Unmatched Accuracy: How Mismatches Can Improve the Accuracy of Swept Frequency Measurements

Abstract

The goal of this article is to shed light on the mystery surrounding the effective source match of three-resistor power dividers and two-resistor power splitters. The distinction between dividers and splitters is often found in the literature but is ambiguous. In common use and described in many microwave textbooks, the three-resistor divider is the component of choice for standard applications. The three-resistor divider is matched at all three ports and can be used both for splitting incoming power into two parts and for combining two signals into one. In contrast, the two-resistor splitter is matched only at the input port but shows a reflection coefficient of 0.25 in the reverse direction at the output ports when terminated in matched loads. The only information commonly found in the literature regarding this type of splitter is that it should be used in leveling loops and reference measurements. As a justification for this advice, the effective source match Γ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> is put forward, which is supposed to be zero for the splitter but gives -0.5 for the divider. This behavior is explained in this article. The calculation of Γ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> is a good example of how to use a signal flow graph and apply Mason's rule. Getting to the bottom of this puzzle leads to digging out some very old publications. The zero reflection coefficient is not always the most clever solution.