Electrical impedance is an important parameter used to describe individual electrical circuit components or a circuit as a whole. Impedance is a complex number, in which the real part is represented by resistance and the imaginary part is represented by reactance. Once the impedance is determined, one can calculate other parameters such as resistance, inductance, capacitance, scattering coefficient, and figure of merit; draw an equivalent circuit of the measured circuit and predict its behavior over the desired frequency band. Several fundamental methods have been developed to measure impedance. Such methods are based on the use of bridges (with or without auto-balancing), resonators, precision current and voltage meters, and network analyzers. The vector network analyzer (VNA) has recently become a powerful tool for analyzing impedance in a broad band, which partially covers the GHz region. One- and two-port circuits for S-parameter measurements allow the user to determine the impedance from milliohms to tens of kilohms using known relationships between the values. The sources of error in such measurements are the analyzer itself and the DUT fixture. In this article, we will describe only those limitations associated with the analyzer, if appropriate de-embedding techniques can minimize the influence of the fixture and thus help to achieve the required measurement stability.
Present-day VNAs perform high-precision S-parameter measurements of one- and multi-port devices. This is achieved using algorithms of VNA precision calibration [1]. Verification methods determining maximum errors in magnitude and phase measurements for transmission and reflection coefficients are available. In VNA uncertainty analysis, apart from maximum error calculation, a covariance matrix-based method [2, 3] involving root-mean-square error calculation is widely used. Knowing the probability distribution law of the error, the root-mean-square and maximum values of the error can be related by a coefficient.
Let us consider the impedance and error calculation methods based on the results of S-parameter measurements performed by a vector network analyzer. The method of linearization is the basis for the mathematical tool of the indirect measurement error calculation. All of calculations herein are carried out using the specifications of the precision S5048 Vector Network Analyzer from Copper Mountain Technologies.
