This paper analyzes transient behaviors of the polarization-mode-dispersion (PMD) vector for the Foschini and Poole's birefringence vector model. We find an asymptotic solution of the corresponding Fokker-Planck equation representing the solution as a superposition of angular components characterized by the Legendre polynomials. The distribution tail for the PMD vector magnitude evolves slowly to the Maxwellian owing to the residual couplings between adjacent angular components. Of particular interest, the distribution tail for the PMD vector magnitude lies well below the Maxwellian fit during the transient.

A high-throughput on-chip monitoring circuit with a digital output is proposed for the variations of the NMOS and PMOS threshold voltages. A voltage-controlled delay line (VCDL) and a time-to-digital converter (TDC) are used to convert a small difference in analog voltage into a large difference in time delay. This circuit was applied to the transistors of W = 10 µm and L = 0.18 µm in a 1616 array matrix fabricated with a 0.18-µm process. The measurement of the threshold voltage shows that the maximum peak-to-peak intra-chip variation of NMOS and PMOS transistors are about 31.7 mV and 32.2 mV, respectively, for the temperature range from -25 to 75. The voltage resolutions of NMOS and PMOS transistors are measured to be 1.10 mV/bit and 3.53 mV/bit at 25, respectively. The 8-bit digital code is generated for the threshold voltage of a transistor in every 125 ns, which corresponds to the 8-MHz throughput.