On antenna efficiency

I rarely write on my blog about things related to my professional work. There are just so many other channels where that goes. But I felt it is time to address one particular issue, that still is very poorly understood and you can read a fantastic amount of nonsense on it. And it is about antenna efficiency (I work with designing antennas and test-systems for antennas).

Antenna efficiency is really something very simple. It is a measure of how much of the power that is sent to the antenna that is actually transmitted out in the air (and since a normal antenna (without amplifiers or other fancy stuff integrated) is reciprocal, this also holds for receiving antennas). So a very simple relation can be stated:

 Where Pin is the power sent to the antenna and Pout is the power transmitted by the antenna. e is called the efficiency or total radiation efficiency of the antenna. For small antennas, such as antennas in mobile phones, IoT equipment and WLAN (WiFi) products, this is the most important metric of an antenna. You want as much power sent to the antenna to enter the air, where it has a potential to reach and receiver. e is a number between 0 and 1, 1 being the best and meaning all power sent to the antenna get radiated.

There are many other parameters that can be stated about an antenna, some only related to the electrical properties. The most common one and, which most people are aware of, is the radiation pattern. This is a function, g(theta, phi) over the sphere indicating how large part of the radiation entering the air that is radiated in a certain direction. This is usually the most important property of a large antenna. You make an antenna large so that it can be used to direct the energy in a certain direction, for example towards a geo-stationary satellite.

Now, radiation pattern play an extremely small role in wireless communication between small terminals, such as computers and WLAN router. The reason is very simple: you have no clue in which direction the router is in relation to you WLAN device. So, ignore the radiation pattern.

The radiation pattern can be combined with the efficiency according to

 

to obtain the gain. This metric compensate for a finite efficiency of the antenna and indicate how large part of the energy sent to the antenna that is radiated in a certain direction.

If the antenna is connected to a transmitter (e.g. a WLAN modem) with a certain output power, P, that can also be added to the above formula, resulting in

 

where EIRP is an abbreviation for equivalent isotropic radiated power, a fancy name for how much power is transmitted in a certain direction (theta, phi). Note that P in this equation is the same as Pin in the first equation and thus

EIPR can be of importance for small antennas in some cases. The most well know is that regulators uses EIRP for limiting power out from a device in many situations. This is sensible since it is reasonable to require that a user does not get exposed to radiation intensity above a certain level.

There is one further property that is very common to look at for a small antenna and that is the return loss. This is a measure of how much energy sent to an antenna that enters the antenna. Some of it gets reflected back and is thus not used. For a small antenna it is common that something between 10 and 90% gets reflected back. Of course, 90% reflected back is not a very good antenna, but it is not uncommon. Making good antenna solutions is hard.

The part of the power that is not reflected back enter the antenna where one of two things can happen: It either gets dissipated in the antenna structure or it gets radiated. Of these, we of course want it to be radiated. The two mechanisms of losses can be combined, and then comprise the total radiation efficiency of the antenna, as used before and one can decompose the two loss mechanisms according to

Now comes my critique. As I stated above, the total radiation efficiency is the most important property of a small antenna. the return loss, er, can be great, the antenna can have some radiation pattern you think looks cool and the gain of the antenna can be this or that. But all of this does not matter of your total radiation efficiency is poor. If does a simple search in the internet for papers on new small antennas, they always state the return loss. And very often they state the radiation pattern. But very very rarely they state the total radiation efficiency. Why. Either because they do not understand what they are doing, or they cannot measure it (since it is hard to measure properly, both in a simulation and in a measurement set-up) and thus, cannot report it. Neither of these are good reasons for not reporting it.

Or, you can read on an otherwise very well informed and good webpage on antennas things like:

"Note that there are no TRP specs, so in general you don't want the WIFI antenna to have too high of an efficiency, or the SAR and peak gain values will require a large conducted power backoff"

This is of course total nonsense! You absolutely wants to as high efficiency as possible and back off output power if you are so lucky to have too high output power (TRP is an abbreviation for total radiated power). That will save energy and by that battery live.