General Description

It is important to match components like an antenna, Surface Acoustic Wave (SAW) filter, Low Noise Amplifier (LNA), switches and other components as all of these components have a specific impedance. This impedance is mainly driven by the internal architecture and parasitic inside of the circuit. According to the maximum power transfer (Jacobi’s law) theorem, the maximum power is reached if the load resistance is equal to the resistance of the source (see the following figure).
Figure 1. Equivalent Circuit Diagram for Maximum Power Transfer

RS – Resistance of the source

RL – Resistance of the load

Note: It is useful to have a standardized value of impedance for every component. It is very common that most of the test equipment, including some RF components, have an input impedance of 50Ω.
This standardized value minimizes the loss in RF signal transfer, but not every component can be designed with a 50Ω impedance, and not every component has a real impedance. Inductive and capacitive influences result in a complex impedance consisting of a real and an imaginary part. In the case of a complex impedance, the maximum power transfer theorem must be extended so that the impedance of the load is equal to the complex conjugate impedance of the source. If this is true, the imaginary influences are eliminated and the real impedance remains. The following figure shows the equivalent circuit diagram for complex conjugate matching.
Figure 2. Equivalent Circuit Diagram for Complex Conjugate Matching

ZS – Source impedance

ZL* – Load impedance (complex conjugate source impedance)