Stacking voltage-controlled oscillators: Analysis and application

The paper proposes a method to regulate the output frequency and duty cycle (phase) of ring oscillator by emulating a resistive voltage divider using purely digital means. To this end an additional master oscillator that can be clocked by an external frequency is connected in series with a slave one. The behavioral model of this system is a stack of voltage-controlled oscillators, since the inherent frequency of ring oscillator depends on its power supply voltage. The paper derives analytical expressions for the PWM output frequency and duty cycle as two interdependent functions of two control frequencies. The obtained theoretical results agree well with the results of simulations.