TABLE OF CONTENTS Microwave circuit theory is a powerful set of tools that allows us to treat microwave devices as circuit elements. Implicitly, we have been using microwave theory throughout this book, in particular our treatment of distributed systems. In this chapter, though, we establish the concepts of network theory on a firm electromagnetics foundation. This leads to a powerful and general set of tools for evaluating the properties of N-ports. In particular, we shall develop the concept of the scattering matrix, or S parameters, and relate it to the more familiar concept of network impedance and admittance matrices. The properties of three-and four-port devices, in particular lossless reciprocal devices, will be studied in depth.
To define microwave circuits, we must first understand where circuit theory comes from. Crudely speaking, circuit theory is an approximation to Maxwell s equations valid when structure dimensions are small relative to the wavelength (at the highest frequency of interest). Alternatively, circuit theory is valid when the speed of light is infinite c ? ?.
For example, at f = 60 Hz, we have
If we arbitrarily require that the dimension be a factor of a thousand smaller than the wavelength, we have
Now let s consider f = 1 GHz. This corresponds to the popular cellular bands. Now ? = c/ f = 30 cm, so using the same requirement we have
This is a lot more restrictive! We see that this is strictly valid for relatively small structures...
