A pulse frequency modulation interpretation of VCOs enabling VCO-ADC architectures with extended noise shaping Articles uri icon

publication date

  • February 2018

start page

  • 444

end page

  • 457


  • 2


  • 65

International Standard Serial Number (ISSN)

  • 1549-8328

Electronic International Standard Serial Number (EISSN)

  • 1558-0806


  • In this paper, we propose to study voltage controlled oscillators (VCOs) based on the equivalence with pulse frequency modulators (PFMs). This approach is applied to the analysis of VCO-based analog-to-digital converters (VCO-ADCs) and deviates significantly from the conventional interpretation, where VCO-ADCs have been described as the first-order Delta Sigma modulators. A first advantage of our approach is that it unveils systematic error components not described by the equivalence with a conventional Delta Sigma modulator. A second advantage is that, by a proper selection of the pulses generated by the PFM, we can theoretically construct an open loop VCO-ADC with an arbitrary noise shaping order. Unfortunately, with the exception of the first-order noise shaping case, the required pulse waveforms cannot easily be implemented on the circuit level. However, we describe circuit techniques to achieve a good approximation of the required pulse waveforms, which can easily be implemented by practical circuits. Finally, our approach enables a straightforward description of multistage Delta Sigma modulator architectures, which is an alternative and practically feasible way to realize a VCO-ADC with extended noise shaping.


  • Electronics
  • Telecommunications


  • delta sigma modulation; data conversion; voltage controlled oscillators; pulse frequency modulation; time encoding