The Antenna Tradeoff Triangle

Dusty sign seen on the wall in Ye Olde Machine Shop:

You can have it:

    Fast
    Accurate
    Cheap

Pick any two.

Every professional pursuit has its tradeoffs which must be managed.  In fact, I believe that it is the principal function of the engineer to manage tradeoffs.  We want airplanes to be strong, but light and affordable.  We want our favorite restaurant to be inexpensive, tasty and prompt.  We want our politicians to be honest, responsive and effective (OK... it's just theoretical). These competing desires are what we call the Tradeoff Triangle.  Sometimes the number of parameters we need to balance exceeds three, but for the purposes of our discussion today, the number shall be three... no more, no less.  Three shall be the number of thine tradeoffs, and the number of the tradeoffs shall be three. Four shalt thou not consider, neither ponder thou two, excepting that thou then proceed to three. Five is right out.

But, I digress.

Let's explore what the job of an antenna is, and where its tradeoffs can be found and thence managed.  And we are going to assume that antennas are reciprocal.  That means they can make radiation from RF current (transmitting), and they can make RF current from radiation (receiving).  In any wireless device, there is a receiver section, a transmitter section or both (transceiver).  These functional blocks are designed by a clever and talented RF guy, and generally interface to the antenna via a transmission line of a certain characteristic impedance; the most familiar values for this impedance are 50- and 75-ohms.  (The reason for the existance of these two values is a good subject for a future blog entry.  Anyone know the history of these choices?)

Usually, I hate it when someone tells me the punchline before I hear the joke.  Sorry, but here it is: Your antenna can be wideband, small or efficient.  BANDWIDTH, SIZE, EFFICIENCY.  Pick any two.  It is a sure sign of Antenna Snake Oil when you see tiny, wideband antennas boasting ultra-high efficiency.  Run the other way.  OK, let's take a closer look...

Antennas operate over limited bands of frequencies.  Sometimes these bands are smaller than we wish they were.  A useful way to think about bandwidths is called "fractional bandwidth" (FBW); for our purposes we'll define fractional bandwidth as the high frequency divided by the low frequency.

For example, modern cell phones generally require antennas that operate from 806 to 915 MHz (FBW=1.14 or 14%) AND 1710 to 1990 MHz (FBW=1.17 or 17%).  This covers all the GSM bands as well as the PCS bands.  Another familiar band is the 2.4 GHz ISM band which is where WiFi lives; this band is 2.4 to 2.5 GHz (FBW=1.04 or 4%).  Yet another example is the 900 MHz ISM band which is often used for wireless phones and other household and office devices; this band is 902 to 928 MHz (FBW=1.03 or 3%).  And finally, we are all familiar with GPS which needs about 10 MHz of bandwidth centered around 1575 MHz (FBW=1.006 or less than 1%).

So, antennas for each of these applications need to operate over the entirety of these bands.  This property, which is the first of our three tradeoffs is loosely called BANDWIDTH.  In the four examples above, note that the fractional bandwidth is representative of how "hard" it is to meet this requirement in light of our (soon to be illuminated) other tradeoffs.  GPS seems easy, and "Quad Band GSM" seems hard.  And so they are.  

Now, using the term "bandwidth" without any further qualification is Engineering Blasphemy (see also my rants about the use of "dB" without a reference).  The bandwidth of an antenna is completely dependent upon what is relevant to the application.  For cellphone applications, it may be the "efficiency bandwidth" or that bandwidth over which the total radiated power (TRP) or the total isotropic sensitivity (TIS) is north of a required value.  For GPS we may be bandwidth-limited by the axial ratio, or the quality of the circular polarization (RHCP in the case of GPS).

Frequently, the bandwidth of concern is the impedance bandwidth, which is the bandwidth over which the antenna's impedance remains within a certain "distance" (on the Smith Chart) of the ideal impedance.  Often this is expressed as Return Loss (10 dB is the usual minimum value), or VSWR (Voltage Standing Wave Ratio) where 2:1 is the usual limit.  If someone uses the term "antenna bandwidth" without explicity saying which bandwidth they are referring to, it is probably the impedance bandwith.  And thereafter they shall be scolded.

The second tradeoff in our triangle is SIZE.  There's different ways to think about  size.  You care about physical size when you are trying to stuff ten pounds of stuff in a five pound bag: you want your consumer product to be as small as possible and the industrial designer has graciously given you a volume which would not host most DNA molecules.  The antenna designer is thinking in terms of wavelengths.  As the antenna volume starts becoming a smaller and smaller fraction of a wavelength, the impedance bandwidth starts shrinking, and the ability to remain efficient with real-world materials starts disappearing.  

In December 1948, Lan Jen Chu published the paper "Physical Limitations of Omni-Directional Antennas", in which he derived a theoretical formula of the bandwidth of an electrically-small antenna.  In the interest of circumnavigating a soporific vortex, the conclusion is thus: the smaller the antenna, the narrower the bandwidth.  So there.

EFFICIENCY is the measure of how much of your RF power is going to be radiated, and how much is going to be turned into heat.  Assuming your goal is not de-icing, heat is an undesireable byproduct.  With real-world materials, especially as we shrink antennas, this becomes a significant concern.  A side-effect of shrinking the antenna is causing the antenna's RF currents to become large enough to make the radiation happen.  These high currents make the material losses which were previously ignorable a very real concern.  I have designed electrically-small loop antennas which have a radiation resistance (the good "resistance") measured in milliohms.  Suddenly the fact that the conductor is copper as opposed to aluminum becomes really important.  The dielectric materials used in trimmer and fixed capacitors for resonating such antennas become critical.

While it is pretty clear that losses in conductors and dielectrics are undesireable from an efficiency standpoint, there lurks in the shadows a side effect as enticing as it is detrimental.  These efficiency-robbing losses make the impedance bandwidth appear larger.  In fact, the higher the losses the wider the impedance bandwidth until the limit where ALL the energy is dissipated in losses and the bandwidth seems "infinite".  The ultimate example is a 50-ohm terminator: a perfect match over a huge bandwidth... and zero radiation.  The Dummy-Load Antenna.  The lesson is clear: When presented with an antenna with unexpectedly large bandwidth for its size, ask about the efficiency.  Oftentimes, this line of questioning is met with a stunned silence at best, or a complete change of topic at worst.  There is a tiny fraction of antenna companies operating today whose business plans depend upon your failing to inquire about efficiency.  I'll say it again: About the Efficiency -  Ask!

The product designer, antenna designer, industrial designer and marketing professional together must all cooperatively grapple with the antenna tradeoff triangle: BANDWIDTH, SIZE, EFFICIENCY.

Like it or not... Pick two.