5.2 Wilkinson Impedance Transformer Splitter/Combiner

The theory and design of splitter/combiners with mixed-mode s-parameter analysis is introduced using the well-known Wilkinson impedance transformer [1]. A description of Wilkinson splitter/combiner design is built from the transmission-line-impedance-transformer pair shown in Figure 5.1. These two transmission lines are one-fourth-wavelength long and have a 70.7 ? impedance and are designed to convert the independent 50 ? output ports ( Z _{2 L} and Z _{3 L}) into two 100 ? ports at the input.

Figure 5.1: Transmission-line-impedance transformer pair designed to convert a 50 ? load to a port impedance of 100 ?.

These two 100 ? input ports are connected in parallel resulting in a composite port 1 impedance with a 50 ?-input impedance. This new circuit is shown in Figure 5.2 with common port 1 impedance, Z ₁ of 50 ? when ports 2 and 3 are terminated in 50 ?.

Figure 5.2: Transmission-line-impedance transformer splitter/combiner circuit with a port 1 impedance of 50 ?.

This is a very logical design process until the design process is reversed with a 50 ? termination, Z _{1 L} placed at the common port 1. Looking into the two output-port impedances, Z ₂ and Z ₃ and 150 ? is seen as shown in Figure 5.3. This output is not matched to 50 ? with 150 ? output impedances. The splitter-design process becomes a difficult...