# How to find the output power of antenna including distance?

I have a PCB and antenna (1) attached to it at the output. Now I would like to measure the output power of the antenna (1) using antenna (2) which is at a distance of D.

I have the readings of the received power from antenna 2, distance, gain, antenna factor, and the frequency.

Can anyone explain how to calculate the output power at the antenna 1 using above mentioned parameters?

• Look up "Friis Transmission Equation": en.wikipedia.org/wiki/Friis_transmission_equation Dec 8, 2021 at 15:41
• In that equation I do not know the gain of the antenna 1. I am using a wire as monopole antenna of length lambda/4 for antenna 1. How can I find the gain of this antenna?
– Sai
Dec 8, 2021 at 15:44
• How can I find the gain of this antenna? Read a book about antennas to learn how to calculate it. Dec 8, 2021 at 15:50
• This answer should provide some assitance. Dec 8, 2021 at 15:54
• Do you want the total output power from the antenna, in all directions, or just in one direction? Dec 8, 2021 at 17:56

I hate to be the Cassandra here, but what you're trying to do is fraught with sources of error.

1. To start off, you need to know accurately the performance of your receive antenna, gain as function of receive angle, in both azimuth and elevation, at your frequency of interest. You might be able to simplify this part of the problem by constraining the transmit and receive antennas to be in the same plane, in which case you would only need to know the receive antenna pattern along a single azimuth cut through the antenna pattern.

Calibrated antennas that provide this type of information are available commercially (such as standard gain horns) but they are not cheap.

1. Next, you need to make sure that you are only measuring the direct path from the transmit to the receive antenna. Any reflections from objects alongside of or behind your transmit and receive antennas will corrupt you measurements. This where RF absorber comes in. This is judiciously placed around (but not in front of) your transmit and receive antennas to absorb and attenuate any RF energy that's not in the direct path between the antennas.

2. You need to make sure there are no other sources of RF energy that could corrupt your measurement. Even a cell phone could create an error.

3. Along with #3, you need to make sure that your receiver properly filters and/or bandwidth limits the incoming frequency so that just the energy from the transmit antenna is being processed.

More as I think of them...

Here's en example illustrating the first problem. These two cases are going to measure significantly different amounts of power at Ant 2. They can be normalized, but only if you know the radiation pattern of both antennas.

This cartoon shows how reflections (multipath) can impact the measured power level.

• I have all the characteristics of the receiving antenna 2. I am using TRILOG Broadband Antenna as antenna 2. But I am performing the test in the open air and there will be lot of reflections as you mentioned.
– Sai
Dec 9, 2021 at 8:03

The Friis transmission path-loss equation in decibels is this: -

$$\color{red}{\boxed{\text{Path loss (dB) = 32.45 + } 20log_{10}(f) + 20log_{10}(d)}}$$

Where $$\f\$$ is in MHz and $$\d\$$ is in kilometres.

So, if you take readings at various distances (2 might be enough) you should be able to factor out all the unknowns and get your answer. Clearly you should know the frequency in MHz so that part of the equation turns into a constant.

If you can gather this data but can't get an answer, report back.

• With this formula, I found that the path loss in my case is 20.76 dB. I received the output power from antenna 2 of -90dBm. I am operating at 868 MHz and distance between both is 3m. Now, how could I find the output power from antenna 1?
– Sai
Dec 8, 2021 at 16:08
• Try at a distance of 6m. The path loss formula will tell you the extra loss and the difference in power values should then imply the originating power from the transmit antenna. Dec 8, 2021 at 16:22
• Now I kept distance of 6m as you said. Here I found that the path loss of 26.78 dB. I received the output power from antenna 2 of -101dBm. So, my transmit output power is -101+90 i.e., -11 dBm or -90+101 i.e., 11dBm?
– Sai
Dec 8, 2021 at 16:40
• Well, it's a good start because you have confirmed that you can effectively apply the Friis path-loss formula on this setup but, the output power is not -11 dBm or +11 dBm. What you need to do next is look at the data sheet for the transmit antenna and understand a little more about the radiation pattern in the direction you have in your setup. It should reveal an attenuation figure at a certain distance. That distance is usually/sometimes specified at $1 \lambda$. Then work out what the path loss is at $1 \lambda$. Dec 8, 2021 at 17:21
• You also need to factor in the antenna gains at both ends; that's simply taking into account in the PL formula that the -90 dBm reading you got at 3 metres is improved by a few dB due to antenna gains. Dec 8, 2021 at 17:23