Traveling Waves and Power Waves

M icrowave equivalent-circuit theory is like a grand old building: elegant, carefully crafted, passed from generation to generation, and rooted in history. Traveling waves, the measureable electromagnetic field solutions of Maxwell’s equations in a transmission line, form the foundation of the theory. You must descend into the basement to see them; not many people do so. It is in this “basement” that I have had the privilege of working on the foundations of the microwave circuit theory with Roger Marks, Bradley Alpert, and others. Together, we explored the underpinnings of the theory and worked toward building a better understanding of microwave equivalent-circuit theory and how it can be applied to the lossy printed transmission lines ubiquitous in modern microwave electronics. The first floor of this grand old structure houses the retail establishments. Clean, neat, and welcoming, here you find the equivalent-circuit voltages and currents of the theory. These voltages and currents are hot items; a steady stream of clients happily snap them up. They mimic low-frequency voltages and currents in lossless transmission lines so well that most clients are not able to distinguish the real article from the microwave equivalent. On the second floor of the building, you find the commodities exchange and business offices populated by the pseudowaves. The pseudowaves can also be referred to as “power-normalized and impedancetransformed scattering waves.” They are all about commerce. Pseudowaves do the buying, selling, and converting, making sure that the equivalent-circuit voltages and currents get into the hands of customers who need them. Pseudowaves mimic traveling waves in a lossless transmission line. Atop the building, there is a 1960s-style addition that raises the ire of the Historical Society, but is seen as a sign of progress by the young architects of the town. The power waves live here. But we get ahead of ourselves. To understand power waves, we have to understand the microwave circuit theory that lies underneath. So let us take a short visitor’s tour of this edifice. If you opt for a more in-depth tour later, [1]–[3] outline conventional microwave circuit theory. I suggest that you then look through [4] and [5] to find out more about how the theory can address lossy printed transmission Dylan Williams