An antenna is an energy conversion device. It converts electrical current to and from electromagnetic radiation. I've been thinking about how antennas work for a while now, and I've been meaning to write down some of those thoughts. This has been driven, in large part, about questions that I had about why you could use a center fed dipole on the fundamental frequency or the third harmonic, but not the second harmonic. It's also been driven by questions that I've read about balanced versus unbalanced antennas and feedlines, and questions like is an off-center fed or end fed dipole a balanced load or an unbalanced load.
The thing is, the works about antenna theory that I've seen aren't particularly accessible to me. I'll keep looking, but I don't hold out much hope. The thing is, I can argue a lot of these things from first principles, and so I'm going to try to do just that. Wish me luck, but be warned: There will be some math.
In order to understand where I'm coming from, I need to make sure that we're on the same page relating to some terms. Electricity comes in two flavors: Direct current (DC) and alternating current (AC). Direct current is an orderly flow of electrons in a single direction. That direct current is driving by something very much like a force called "electromotive force" or emf or voltage. In most circuits, the current is related to the voltage through a characteristic of the circuit called the "resistance" and this relation is called Ohm's Law. The current is proportional to the voltage and the resistance is the constant of proportionality, where the voltage is the resistance times the current.
Alternating current is a different animal. Alternating current is an orderly oscillation of electrons about a point in a cycle. I found the idea that electrons doing work while they move from place to place to be easy to understand, but alternating current had electrons that move back and forth and don't really go anywhere. I couldn't see how that could do anything useful, until I realized that ocean waves can transfer energy to a beach, but the water doesn't leave the ocean. It's the moving energy that's important, the electrons are just a medium that carries the energy. In this case, the amount of current is proportional to the amount the electrons move in each cycle, but they always keep coming back to the same places.
The thing is, AC circuits have the same relation between voltage and current that DC circuits do. There is a constant of proportionality between the voltage and the current, but this time it complicated by the fact that the voltage and the current aren't necessarily in step with each other. If the voltage and current are in step, then the constant of proportionality is a resistance, just like what is seen in a DC circuit. If one leads the other by 90 degrees of the cycle, it is called a reactance. Of course, in the typical case, there will be a phase shift of something other than 90 degrees, and that's made by combining a resistance with a reactance to get an impedance.
The reason the phase shift is important is because of that energy thing I mentioned earlier. The rate of energy transfer in a DC circuit is the voltage times the current. Since they're both constants, that works. In an AC circuit, everything varies continuously, so you have to add up the current times the voltage over all of zillions of points, a process which is known as integration. The thing is, if the current and the voltage change together, at some parts of the cycle you'll have positive voltage and positive current, making positive power, and at some parts of the cycle you'll have negative voltage and negative current, making positive power. Got that?
But with a pure reactance, you get all four combinations of positive and negative voltage and current, and they add up in such a way so as to sum to zero. That means that a purely reactive circuit gives back exactly as much energy as they take in which makes it a device for storing energy for part of a cycle. For a circuit that has an impedance with a nonzero reactance, some of the energy will be stored in each cycle, and some will be consumed.
So, now we have our first result: An antenna that is working properly appears as a resistance. As far as the electrical circuit is concerned, energy goes in and doesn't come back out.
The convention is to write resistance as a real number, and reactance as an imaginary number, which is a real number multiplied by the imaginary square root of -1. It's important to note that reactance comes in two flavors, capacitive reactance, which is considered negative an inductive reactance, which is considered positive.