Measurement of Reflection and Transmission Coefficients Using Finite Impulse Response Least-Squares Estimation

A measurement technique to reduce the error of measured frequency-domain reflection and transmission coefficients, in particular, scattering parameters (S-parameters) measured with a vector network analyzer (VNA), and load reflection coefficients measured in wideband active load-pull system, is proposed. The technique models either the incident or reflected wave as the output of a finite impulse response (FIR) filter, and subsequently apply least-squares estimation (LSE) to estimate the reflection or transmission coefficients which minimize the error of said wave. When compared against the existing technique, the proposed technique offers precision improvement to the estimated reflection and transmission coefficients. Faster VNA measurements using up to 15-MHz intermediate frequency (IF) bandwidth are experimentally shown to be significantly improved to give good correspondence with slower measurements using 100-Hz IF bandwidth as reference. Error improvement across the measurement bandwidth of more than 17 dB is experimentally observed. Furthermore, the improvement is applicable to both the frequency regions with higher and lower signal to noise ratios of the reflected waves. On the other hand, applying the proposed technique in a wideband active load-pull system to estimate the load reflection coefficients, results in significant error improvement over the existing technique. The error improvement is also experimentally observed both in the in-band 3-dB bandwidth frequency region of the wideband modulated test signal and the out-of-band intermodulation frequency regions, where error improvement of 36 dB is observed.