| dc.description.abstract | Frequency responses (S-parameters) obtained through simulations, measurements, and
various algorithmic applications must be verified for causality before use. Violating causality
implies that the frequency response does not adhere to the physical properties of the real world,
leading to incorrect outcomes in applications related to signal integrity. However, there is
limited research on how to accurately determine causality. Moreover, if we successfully identify
a causality breach in a frequency response, how should it be corrected to satisfy causality, and
what constitutes the best correction? These are questions worth exploring.
This study first establishes a method for assessing causality, choosing the dispersion
relation (Hilbert transform) as the primary method among various evaluation techniques. We
address truncation errors through dispersion relation with subtractions and estimate delay times.
By shifting delay times, we adjust the response to a position where causality can be correctly
assessed. Through these methods, we can precisely determine the causality of frequency
responses and identify the violated bands. For measured data, we can remeasure the violated
bands. However, simulating frequency responses often consumes considerable time. Re
simulation would be time-consuming, leading many to choose to enhance causality directly
through algorithms.
In dealing with frequency responses that violate causality, a common approach is to use
macromodeling to reconstruct the frequency response. However, macromodeling does not
always succeed in accurately creating the model. This study, through the results of causality
assessment and focusing on the violated bands, aims to correct these to achieve a response that meets causality assessment criteria. This method theoretically achieves the minimal
modification of the frequency response by only correcting the violated bands. However,
practical tests do not guarantee the minimal modification of the frequency response, and the
efficiency of enhancing causality depends on the stringency of the causality assessment.
Establishing the stringency of the assessment and the effectiveness of causality enhancement
are directions for further research in the future. | en_US |