There is a basic principle of antennae that is so unexpected (to the uninitiated student) that some people refuse to believe it's true the first time they hear it. The principle is called the Reciprocity Theorem. Its consequences are that, if we are using the same input and output gain, then regardless of differences in our antenna gain, if one I can hear you, you can hear me. This month, we'll explore this concept and its implications.
Consider the case where an AP has a 12 dBi omni antenna attached and a client has a 2 dBi omni antenna on a PCMCIA card. Both the AP and the client are using 15 dBm of transmit power. It might not surprise you that the AP's high-gain antenna can push a signal a long way out to the client, but you might guess that the client's low-gain antenna couldn't get a signal back to the AP. You'd be wrong. Antenna reciprocity basically means that the exact same qualities that make an antenna good at transmitting a signal also make it good at receiving a signal. To put it another way, the Rayleigh-Helmholtz reciprocity theorem states:
If an electromagnetic force of some particular magnitude is applied to the terminals of antenna "A" and the received current is measured at some other antenna "B" then an equal current (in both amplitude and phase) will be obtained at the terminals of antenna "A" if the same electromagnetic force is applied to the terminals of antenna "B".
As an analogy for an RF antenna, imagine a paddle sticking up out of the smooth surface of a lake. Another paddle is sticking up at the opposite end of the lake. One paddle begins to oscillate back and forth, creating waves that push on the other paddle, causing it to move. In our analogy, the paddles are antennas and the waves are RF waves. To carry the analogy further, imagine that one paddle is much bigger than the other--it represents our high-gain antenna. When the big paddle oscillates, it makes much bigger waves, causing the smaller antenna to move more even though it's got a smaller surface area. When the little paddle oscillates, on the other hand, the big paddle's increased surface area causes it to move more as well! The analogy fails somewhat because, in reality the increased mass of the big paddle would give it enough inertia that it wouldn't really move more, but for the sake of the analogy, the antennas are massless.
Antenna reciprocity arises from a property of physics equations called "time-symmetry". Time symmetry means that it doesn't matter whether time runs forwards or backwards, the physics equations should work out the same. Time symmetry is one of the touchstones of new physics theories. Any theory that violates time symmetry is called into serious question. To understand the significance of time symmetry, consider a pool table with a white ball near one end and a black ball in the center. The white pool ball is accelerated by the force of impact with the cue stick and travels towards the center of the pool table. In the center, the white ball strikes the black ball in a straight, center-to-center impact. The inertia of the white ball is transferred to the black ball and it is now accelerated away from the white ball in a straight line, leaving the white ball stationary at the point of impact. If you were to make a movie of the two balls striking and then played the movie backwards, it would show exactly the same thing except now it would be the black ball that starred in the opening scene of the movie. If the mass, velocity, and other characteristics of the Amazing Pool Ball Adventure movie were represented through mathematical equations, the equations would not be time dependent. Time could run forward or backward and the results would be identical.
To some readers, the reciprocity theorem may be new. The implications of antenna reciprocity are far reaching and, if this is the first time you've encountered the concept, the implications may be too hard to accept without proof. In fact, not only is reciprocity demonstrable in the lab and in real-world installations, but the physicists of the world can provide mathematical proof that the theorem holds true. If the antennae and the space between them are replaced with a network of linear, passive, bilateral impedances, then the current through the network can be calculated in accordance with standard practices in electronics theory. Whether on paper or in practice, given the same input power on both ends, "If you can hear me, then I can hear you!"
Next month, we'll discuss some of the real-world implications of antenna reciprocity
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