Reciprocity normalized matrix representation of quasi-TEM multimode multiports

Abstract

Generalized scattering parameters and the impedance matrix of multimode quasi‐TEM networks are related using a normalization impedance matrix. The corresponding formula appears to be an extension of the usual single‐mode multiports ones. Theoretical and measured parameters are compared for a multimode one‐port and an asymmetrical coupled‐strip four‐port. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 20: 214–218, 1999.

Improved Multimode TRL Calibration Method for Characterization of Homogeneous Differential Discontinuities

“…Becauseˆ 1 ,ˆ 2 , and A 0 are already known, substituting (21) into (17), (18), and (22) only leads to another three known expressions of K 1 K T 2 . Therefore, there exists redundancy in the equation set, which is composed of (17), (18), (21), and (22). Equation (21) alone is sufficient to represent all the information provided by the reciprocity of the reflect standard and transition structures.…”

“…It can be noted that the proposed multimode TRL de-embedding procedure only requires single symmetrical reflect standard. Actually, if another reflect standard with high cross-mode reflection is used, the reciprocity represented by (17) or (18) can also be used to determine G 1 , G 2 . This means the proposed multimode TRL can also be used as a one-step calibration procedure if two reflect standards are used.…”

“…If the coupling is extremely weak and even negligible, the differential lines at each side of the DUT can be considered as uncoupled differential pairs. In that case, several calibration/de-embedding methods, including those based on the single-mode S-parameter theory [13]- [18], can reach the goal of error correction. However, if the coupling cannot be ignored, which usually happens in practical highspeed differential pairs, the techniques [4]- [12] based on the multimode S-parameter theory [1], [4] are more desirable.…”

Design of cascaded three‐conductor coupled line filter

“…Impedance matrix (Z) of each two line asymmetrical coupled line with aperture in the ground plane is calculated using the even-and odd-mode characteristic impedances and phase velocities. The 4 3 4 impedance matrix of the two-conductor coupled line is calculated using (1)(2)(3)(4) Z oe and Z oe are the even-mode impedance and odd mode impedance of the asymmetrical two-conductor coupled line, respectively. The above impedance matrix is reduced to 2 3 2 impedance matrix after applying the terminations (open) and loading (half wavelength short circuited line) at the ports.…”

“…In Ref. [2], normalized impedance matrix is used to solve the coupled line problems. Spectral domain approach, Fourier transforms approach, variational techniques, and integral equation method are some of the other methods for analyzing coupled lines [3][4][5][6].…”