Matching circuits using LC elements are widely applied to high-frequency circuits such as power amplifier (PA) and low-noise amplifier (LNA). For determining matching condition of multi-stage matching circuits, this paper shows that any multi-stage LC-Ladder matching circuit with resistive termination can be decomposed to the extended L-type matching circuits with resistive termination containing negative elements where the analytical solution exists. The matching conditions of each extended L-type matching circuit are obtained easily from the termination resistances and the design frequency. By synthesizing these simple analysis solutions, it is possible to systematically determine the solution even in a large number of stages (high order) matching circuits.

This paper proposes a closed-form eye-diagram model for on-chip distortionless transmission lines with intentionally inserted shunt conductance. We derive expressions of eye-opening both in voltage and time, by assuming a piece-wise linear waveform model. The model is experimentally verified with various length, shunt conductance and resistive termination. We also apply the proposed model to design space exploration, and demonstrate that the proposed model helps estimate the optimal shunt conductance and resistive termination according to required signaling length and throughput.