Boom Aimed at the Neighbour's Balcony
An operator is planning a 430 MHz station: 50 W into a 9 dBd Yagi on a 6 m mast at the end of a single-storey roof, putting the antenna about 8 m above ground. The nearest neighbour's first-floor balcony is 4 m away horizontally and at the same height as the antenna, and the plan is for the main lobe to point straight at it. The operator intends to work to the general-public power-density reference level at 430 MHz, about 2 W/m2, and to keep at least 6 dB below it. On the other side of the roof is the 240 V overhead service line to the house, and the mast will be raised by two people using a ladder.
1. Compute the power density at the balcony and assess the plan against the operator's own target.
Read the worked answer
Convert the gain
9 dBd = 11.15 dBi -> gain factor 10^(11.15/10) = 13.0
EIRP
50 W x 13.0 = 651 W
Far-field power density at 4 m
S = EIRP / (4 x pi x d^2) = 651 / (4 x pi x 16) = about 3.2 W/m2
Distance needed for the target levels
d = sqrt(EIRP / (4 x pi x S))
- For 2 W/m2: d = sqrt(651/25.1) = 5.1 m
- For 1 W/m2 (the 6 dB margin target): d = sqrt(651/12.6) = 7.2 m
Verdict
At 3.2 W/m2 the plan exceeds the reference level and is three times the operator's own 1 W/m2 goal. It fails.
Caveat to state
Close to a high-gain antenna the far-field formula is optimistic - the reactive near field and the real pattern matter. Treat these distances as minimums and, for a permanent installation, assess with the antenna's actual pattern and the applicable current reference levels and averaging rules.
2. Give practical options in order of preference, and address the service line and the lifting plan.
Read the worked answer
Getting the exposure down
- Aim away. Rotate the boom so the balcony sits in a side lobe rather than the main lobe. A well-designed Yagi's side lobes are typically 15-25 dB down, which brings 3.2 W/m2 to well under 1 W/m2. This is free.
- Move it. Shift the antenna along the roof until the balcony is more than about 8 m away and off-axis.
- Reduce power. For 1 W/m2 at 4 m you need EIRP <= 4 x pi x 16 x 1 = 201 W, i.e. 201/13 = about 15 W into this antenna - a big sacrifice, which is why antenna siting comes first.
- Change the height or tilt so the horizontal main beam is not at balcony height.
Recheck the assessment whenever the power, antenna or siting changes.
The service line
Treat it as live at all times and keep the mast and any antenna well clear, so that neither the mast itself nor a dropped element can approach it. Confirm the clearance rules with the supply authority before starting, and plan the lift so the mast is never in a position to fall or swing toward the line.
The lift
Two people, a ladder footed and tied, no work in wind or on a wet roof, gloves and eye protection, and a clear drop zone below. Never work alone at height, and stop the job if the lift cannot be controlled away from the line.
3. The operator later fits a 13 dBd Yagi. What must be re-examined?
Read the worked answer
Gain change
13 dBd - 9 dBd = 4 dB more gain, a factor of 10^(4/10) = 2.5.
New EIRP = 651 x 2.5 = about 1.63 kW
New distances
Required distance scales with the square root of EIRP, so it grows by sqrt(2.5) = 1.58:
- 1 W/m2 target: 7.2 x 1.58 = about 11.4 m
- 2 W/m2 level: 5.1 x 1.58 = about 8 m
Now the balcony at 4 m is even more exposed, so aiming the beam elsewhere becomes essential rather than merely prudent.
Principle
Compliance is a property of the whole installation, not of the transceiver. Any change of antenna gain, power, height or direction invalidates the earlier assessment and must be redone - whoever inherits the station should be able to find that judgement written down.