1.2 A Practical Measurement Focus
The techniques used for component measurements in the microware world change dramatically depending upon the attributes of the components; thus, the first step in describing the optimum measurement methods is understanding the expected behavior of the DUT. In describing the attributes and measurements of microwave components it is tempting to go back to first principles and derive all the underlying mathematics for each component and measurement described, but such an endeavor would require several volumes to complete. One could literally write a book on the all the attributes of almost any single component, so for this book the focus will be on only those final results useful for describing practical attributes of the components to be characterized, with quotes and references of many results without the underlying derivation.
There have been examples of books on microwave measurements that focus on the metrology kind of measurements (Collier and Skinner 2007) made in national laboratories such as the National Institute for Standards and Technology (NIST, USA) or the National Physical Laboratory (NPL, UK), but the methods used there don't transfer well or at all to the commercial market. For the most part, the focus of this book will be on practical measurement examples of components found in commercial and aerospace/defense industries. The measurements focus will be commercial characterization rather than the kinds of metrology found in standards labs.
Also, while there has been a great deal written about components in general or ideal terms, as well as much academic analysis of these idealized components, in practice these components contain significant parasitic effects that cause their behavior to differ dramatically from that described in many textbooks. Unfortunately, these effects are often not well understood, or difficult to consider in an analytic sense, and so are revealed only during an actual measurement of a physical devices. In this chapter, the idealized analysis of many components is described, but the descriptions are extended to some of the real‐world detriments that cause these components' behavior to vary from the expected analytical response.
1.3 Definition of Microwave Parameters
In this section, many of the relevant parameters used in microwave components are derived from the fundamental measurements of voltage and current on the ports. For simplicity, the derivations will focus on measurements made under the conditions of termination in real valued impedances, with the goal of providing mathematical derivations that are straightforward to follow and readily applicable to practical cases.
In microwave measurements, the fundamental parameter of measurement is power. One of the key goals of microwave circuit design is to optimize the power transfer from one circuit to another such as from an amplifier to an antenna. In the microwave world, power is almost always referred to as either an incident power or a reflected power, in the context of power traveling along a transmission structure. The concept of traveling waves is of fundamental importance to understanding microwave measurements, and to engineers who haven't had a course on transmission lines and traveling waves, and even some who have, the concept of power flow and traveling waves can be confusing.
1.3.1 S‐Parameter Primer
S‐parameters have been developed in the context of microwave measurements but have a clear relationship to voltages and currents that are the common reference for most electrical engineers. This section will develop the definition of traveling waves and from that the definition of S‐parameters, in a way that is both rigorous and ideally intuitive; the development will be incremental, rather than just quoting results, in hopes of engendering an intuitive understanding.
This signal traveling along a transmission line is known as a traveling wave (Marks and Williams 1992) and has a forward component and a reverse component. Figure 1.1 shows the schematic of a two‐wire transmission structure with a source and a load.
Figure 1.1 Voltage source and two‐wire system.
If the voltage from the source is sinusoidal, it is represented by the phasor notation
(1.1)
The voltage and current at the load are
(1.2)
The voltage along the line is defined as V(z), and the current at each point is I(z). The impedance of the transmission line provides for a relationship between the voltage and the current. At the reference point, the total voltage is V(0) and is equal to V1; the total current is I(0). The power delivered to the load can be described as
(1.3)
where PF is called the forward power, and PR is called the reverse power. To put this in terms of the voltage and current of Figure 1.1, the total voltage at the port can be defined as the sum of the forward voltage wave traveling into the port and the reverse voltage wave emerging from the port.
The forward voltage wave represents a power traveling toward the load, or transferring from the source to the load, and the reflected voltage wave represents power traveling toward the source. To be formal, for a sinusoidal voltage source, the voltage as a function of time is
(1.5)
From this it is clear that
(1.6)
The
Considering the source impedance ZS and the line or port impedance Z0, and simplifying a little by making ZS = Z0 and considering the case where Z0 is pure‐real, one can relate the forward and reverse voltage to an equivalent power wave. If one looks at the reference point of Figure 1.1 and one had the possibility to insert a current probe as well as had a voltage probe, one could monitor the voltage and current.
The source voltage must equal the sum of the voltage at port 1 and the voltage drop of the current flowing through the source impedance.
(1.7)
