The Rayleigh-Helmholtz reciprocity theorem states the following:

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”.

Perhaps the most unexpected implication of the reciprocity theorem is that a hacker who is trying to penetrate your wireless network doesnʼt have to be in the parking lot. They can be many miles away using a directional antenna. If they can transmit to you then they can hear your transmissions as well. Remember, of course, that the theorem demands that both stations have the same antenna input power.

To some readers the reciprocity theorem may be new. The implications of antenna reciprocity are far reaching and, if this is the first time youʼve 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 realworld 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!”

Practical Considerations Related to Antenna Reciprocity

One practical application of the reciprocity theorem is in the determination of an antennaʼs reception pattern. Assume that youʼre working with 802.11 client machines having a 100 mW output power and using simple omnidirectional antennae. Youʼre considering implementing some type of directional or other high-gain antenna. Perhaps youʼre thinking of using a panel antenna at the end of a long hallway, thinking that it could be used to communicate to offices on either side of the hallway. Will the panel antenna be able to receive signals from the client machines in the offices? You can answer this question by calculating (or considering) the radiation pattern that would result if you transmitted a 100 mW signal from the panel antenna. Since the power on antenna “A” (the panel) is the same

as that which will be coming from antenna “B” (the client machineʼs NIC), the reciprocity theorem is applicable and, if the client would be able to hear the panel then the panel will be able to hear the client. The power flow is the same in either direction.

When you consider the reciprocity theorem in the context of an 802.11 access point some interesting observations can be made. The two antennae on an 802.11 access point implement antenna diversity. Only one of them is used to transmit at a time and the selection of which one should be used is based on which one previously received the stronger signal. Antenna diversity provides a way to partially compensate for the location of various transmitting sources and the possible types of signal effects that might be introduced by the environment (multi-path reflections, refraction, absorption, dispersion, signal interference, all of which will be discussed). The access point transmits back with the antenna that received the stronger signal.

Thinking about the doughnut-shaped transmission/reception volume that surrounds a dipole radiator, youʼll see that the orientation (up, down, left, part-of-the-way left, etc). makes a tremendous difference for the orientation of the radiation field. With an antenna sticking straight up the doughnut lies parallel to the floor. With the antenna pointing straight out towards the back of the access point

Copyright 2003 - Joseph Bardwell