WOBBLdipole
dipole. Is this 58 mm dipole tuned for 2.4 GHz, and does the link reach across a 25 m office?
OK
The 58 mm dipole resonates at 2395 MHz (-1.8% from 2440 MHz), with 77.5 + j11.5 ohm and S11 of -12.6 dB against 50 ohm at 2440 MHz. Peak gain 2.14 dBi. At 25 m the median received power is -67.4 dBm, 24.6 dB above the -92 dBm sensitivity, and the link holds out to 61.8 m in 90% of spots and 165 m in half of them (office).
resonance
2395 MHz
S11
-12.6 dB
impedance
77.5 + j11.5 ohm
gain
2.14 dBi
range, 90%
61.8 m
Confidence medium
- the range comes from an empirical path loss model with 10 dB of shadowing
Simulation
Checks
| status | check | result |
|---|---|---|
| pass | mesh convergence | input impedance magnitude settled: 78.3 -> 78.4 ohm over 2 meshes, last change 0.1% |
| pass | boundary distance | moving the absorbing boundary half again as far out changes the impedance from 77.5 + j11.4 ohm to 77.4 + j11.6 ohm (0.31%) |
| pass | power balance | power fed in at the gap 12.6 mW, power leaving through the outer boundary 12.6 mW (5.4e-08% apart) |
| pass | pattern power | the radiation integral of the current along the wire gives 24.6 mW against 25.3 mW fed to the full dipole (2.7% apart) |
| pass | closed form | resonance at 2395 MHz with 72.8 ohm, against 73.1 ohm for a thin half wave dipole (0.35% apart). Induced EMF theory puts this length at 61.9 + j4.68 ohm at 2440 MHz, the field solve 77.5 + j11.4 ohm |
| pass | free space bound | the office model's median range 165 m is within the free space limit 2016 m |
| info | link uncertainty | shadow fading of 10 dB moves the range from 165 m (half the spots) to 61.8 m (90% of spots), and a power loss coefficient 3 lower or higher gives 104 to 291 m |
Assumptions
- Solved with the axisymmetric model, no 3D solve was needed. A straight wire is a body of revolution, so the axisymmetric full wave solve is exact for it. Give a finite ground plate or put the antenna near something and it is solved in 3D.
- Center fed dipole in free space, wire diameter 1 mm, fed across a 1 mm gap (delta gap).
- Axisymmetric full wave solve, and the outer boundary absorbs outgoing waves to first order.
- Copper conductor loss from the skin effect, 0.15% of the power. No feed line, balun or nearby objects.
- Path loss from the ITU-R P.1238 site general indoor model (power loss coefficient 30, 10 dB shadow fading, for a typical office) at 2440 MHz.
- Link budget 10.0 dBm out, 2.14 dBi and 2.14 dBi antennas, 0.0 dB of other losses, -92.0 dBm sensitivity, and a fading margin of 12.8 dB for 90% of spots.