# Relating dBµ and dBf

Broadcasters usually specify electromagnetic field strength in dBµ, which is dB above 1 µV/m. Receiver manufacturers typically specify sensitivity in dBf, which is dB above 1 femtowatt (10−15 W). I wondered how the two were related.

With AO 8.50 I modeled two dipoles 1 km apart in free space. I drove one dipole and calculated the field strength in dBµ at the other. Then I calculated the power the second dipole delivered to a 75Ω load in dBf. The difference between the two figures provides a conversion constant.

I used halfwave dipoles with thin lossless conductors. Using 30 analysis segments per halfwave, the dipole impedance is 75.6 + j44.8 Ω. I added series −j44.8Ω loads to cancel the reactances. With a 1-kW source at one dipole, the field at the other is 0.222 V/m, or 106.9 dBµ. A 1-V source at the transmit antenna yields a 5.31-µA load current at the receive antenna. The power delivered to the load is (5.31×10−6)2 × 75 = 2.11×10−9 W, or 63.2 dBf. The 1-V transmit source across 75.6Ω is a power of 12 ⁄ 75.6 = 13.23 mW. This is 48.8 dB below 1 kW. Therefore the field strength at this drive level is 106.9 − 48.8 = 58.1 dBµ. This field strength yields a signal power of 63.2 dBf, so

dBf = dBµ + 5.1 + G - L

where G is antenna gain in dBd and L is the sum of feedline and balun losses.

A 60-dBµ FCC service contour yields 65 dBf for a dipole with a short feedline. This happens to be the standard IEEE 185-1975 signal level for several receiver measurements, including S/N.

## Antenna File

```Two dipoles 1 km apart
Free Space Symmetric
98 MHz
2 wires, meters
a = 299.792458 / 98 / 4
1      0 -a 0      0  a 0   2E-8
1   1000 -a 0   1000  a 0   2E-8
1 source
Wire 1, center
2 loads
Impedance loads
Wire 1, center  0 -44.8
Wire 2, center 75 -44.8
```

January 15, 201288–108 MHz