Minimizing the start-up energy of a 3-stage inverter crystal oscillator

Crystal oscillators are commonly used components in electronic circuits to generate a certain frequency. In order to start-up a crystal oscillator, a negative resistance is needed. In classical methods often a single inverter is used to start-up the oscillator. However, the negative resistance of this single inverter stage implementation is limited, which increases the start-up time and therefore the start-up energy. In order to remove this limit on the negative resistance, a three-stage inverter implementation with capacitive loads can be used. This circuit has several design freedoms, which all have a certain effect on the total start-up energy. In this research an analysis is presented in which the influence of the different design parameters on the start-up energy is investigated. From this analysis it followed that for increasing values of the transconductance of each inverter stage, the start-up energy increases rapidly, so the increase in gain does not compensate the increase in energy. Furthermore it was found that the negative resistance can theoretically become infinitely big for certain combinations of parameter values. However, it is also demonstrated that when the negative resistance increases, the effect of parameter variations also increases. This increasing sensitivity to parameter variations can cause the negative resistance to become positive, which means that the crystal oscillator will not operate anymore. Therefore a safety margin can be defined when determining the value of the negative resistance. Furthermore the start-up energy that can be achieved with the single stage inverter implementation is determined and compared with the minimum start-up energy that is achieved with the three stage inverter implementation. From this comparison it followed that the three stage inverter has a start-up energy that is several orders of magnitude lower than the start-up energy of the single stage inverter. The calculations performed during the analysis are tested with different simulations. With these simulations it is verified that the energy consumption indeed decreases for decreasing values of the transconductance. Furthermore it followed from the simulations that due to the small transconductance the final amplitude of the oscillation is limited. However, in order to increase the amplitude with a certain factor, the start-up energy increases with a factor that is considerably higher. Therefore the amplitude of the oscillation should be kept as low as possible.