How to calculate the antenna transmitted power given the gains - Page 1
Forum section: electronics / rf-microwave

author: raff5184
author_rank: Regular Contributor
timestamp: April 02, 2019, 03:26:24 pm
content: Hi all,I'm trying to calculate the transmitted power of an antenna. The setup is the following "chain":(1) USRP radio with SBX daughterboardhttps://www.ettus.com/all-products/SBX/(should have a gain of about 5, but I'm not sure what it means)(2) HMC453QS16 power amplifier, whose 1-dB compression point is30dBm(3) MT-242025, a7 dBiRHCP RFID antennaFreq 915 MHz.I know the gain of this transmitting system, the distance and in which conditions it was measured.Is it possible to calculate the transmitted and/or the received power knowing the gain? And if so, how? I don't have this system (I am reading about it on an article) so I can't perform measurements on it.

author: radiolistener
author_rank: Super Contributor
timestamp: April 02, 2019, 06:19:49 pm
content: The key points here:- SBX 400-4400 transmitter output power: 100 mW- HMC453QS16G power amplifier gain: 15 dB @ 900 MHz- MT-242025 antenna gain: 7 dBiFrom this data you can calculate:- transmitter output power in dBm: 100 mW = 20 dBm- radiated power: 20 dBm + 15 dB = 35 dBm = 3.162 WThis is a power that your system transmits into environment. Of course some power will be lost in the cable and other things, we don't take into account these losses for this calculation. If you know your cable loss and antenna efficiency you can consider it by substract cable loss from 35 dBm and consider antenna efficiency for the result.But your antenna has a gain, it means that it transmits more power in the main direction lobe due to reduce the radiation power in other directions. If you place receiver in the main direction lobe of the transmitter antenna it will be equivalent to higher power transmitter for isotropic radiator. The difference is represented by antenna gain. So, if you place your receiver in the main lobe of your transmitter antenna, the receiver will see your transmitter as the following power:35 dBm + 7 dBi = 42 dBm = 15.848 WTo make it clearer, your transmitter still radiates 3.162 W. But your antenna radiates this power not to all directions around antenna. It directs and concentrates this power in the main direction lobe. The same like torch reflects all power of lamp into single direction with help of reflector. For receiver placed at the main lobe of transmitter antenna it will be equals to isotropic radiator (which radiates power to all directions equally, like lamp with no reflectors) with power 15.848 W.In order to be precise, you're also needs to consider signal loss in the coax cable between amplifier and antenna and antenna SWR. High loss or high SWR may reduce radiation power dramatically. For 915 MHz each meter of coax cable is significant and cable quality also is very important.Regarding to the loss on the distance, you can calculate it with formulaloss = k + 20 * log10(F * L),wherek = 20 * log10( 4 * pi / c ) + 20 * log10(1'000'000 Hz * 1'000 m) = 32.44778322 (for MHz and km units)F - frequency in MHzL - distance in kmYou should substract that loss. For example, you have 1 km and 915 MHz, so the distance loss will be:loss = k + 20 * log10(1 * 915) = 91.68 dBIf you're using the same antenna with gain 7 dBi for transmitter and receiver and both properly directed to each other and both mateched with 50 Ohm impedance (SWR=1), then total loss from transmitter antenna connector to receiver antenna connector will be:7 dBi - 91.68 dB + 7 dBi = -77.68 dBIf you put 35 dBm from your power amplifier to transmitter antenna, then you will get 35 dBm - 77.68 dB = -42.68 dBm from receiver antenna connector.We consider that there is free space between both antennas, so there is no loss on third party items placed on the wave path. In the real world something can block the path between the antennas, for example trees or tree leaves it will leads to additional loss and also should be considered.

author: hendorog
author_rank: Super Contributor
timestamp: April 02, 2019, 06:40:29 pm
content: As mentioned in the OP, the power amp will be in compression at 35dBmTypical output P1dB is 32dBm according to the datasheet and it saturates at 32.5dBm.There will be a few dB of attenuation between the Tx and the power amp to avoid that as you said its an existing product.Taking that into consideration the calcs are a bit too high.The receiver will see free path loss too. You can use a calculator to estimate that - here is one google found which takes the Rx/Tx antenna gain into account:https://www.everythingrf.com/rf-calculators/free-space-path-loss-calculator

author: radiolistener
author_rank: Super Contributor
timestamp: April 02, 2019, 06:52:48 pm
content: Quote from: hendorog on April 02, 2019, 06:40:29 pmyeah, it also should be considered

author: raff5184
author_rank: Regular Contributor
timestamp: April 02, 2019, 07:45:36 pm
content: Great and very clear thank you. So basically there are no losses in the coax because it's a very short link (few cm).Last question, how can I calculate the power intensity (W/m^2) at the rx location in a small area around the axis of the main lobe? In other words, if the direction of the main lobe is from A to B, what is the power intensity in the proximity of B (say a maximum divergence of 2cm from B)?I say in the proximity of B so that the power can be considered constant in every point of that 2x2 cm^2 area

author: radiolistener
author_rank: Super Contributor
timestamp: April 02, 2019, 08:11:21 pm
content: For very short distance, which falls in the Near Field region of antenna such calculation won't works.You can split region around antenna into 3 zones:- Reactive Near Field region (there is no direction lobe)- Radiation Near Field region (there is some dependency on direction, but direction lobes still not formed finally)- Far Field regionYou can apply such calculation for Far Field region only. For Near Field region it will be much more complex.For very short antennas Reactive Near Field region is more complex. For a very short dipole, or equivalent radiator, the outer boundary is commonly taken to exist at a distance:R1min = λ / (2 * pi)According to docs, MT-242025 antenna has dimensions 190 x 190 x 30mm, so it's D = 0.19 m.For 915 MHz λ = 0.3276 m.Given that we have:R1 = 0.62 * sqrt(0.19^3 / 0.3276) = 0.0897 m = 8.97 cmR2 = 2 * 0.19^2 / 0.3276 = 0.2204 m = 22.04 cmSo, you're need to perform measurement and calculations for distance between both antennas not less than 22 cm. It's better to use at least 1 meter or more in order to reduce Near Field influence. Because in the Near Field region it works in different way.

author: raff5184
author_rank: Regular Contributor
timestamp: April 02, 2019, 08:20:52 pm
content: oh I think my question wasn't clear. Sure I meant in the far field region, say in the green spot (an area of about 2x2 cm^2)

author: radiolistener
author_rank: Super Contributor
timestamp: April 02, 2019, 08:47:03 pm
content: If you're mean power flux density, you can calculate it for Far Field region with the following formula:S = P * Ga / (40 * pi * D^2)whereS = power flux density in mW/cm^2P = power in WattsGa = antenna gain (times for power, not decibels, because power in Watts)D = distance in metersIn your case, for 35 dBm power from amplifier, 7 dBi gain and 1 km distance it will be:35 dBm = 3.162 7 dBi = 5 times for powerS = 3.162 * 5 / (40 * pi * 1000^2) = 0.000000126 mW/cm^2 = 126 [pW/cm^2]where 3.162 * 5 = 15.8 W is equivalent power for isotropic radiator.See previous example 35 dBm + 7 dBi = 42 dBm = 15.848 W.For 1 meter distance it will be 15.848 W / (40 * pi * 1^2) = 0.126 [mW/cm^2], etc.

author: raff5184
author_rank: Regular Contributor
timestamp: April 02, 2019, 09:14:18 pm
content: Amazing, thank you!

author: radiolistener
author_rank: Super Contributor
timestamp: April 02, 2019, 09:27:28 pm
content: Note, this formula is approximation for Far Field region.If you will use it for Near Field region it will get error, because lobe is changing in this region and near field influence.

author: radiolistener
author_rank: Super Contributor
timestamp: April 02, 2019, 10:31:03 pm
content: if you're thinking about FCC limits, as I know there is limit F/1500 mW/cm^2 for the frequency band 300...1500 MHz (needs to check it).For 915 MHz it will be 915/1500 = 0.61 mW/cm^2.So, you can calculate safe distance for 35 dBm = 3.162 W power amplifier output and 7 dBi antenna gain:sqrt( 15.848 / (40 * pi * 0.61) ) = 0.46 m = 46 cm

author: raff5184
author_rank: Regular Contributor
timestamp: April 03, 2019, 12:04:28 am
content: Yes I was also trying to calculate the FDA exposure limit that is set to 10mW/cm2.Thanks

author: radiolistener
author_rank: Super Contributor
timestamp: April 03, 2019, 01:33:51 am
content: 3.1 W RF output with 7 dBi gain antenna will not exceed 10 mW/cm2 limit in the far field region (distance > 22 cm for your case).But this limit will be easy exceeded in the near field region. For the near field, there is need for measurements.You can estimate field strength in the near field of antenna with electromagnetic field simulation software.The most simple simulator is MMANA-GAL-PRO:http://gal-ana.de/promm/Help/It allows to estimate field strength in the near field region (both E and H components).