Energy Fundamentals of Radio

Chapter 8The Least You Need to Know About Antennas

As with pretty much all of the other chapters in this book, our ambitions here are big. We seek to equip the reader with a minimal, yet powerful, basis for understanding antennas.

Antennas are the physical structures that launch our modulated electromagnetic waves into space at the output of the transmitter. Other antennas then gather those modulated waves for subsequent decoding in the receiver. The stock in trade of E&M theory up to this point—the perfect sphere, the infinitely long cylinder, the point charge, and, of course, the infinite plane—these abstractions abandon us here. We are stuck instead with finite structures that lack the symmetry that so often simplifies Maxwell’s equations. We must make do.

It turns out that the Hertzian dipole, combined with superposition, will get us a long way. Let’s get into it.

8.1 The Friis Equation

We’re going to kick off our antenna study by examining something of a “mystery” in the telecommunications field. It is not a mystery in the ordinary sense of the word: almost everyone knows the final answer, and there is no question that that final answer is correct. But figuring out the why of things proves to be an odyssey, or at least it did for the author.

Our mystery concerns the famous Friis equation,¹ which governs the received signal power in a wireless link. We show the setup in Figure 8.1. The Friis equation answers the following question. For a given transmit power $P_{\mathrm{t}}$, what ...