Improving The Reliability of The Multiline TRL Calibration Algorithm

An Impedance Transition Method to Verify the Reference Impedance of Multiline TRL Calibration

“…It should be noted that we have not considered the terms k g and k h in the above equations, because the transition segments are reciprocal devices (i.e., S 12 = S 21 ) and the terms k g and k h are implicitly contained in g 11 and h 11 through the conversion relationship between S-and T-parameters, as stated in (2). Therefore, there is no mathematical benefit in including k g and k h in the derivation.…”

“…The precision of the mTRL calibration comes from the fact that transmission line standards can be manufactured with high accuracy compared to their resistive standards counterparts. Furthermore, the mTRL algorithm presented in [2] improves the original algorithm by eliminating the need to assume a first-order perturbation in the error boxes.…”

Multimode Multiline TRL Calibration of Vector Network Analyzers

“…Thus, if we form a tensor T containing the transmission parameters of k lines of different lengths, but with identical excitation transitions, the CPD obtains the matrices Ẋ, Ẏ and D in equations ( 8) and ( 9), except for a permutation matrix and a scaling factor matrix. Note that the CPD is a tensor decomposition that is unique, save for a permutation and scaling factors, when the sum of the ranks of the factor matrices, defined as the number of linearly independent columns, is greater than or equal to 2F + 2, being F the number of summation elements in (5). In the MMTRL procedure for N non-degenerated modes, matrices Ẋ, Ẏ and D are ranked 2N and the summation elements in (5) is 2N .…”

“…In this case, a higher degree of accuracy in the measurement is achieved by increasing the number of calibration standards (the number of measured lines, which do only differ in length). Recently, some improvements to the calibration procedure have been published based on different concepts [2,5,9,10]. For example, in [2,9,10] a tensor decomposition has been introduced for the implementation of the MTRL.…”

“…For example, in [2,9,10] a tensor decomposition has been introduced for the implementation of the MTRL. And in [5] the MTRL formulation has been posed and solved with exclusively 2D matrix operations. However, if we focus on two situations of undeniable interest, i.e., multimode devices and out-of-band characterization, none of previous measurement procedures are valid.…”