Eye-Diagram Estimation Methods for Voltage-and Probability-Dependent PAM-4 Signal on Stacked Through-Silicon Vias (TSVs)

This paper proposes eye-diagram estimation methods for voltage-and probability-dependent pulse amplitude modulation (PAM4) signal on stacked through-silicon vias (TSVs). To satisfy demands on a high-speed and small form factor, the number of TSVs and the data rate on the TSVs have been increased. The number of stacked TSVs is related to the electrical performance due to its electrical length. The non-return-zero (NRZ) has a transition time depending on a data rate, thus the NRZ has high-frequency components for the high-speed channel. The PAM4 has been emerged as an alternative for the NRZ, because the PAM4 has lower bandwidth than that of the NRZ. However, the PAM4 additionally has 9 dB conversion loss for multiple logic states. Therefore, the comparison between the PAM4 and NRZ should be required for the high-speed channel. The proposed estimation method for the PAM4 can obtain the eye-diagram using a single bit response (SBR) of the channel. The proposed methods provides not only the eye-diagram but also a data-dependent jitter (DDJ), random jitter (RJ), and bit-error rate (BER) analysis. For verification, the estimated eye-diagrams and the MATLAB-based eye-diagrams are compared. Because their eye-diagrams are nearly the same, the proposed methods for the PAM4 on the stacked TSVs are validated.