| The bang-bang CDR became widely used, however it reveals a lack of theory and mathematical driven analysis of the loop characteristics and parameters, due to having nonlinear phase detector and sampling in the system, which prevents the use of the PLL linear theory in analysis.; The thesis develops a complete set of mathematical equations, inequalities and conditions to explain and characterize both first and second order bang-bang CDR, giving accurate equations for phase step response, frequency step response, sinusoidal operating conditions, and jitter performance as a function of design parameters. A novel analysis describes the stability conditions of the second order loop where the stability factor was defined as a function of the idling order mode, which helps to explain why the loop experiences a wander in the event of a long run pattern of the incoming data stream. The thesis develops novel formulas of both slope overload conditions and signal-to-noise ratio to Gaussian random input jitter as a function of bit-error-rate. |
