LRM and LRRM Calibrations with Automatic Determination of Load Inductance

New theoretical analysis of the LRRM calibration technique for vector network analyzers

“…The next step is to compute the actual value of by using (or ). In [10], an expression is given that relates the computed (measured) reflect admittance to its actual value whenever the match standard is improperly defined (expression (1) of [10]) (33) where and are the actual and defined values for the match admittance, respectively. Equation (33) can be interpreted as a change in the calibration reference-impedance, from (defined value) to .…”

“…Based on this theory [14], it is shown that the 'reference-impedance' (to which the LRRM calibration is referred) cannot generally be defined whenever nonideal standards are used. This consideration leads to a general expression 0018-9456/01$10.00 © 2001 IEEE for that, in contrast with (3) of [10], does not assume a reference-impedance. The expression is used to accurately determine , demonstrating accuracy improvements in the calibration.…”

“…Since those requirements are not fulfilled in practice, the LRM calibration accuracy is reduced. The four-standards LRRM (line-reflect-reflect-match) calibration technique was proposed (but not mathematically developed) in [10], as an improvement with respect to LRM. The main advantage of Manuscript received April 11, 1997;revised May 31, 2001.…”

“…The key point in the LRRM technique is an accurate determination of inductance from the computed reflection coefficient, , of a measured reflect standard. In [10] a simple expression to compute from is proposed [expr. (3) of [10]].…”

“…In [10] a simple expression to compute from is proposed [expr. (3) of [10]]. In this expression, it is implicitly assumed that a reference-impedance (to which the calibration is referred) does exist and equals the match impedance.…”