Generalized and Simplified Analysis of Two-Port N -Path LPTV Delay-Lines

This paper presents a generalized and simplified theoretical framework for the analysis of a variety of two-port linear, periodically time-variant (LPTV) true-time-delay (TTD) lines. The analysis is done almost entirely in the time domain using impulse response. The two-port analysis is split into two different phases of operation, each modeled as an LTI operation; one in the sampled domain and the other in the continuous-time domain. In the first phase (step 1), the approach leverages adjoint-network analysis to find the impulse response (and by extension, the transfer function) between the input and the samples on the N-path capacitors. This simplifies the analysis, while establishing an LTI relationship between the input and the samples. In the second phase of the analysis the continuous-time voltage through the output port is evaluated. Recognizing that the samples on the N-path capacitors act as the input for the continuous-time output through the output port, this analysis (step 2) is shown to reduce to another LTI operation. Unlike conventional kernel-based methods, the framework can readily handle N-path two-port architectures while incorporating the effect of non-idealities, like non-zero on-resistance of the switches, and non-zero capacitors at the two ports without introducing additional analytical complexity. An extension of the methodology is also shown to accurately analyze the frequency response if there is an overlap between the clocks connecting the ports and also to evaluate the input impedance of the two-port delay-line accurately. The analytical expressions derived through this framework is shown to have excellent agreement with circuit-level simulations.