade history and should be checked before the new path calculation is finalised.