A Novel Reformulation of LNN Calibration Algorithm

In this article, the line-network-network (LNN) calibration algorithm is reformulated in a novel and simple way, which introduces three wave ratios as the calibration coefficients instead of the common seven error terms. Meanwhile, by using three forms of T-matrix, pseudo-T-matrix, and normalized T-matrix to represent different networks in the error model, an eigenvalue problem similar to that in thru–reflect–line (TRL) calibration can be concluded after a series of simple matrix operations. Then by solving the eigenvalue problem and utilizing the symmetry property from the standard definitions, three wave ratios can be easily calculated to finish the calibration. Different from the classical LNN, the proposed algorithm considers the physical length of the obstacle (the key component of the standards). In addition, the proposed algorithm is also applicable to the line-reflect-reflect (LRR) calibration without the need to modify the formulas, exhibiting a good generality. Experimental verifications of the reformulated LNN using microstrip-based calibration standards are given.