Analytical Determinant of the Noise Parameter Extraction Matrix and Its Applications

We derive an analytical expression of the determinant of the 4 × 4 noise parameter extraction matrix based on a slight modification of the matrix in the works of Hu and Weinreh [2004]. We specialize the derivation to a very useful and practicable case in which one of the impedance points is the center of the Smith chart. The resulting expression is simple and provides very useful guidance for impedance selection. We illustrate this with an example of a wideband noise parameter extraction in the low-frequency radio astronomy band of 50 to 350 MHz.