Observations on the resolution and tones in First Order Noise Shaping Time-to-Digital Converters

In this paper we report some observations on the resolution and tones of First Order Noise Shaping Local-Oscillator Based Time-to-Digital Converters (LO TDCs). We describe the architecture and governing equations of the LO TDC. We introduce equations to predict the resolution of the system “LO TDC plus moving average filter” and the frequency and amplitude of the largest amplitude tone in the spectrum of the TDC output when the input is constant. We describe briefly the block diagrams of a Matlab model of the LO TDC and its implementation on an FPGA. Finally, we compare analytical predictions of the amplitude and frequency of the largest tone in the spectrum with simulations and experimental results. The prediction of the powers and positions of the tones in the TDC output spectrum is fundamental for the design of the system in which the TDC has to be used.