Unifying interpretation of reflection coefficient and smith chart definitions

This study develops a unifying theory that defines a single transformation from the impedance Z to the reflection coefficient Γ plane independently of the impedance normalisation in use; and the real or complex nature of the characteristic impedance Z₀. The study starts off from the Kurokawa´s definition of reflection coefficient to discuss the required steps to map Z into Γ and highlights the differences that exist between Kurokawa´s and the standard Γ definition. As a logical consequence of the previous discussion, a new definition of reflection coefficient is proposed and validated: the apparent differences stemming from either the standard or Kurokawa´s definition of reflection coefficient Γ are easily interpreted as particular cases of the proposed transformation. In the process, the study´s unifying definition of reflection coefficient allows and facilitates one consistent interpretation of the Smith chart among the possible Γ definitions, including Kurokawa´s. Experimental data supporting the study´s conclusions are also presented.