A simple variable-length ring oscillator (VLRO) in which a selectable number of inverters is shunted using bypass transistors is introduced. A range of frequencies can be selected by activating or deactivating the bypass circuitry. LTspice simulations demonstrating the performance are presented. BSIM4 transistor models using 50 nm gate lengths are used in the design of the inverters and bypass transistors. The fundamental frequency generated by each VLRO is determined via Fourier transforms of

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... he output square wave. The data show that the VLRO can effectively generate a wide range of frequencies in a large number of steps based on the selection of bypass transistors that are activated. The prototypical circuit presented here uses 45 CMOS inverters to generate a range of frequencies between about 0.56 GHz and 1.4 GHz. Four different VLROs that demonstrate the ability to synthesize frequencies based on external inputs are presented. Based on the chosen VLRO design, anywhere from 6 to 16 unique frequencies can be selected over the frequency range.