Linearity Improvement in Vernier Delay Chain Based Time Difference Amplifiers for Fluorescence Spectroscopy

Time difference amplifiers (TDAs) are critical for fluorescence spectroscopy, requiring high linearity to amplify picosecond-scale time differences. This work presents a vernier delay chain-based TDA with a differential architecture, achieving an application targeted gain of $2.25 \text{pS} / \text{pS}$ across a wide $10 \text{ps}-1 \text{ns}$ input range. Fabricated in $0.13 \mu \mathrm{m}$ CMOS, the TDA demonstrates a low 3.78 % RMS gain error and robust $\pm 8 \%$ gain variation across PVT corners, with only 4 mW power consumption. By using discrete-time delay selection via multiplexers, it eliminates analog tuning, enhancing PVT stability and layout simplicity. Validated through simulation and post-silicon measurements, this TDA offers high linearity for high-precision fluorescence spectroscopy, with potential for closed-loop gain stabilization. Linearity was validated via simulation down to 10 ps; measurements were limited by ESD constraints.