Paper A -58dBc-Worst-Fractional-Spur and -234dB-FoM, 5.5GHz Ring-DCO-Based Fractional-N DPLL Using a Time-Invariant-Probability Modulator, Generating a Nonlinearity-Robust DTC-Control Word

ISSCC 2020 17.3

From Jaehyouk Choi’s Paper

The concept of this work is from Micheal Peter Kennedy’s Paper that showed that if the expected value of an arbitrary analog or digial signal \(X\), \(E[X](t)\), is constant over time, the power spectral density (PSD) of \(X\) shows no spurious tones. This leads to the idea that, if we can modulate \(D_{DCW}\) such that its probability density function (PDF) is time-invatiant, \(E[\tau_{DTC}](t)\) becomes constant over time even after passing a nonlinear \(f_{DTC}(D_{DCW})\), so the PSD of \(\tau_{DTC}\) has no fractoinal spurs.

For a random process \(Y\), \(E[Y](t)\) is constant over time \(\implies\) PSD of \(Y\) shows no spurs.