dBi stands for deciBel Isotropic [1]. It is the gain of an antenna relative to that of an ideal isotropic antenna that radiates energy equally in all directions.
dBm [2] is the power relative to one milliwatt. dBm can be directly converted to Watt and vice versa.
This tool uses the
- Power at the output of a transmitter (dBm)
- Cable loss (dB) and
- Effective Isotropic Radiated Power or EIRP (dBm)
to find the required antenna gain in dBi.
dBi to dBm Formula
GAnt = EIRP – PTx + LC
The gain of an antenna is equal to the EIRP minus the transmit power plus the cable losses.
Background
EIRP is the power that would have to be radiated by an isotropic antenna to provide the same signal level as the actual source antenna in the direction of the antenna’s strongest beam. The equation itself is derived from the EIRP.
PTx is the transmit power measured at the output connector of a transmitter. It is expressed either in Watt or dBm. The equation above uses the dBm equivalent. This tool can be used to convert from Watt to dBm.
LC is the insertion loss due to the antenna cable. Expressed in dB it depends on frequency of operation, length, quality and construction of the cable.
GAnt is the gain of the antenna in dBi. It can also be calculated from the wavelength and antenna factor.
Example Application
The maximum EIRP for a LoRa wireless device operating at 922 MHz in Japan is +27 dBm.
This number guides the RF engineer and users of the product in antenna selection.
Assuming a cable loss of 1 dB and a maximum output power from the transmitter of +15 dBm, the maximum allowable antenna gain is 13 dBi.
💡 The higher the cable loss, the higher the allowable antenna gain for a fixed transmitter power. The gain overcomes the cable loss. As well, the higher the transmitter power, the smaller the max antenna gain to keep within the regulatory limits.
Despite this restriction on EIRP for LoRa, there is widespread use of high gain antennas for Helium applications in conjunction with bi-directional amplifiers.
In general, exceeding the limit would result in RF interference issues for other products operating in the same or neighboring frequency ranges. It’s likely not as much of a problem for LoRa on account of the short time duration of the signals.
Wi-Fi manufacturers deter the use of high gain antennas by using RP-SMA connectors on the output. This makes it a little more difficult to attach high gain antennas most of which are equipped with N or SMA-M connectors.
âš¡ The peak power of Wi-Fi is higher than that of LoRa and as a result Radio Frequency interference causes bigger issues. High dBi gain antennas are very disruptive to neighboring Wi-Fi networks.
dBm to dBi Table
The FCC specifies a max EIRP of +36 dBm for Wi-Fi systems. The table below shows the max antenna gain (dBi) for this transmit power (dBm) level with no cable loss.
| Antenna Gain (dBi) | Transmit Power (dBm) |
| 56 | -20 |
| 55 | -19 |
| 54 | -18 |
| 53 | -17 |
| 52 | -16 |
| 51 | -15 |
| 50 | -14 |
| 49 | -13 |
| 48 | -12 |
| 47 | -11 |
| 46 | -10 |
| 45 | -9 |
| 44 | -8 |
| 43 | -7 |
| 42 | -6 |
| 41 | -5 |
| 40 | -4 |
| 39 | -3 |
| 38 | -2 |
| 37 | -1 |
| 36 | 0 |
| 35 | 1 |
| 34 | 2 |
| 33 | 3 |
| 32 | 4 |
| 31 | 5 |
| 30 | 6 |
| 29 | 7 |
| 28 | 8 |
| 27 | 9 |
| 26 | 10 |
| 25 | 11 |
| 24 | 12 |
| 23 | 13 |
| 22 | 14 |
| 21 | 15 |
| 20 | 16 |
| 19 | 17 |
| 18 | 18 |
| 17 | 19 |
| 16 | 20 |
| 15 | 21 |
| 14 | 22 |
| 13 | 23 |
| 12 | 24 |
| 11 | 25 |
| 10 | 26 |
| 9 | 27 |
| 8 | 28 |
| 7 | 29 |
| 6 | 30 |
| 5 | 31 |
| 4 | 32 |
| 3 | 33 |
| 2 | 34 |
| 1 | 35 |
| 0 | 36 |
| -1 | 37 |
| -2 | 38 |
| -3 | 39 |
| -4 | 40 |
| -5 | 41 |
| -6 | 42 |
| -7 | 43 |
| -8 | 44 |
| -9 | 45 |
| -10 | 46 |
| -11 | 47 |
| -12 | 48 |
| -13 | 49 |
| -14 | 50 |
References
[1] deciBel Isotropic on Wikipedia
[2] dBm on Wikipedia