Calculation of maximal applicable gain for the generalized and the direct method for extreme impedances measurement

A mathematical approach for determining the maximal applicable gain of amplifiers, that are used in two recently introduced methods for measurement of extreme input impedances using a common vector network analyzer (VNA) - the generalized method and the direct method - is presented. These two measurement methods exhibit outstanding measurement sensitivity for extreme impedance values - impedances significantly higher or lower than the 50 Ω reference impedance of common measurement systems. The measurement sensitivity is better when gain of the used amplifiers is higher. However, the gain is limited by nonlinearity of the amplifiers and the receivers of the vector network analyzer. Therefore, the gain calculation is derived to make possible to fully exploit the capabilities of the measurement methods without loosing accuracy due to nonlinear effects. An example of calculation for one experimental setup is also presented.