Extracting Out-Of-Plane Dielectric Tensor in Heterogeneous Packaging Core
Extracting out-of-plane permittivity requires guarded parallel-plate or re-entrant cavity tests to isolate vertical flux fields from in-plane glass weave effects.
Multi-Line TRL
Calibration Precision
A multi-line calibration technique uses multiple transmission lines of varying lengths to calibrate vector network analyzers for high-frequency measurements on printed circuit boards. The multi-line TRL method improves upon the standard through-reflect-line calibration by using redundant line standards to extend the highly accurate frequency range of the calibration and resolve phase ambiguities. This mathematical procedure determines the systematic errors of the measurement setup, which allows engineers to extract the true electrical properties of transmission lines and dielectric materials directly on the board.
It operates as the primary calibration method for high-frequency characterization up to one hundred gigahertz.
Measurement Setup
Designing the calibration standards involves fabricating a short through connection, a high-reflection standard such as an open or short, and at least two transmission lines of different lengths on the same substrate panel. The length differences between these lines are selected so that the phase difference of the propagating waves avoids multiples of one hundred and eighty degrees, which would cause mathematical singularities in the calibration algorithm. By measuring these standards, the network analyzer calculates the propagation constant and the characteristic impedance of the lines, which removes the need to make assumptions about the dielectric properties of the board.
This self-consistent approach compensates for variations in trace width and substrate thickness across different fabrication batches.
Precision Validation
Verifying the results involves measuring a separate verification line that was not used in the initial calibration process and comparing its extracted scattering parameters against theoretical predictions. If the calibration was successful, the insertion loss of the verification line will scale linearly with frequency and the reflection coefficient will remain very low. This validation step is necessary to confirm that cable movements or temperature shifts did not degrade the calibration before measuring the devices under test.