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

conductance (Gm) and the reciprocal of the resistance (1/R) if the amplitude ofoscillation is not too large. If the amplitude of oscillation is larger, the excess noisefactor will be even larger.gdoGmVinFig. 29 gdo for different negative conductancesSince the oscillation amplitude only depends on the tail current of the negative Gm celland the parallel equivalent resistance, by designing a Gm cell with the smallest peakGm will give the best phase noise performance. The Gm should be always a bit largerthan 1/R within the oscillation range. This can be done by using the transistors with asmall W/L ratio to implement the negative Gm cell. However, since the negative Gm isjust a bit larger than the 1/R. When the loss of the LC tanks is larger due to incorrectmodeling of the inductor or varactor, the oscillator cannot oscillate. For example, asshown in Fig. 30, for an oscillator with optimal W/L transistors, if the loss is double,then four times of the original current is needed to compensate the loss. It is because thepeak tranconductance of the transistor is proportional to the square root of the current.As a result, at least four times of the original current is required for the doublecompensation and provide an unexpected double amplitude. However, if the designednegative conductance has a larger peak value, only double of current are need to43