Hi,

"dBi" is the unit of measure for the gain of an antenna relative to the gain of an isotropic radiator. The radiation pattern of an isotropic source is perfectly spherical. An isotropic radiator exists only in theory, but is used as a reference for the gain of real antennas.

The peak gain of a 1/2-wave, center-fed dipole in free space is 2.15 dBi, because due to its directional radiation pattern that gain is 2.15 dB (1.64X) greater than from an isotropic radiator.

The gain of an antenna sometimes is given with respect to that of a 1/2-wave, center-fed dipole in free space. In that case the unit of measure is "dBd." Gain in dBd can be converted to dBi by adding 2.15 dB to the gain expressed in dBd. So an antenna with a gain of 3 dBd has a gain of 5.15 dBi.

Some antenna manufacturers prefer to use dBi when specifying antenna gain because it results in a larger, more impressive number. But for the same antenna input power an antenna with 3 dBd gain in a given direction produces exactly the same radiated field as one with 5.15 dBi gain in that direction.

Convert the published gain for a free-space path in the direction of interest as given in dBi to a multiplier, using 10^(dBi/10).

As examples, a gain of zero dBi (an isotropic source) is a multiplier of 10^(0/10) = 1, and a gain of 2.15 dBi is a multiplier of 10^(2.15/10) = 1.64 (approx).

The gains of both the tx and rx antenna must be calculated for the Friis equation, and used for Gt and Gr, respectively.

Both the path distance R and the wavelength (lambda) must be entered in the same unit of measure.

Pt is the power in watts delivered to the transmit antenna, and Pr is the impedance-matched power in watts available at the terminals of the receive antenna, assuming that the polarization of both antennas is the same.

Doing the math for a 1,000 meter, 100 MHz free-space path with 100 watts applied to a tx antenna with 2.15 dBi gain, and a rx antenna with 6 dBi gain:

Pr = Pt*Gt*Gr*(lambda/(4*pi*R))^2

Pr = 100*1.64*3.98*(3/(12.566*1000))^2 = 0.000 037 watts, approx, or about 37 microwatts.

Note that this equation is not valid for path lengths less than several free-space wavelengths.

Thanks,

Hi,

"dBi" is the unit of measure for the gain of an antenna relative to the gain of an isotropic radiator. The radiation pattern of an isotropic source is perfectly spherical. An isotropic radiator exists only in theory, but is used as a reference for the gain of real antennas.

The peak gain of a 1/2-wave, center-fed dipole in free space is 2.15 dBi, because due to its directional radiation pattern that gain is 2.15 dB (1.64X) greater than from an isotropic radiator.

The gain of an antenna sometimes is given with respect to that of a 1/2-wave, center-fed dipole in free space. In that case the unit of measure is "dBd." Gain in dBd can be converted to dBi by adding 2.15 dB to the gain expressed in dBd. So an antenna with a gain of 3 dBd has a gain of 5.15 dBi.

Some antenna manufacturers prefer to use dBi when specifying antenna gain because it results in a larger, more impressive number. But for the same antenna input power an antenna with 3 dBd gain in a given direction produces exactly the same radiated field as one with 5.15 dBi gain in that direction.

Convert the published gain for a free-space path in the direction of interest as given in dBi to a multiplier, using 10^(dBi/10).

As examples, a gain of zero dBi (an isotropic source) is a multiplier of 10^(0/10) = 1, and a gain of 2.15 dBi is a multiplier of 10^(2.15/10) = 1.64 (approx).

The gains of both the tx and rx antenna must be calculated for the Friis equation, and used for Gt and Gr, respectively.

Both the path distance R and the wavelength (lambda) must be entered in the same unit of measure.

Pt is the power in watts delivered to the transmit antenna, and Pr is the impedance-matched power in watts available at the terminals of the receive antenna, assuming that the polarization of both antennas is the same.

Doing the math for a 1,000 meter, 100 MHz free-space path with 100 watts applied to a tx antenna with 2.15 dBi gain, and a rx antenna with 6 dBi gain:

Pr = Pt*Gt*Gr*(lambda/(4*pi*R))^2

Pr = 100*1.64*3.98*(3/(12.566*1000))^2 = 0.000 037 watts, approx, or about 37 microwatts.

Note that this equation is not valid for path lengths less than several free-space wavelengths.

Thanks,

Hi, you may refer to the attached file. It is so helpful. To my knowledge, the conversion should be applied to the Effective Isotropically Radiated Power or to the received power, not to the antenna gain. 

Pr(dBm)=Pt(dBm)+Gt(antenna gain of transmitter(dBi))+Gr(antenna gain of receiver(dBi))-free space loss (20*log(4*pi*d/lambda))

then you can converet Pr(dBm) to Watt

Strictly speaking, the only valid answer to your questions is: you cannot. You were asking to convert 6.85 dBi into Watt. This is impossible since dBi is not a unit of power, hence there is no equivalent in Watt.

When you see dBs always think of ratios, dB is a logarithmic ratio of powers. So 10 dB has no meaning in terms of power, it just means "10 times more".

Of course, there are ways to express powers logarithmically, that is, relative to a reference power. This is that dBm and dBW are for: they are telling you how much stronger (how many dB) a given power is relative to a reference power of 1 mW or 1 W, respectively. So 6 dBm = 6 dB more than 1 mW = 4 times 1 mW = 4 mW.

As it has been explained very nicely by Smrity Dwivedi, dBi is a unit that is used in conjunction with antennas, as an answer to the question: how much more power does a directive antenna receive from its main beam direction compared to an antenna that is not directive at all ("isotropic", hence the i). So if you're given that your antenna has a gain of 6.85 dBi it means that it receives (or transmits) 4.8 times more power in its main beam direction than an isotropic antenna would.

If you want to know how much power you receive you need to put it into relation with the incident power on the antenna. Depending on what's your setup there are many ways to do so, a simple one being given by the Friis equation, as Alhareth was pointing out. Note that this implicitly assumes that the antenna is pointed perfectly, i.e., it receives exactly from its main beam direction. Whether or not this is realistic depends on your application.

Antenna gain is a ratio. So, it does not have any units. However, it is represented in dBi to compare with the isotropic radiator. Your antenna gain is 6.85dBi means in absolute value it comes out to be 4.842 (Use 10 log (Gain in abs) = Gain in dBi). Your antenna radiating power is 4.842times than the power at that point of isotropic radiator.  

Thanks all for your valuable answers, I will take a look on the equations and information that shared with me.

However gain is unitless quantity. Based on your requirements, you can use this quantity.