Measurement of Extreme Impedances with the S Parameters

High frequency measurement of extreme impedances, such as the Equivalent-Series-Resistance (ESR) of an ultra high-Q capacitor, can be performed with specific and costly instrumentation whose principle is generally based upon a coaxial resonant line or a resonant cavity [1]. A cost-effective solution for measuring impedances at high frequencies is the classical One-Port reflection technique that can be performed with a Vector Network Analyzer (VNA). In [2], only this technique was considered, and the analysis was limited to a relative error of 10%; nevertheless, this work showed that the reflection technique is unsuited for measuring extreme impedances. In [3], all of the impedance measurement techniques that can be performed with a VNA are presented and compared. This analysis confirmed the limitations of the reflection technique and showed the abilities of the transmission technique for measuring extreme impedances. Unfortunately, these comparisons were based on absolute errors of the measured impedance (ΔZ) that are not significant for an engineer who needs to select the best method. Moreover, in [2], [3], the analyses are not extended to the negative resistances, and the resistance's sign inversion error is not considered.