MPhil thesis of Lo Chi Wa - Department of Electronic & Computer ...

Phase mismatchTypical designThis proposeddesignTimeFig. 80 Phase error with time of coupled LC oscillators without common source connection and withconnectionDesign considerationsIn addition to the LC oscillator, the size of the four coupling transistors and their biasneed to be designed. The four transistors form a 4-stage-ring-oscillator-like frame forthe two LC oscillators to be put inside as shown in Fig. 81. The frame tries to maintainthe quadrature-phase relationship between the two LC oscillators, while the twoimperfectly matched LC oscillators try to oscillate at different frequencies and break thequadrature-phase relationship. At the same time, the LC oscillators maintain the purityof the frequency while the ring oscillator gives a poor phase noise. Thus, it is a tradeoffbetween the quadrature-phase maintenance and the phase-noise performance. The ratioof transistor sizes and biases of the coupling transistors (the ring oscillator) to thenegative feedback transistors in LC oscillator determines whether the whole oscillator iscloser to being either a ring oscillator with poor phase noise but good phase matching ora LC oscillator with poor phase matching but good phase noise. The tradeoff should bemade based on the mismatches of the LC tanks, the quadrature phase, and phase noise84