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Polarize Me December 14, 2010

Posted by mareserinitatis in electromagnetics, engineering, physics, research, Uncategorized.
Tags: antennas, polarization
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The first time I saw Rush in concert, they were on their Counterparts Tour. My favorite song from that album is “Animate”, which begins with the words, “Polarize Me.”

I think part of the song could be talking about an antenna. (Hey, if Brittany Spears can do semiconductor physics, can’t Rush do electrical engineering???)

Polarize Me

Most people have at least a passing familiarity with polarized light. Polarized light and antenna polarization are working on the same concept here: polarization deals with electromagnetic waves and the way they’re ‘oriented’.

Light and other electromagnetic waves in free space will travel as a transverse electromagnetic (TEM) wave. This means that the electric field will be orthogonal to the direction of propagation, and the magnetic field will be orthogonal to both of them. We can imagine a light (or any other electromagnetic wave) looking like this:

In this image, ‘k’ indicates the direction in which the wave is propagating; in this case, it is traveling from left to right. The infinitely thin electric field (in blue) is shown be be vertical, and the magnetic field (in red) is horizontal. All three are orthogonal and imbue us with that sense of happiness that comes from observing neat and easy rectilinear behavior.

The thing is, the EM wave doesn’t have to operate this way. We could just as easily have the electric field in the horizontal plane and the magnetic field in the vertical plane. Or, if you want to be really crazy, maybe the electric field is sitting at 15° while the magnetic field is at -75°. No matter how much we rotate our wave, as long as our electric field stays within that plane over time (and the magnetic field stays in its plane), then the wave is said to be linearly polarized.

Now what happens if the fields start to rotate over time? We’re going to only look at the electric field. Just remember, however, that the magnetic field is also there and it’s always orthogonal to both the electric field and the direction of propagation.

Anyway, our electric field starts rotating over time, but each time we check it, it has the same strength or magnitude. We can imagine that the edge of the field would trace a circle, if we are looking at the wave along the direction of propagation. This would be a circularly polarized wave. Mathematically, we can take the wave at any point and decompose into parts – a vertical part and a horizontal part.

In this image, you can image that the vector A could be created by adding horizontal vector of two units to a vertical vector of three units.

If it’s traveling in a circle, it’s intuitive to think about our electric field vector as made up of a horizontal vector and vertical vector. As the field makes one complete circle, we can add how much each direction contributes to the overall field. We would see that half the field would be horizontal and half would be vertical.

For the sake of completeness, there other things we can discuss, like elliptically polarized-waves as well as right- and left-handedness, but those are extraneous to the point at hand. We’ll save them for another day.

Sensitize Me

A monopole antenna is basically a straight wire or metal bar that is connected to the ground (or a ground plane). A good example is the antenna on a car. Suffice it to say that because it is the shape of a line, it will create a linearly polarized EM wave. In fact, the electric field polarization will be in the plane created by the direction of propagation and the antenna itself.

Have you ever wondered why antennas stick straight up from cars? It’s because the broadcasting antenna is also vertical:

You see, the broadcasting tower is vertical and creates a vertically polarized wave. If this wave will create a current on the receiving antenna (i.e. the one on your car), it will work best if it is also vertical. It can be at an angle, but then the signal it receives won’t be as strong. And if the antenna is horizontal, then it won’t be able to see the electric field at all, and your radio won’t pick up anything.

Let’s now imagine that the radio tower were able to put out a circularly polarized wave. If our car antenna is still a good old monopole (or whip antenna, as some people like to call them), then it would only pick up the part of the field that is vertically polarized. Half of the signal is in the horizontal polarization, so we wouldn’t catch that part of the signal. Overall, it would look like we had half the signal strength as when our radio tower was vertical. If we want a more sensitive receiving antenna, it helps to make sure it is polarized in the same direction as our transmitting antenna.

Criticize Me

When you’re working with antennas that may have different polarizations, we can talk about the polarization mismatch factor. This is a numerical value we can plug into the Friis Transmission Equation to help us estimate how much power will be transferred from a transmitting antenna to a receiving antenna. There’s a fun vector equation which will give you the quantity, but I’ll skip that and say that it’s quite well known that he polarization mismatch for a linear to circular antenna (or vice versa) is 0.5.

So why did I spend all this time talking about polarization? Because I needed to rant, and I wasn’t sure you’d understand the point without the background.

I finally finished up a lit review I was working on, and one of the last papers I read annoyed me because they stated that when they went from a linearly to a circularly polarized transmitting antenna (they were using a linearly polarized receiving antenna), their received power dropped by half. I found this annoying because it’s bloody obvious to anyone who works in antennas (and hopefully to you, having read my long-winded explanation). It need not be stated in a paper. In fact, it shouldn’t be. It is one of those things you can and should do in the lab to verify that your testing procedure is set up correctly, but it certainly shouldn’t be reported in the results section of a journal article.

Now that I have that off my chest, I’m going to go listen to the rest of Animate.