Abstract
This paper investigates a unified theory to derive vector network analyzer calibration algorithms based on the T-matrix representation, by which means the line-reflect-match (LRM), line-reflect-match-match (LRMM), and the line-reflect-reflect-match (LRRM) calibrations are formulated. The proposed calibration theory is more general than other versions of LRM, LRMM, and LRRM in that an arbitrary known two-port device can be used as the line standard L, rather than a perfect thru or transmission line. Experimental verifications of the proposed theory using on-wafer calibrations from 0.5 GHz to 110 GHz are given.
Highlights
The vector network analyzer (VNA) is the workhorse in most microwave laboratories, and its calibration technique has been well-developed through several decades [1]
VNA calibrations apply switch corrections independently andand ignore (or(or pre-correct) inthe theerror errormodel model shown in corrections independently ignore pre-correct)crosstalk, crosstalk, resulting resulting in shown corrections independently and ignore crosstalk, resulting in the error model shown in Figure 1 [24,25]
This paper develops a theory for reformulations of LRM/LRMM/LRRM calibrations
Summary
The vector network analyzer (VNA) is the workhorse in most microwave laboratories, and its calibration technique has been well-developed through several decades [1]. This work further develops the previous theory, and the developed theory applies to LRM/LRMM/LRRM calibrations This theory constructs the T-matrices of error boxes by using single-port measurements, and newly introduces three wave ratios to express the error boxes in the algorithm. E.g., LRRM [12], allow the reduction of calibration unknowns to three by utilizing a two-port standard measurement, but a perfect thru or a known transmission line is often required for the convenience of analytical derivation [21,22] In this theory, a unified mathematical framework is developed for LRM/LRMM/LRRM calibrations, and the line standard L can be an arbitrary known two-port standard.
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