A method generating a time-varying threshold to keep the time-over-threshold linear with nuclear pulse amplitudes

Due to the non-linear relationship between the time-over-threshold (TOT) and nuclear pulse amplitudes, the pulse amplitude digitization via traditional TOT scheme could not be expected to have a high measurement performance. To obtain the linear relationship, one can either modify the falling edge of the signal to be measured, or compare the signal with a time-varying threshold. In our previous work, we have demonstrated this time-varying threshold is exist and could be generated to a given detector. In this paper, we propose a more generally applicable analog method to produce the time-varying threshold, so that the time-over-dynamic-threshold (TODT) time is theoretically linear with the amplitude of signals. We also build a practical circuit with discrete components to prove the proposal and the test results show that the linearity of the conversion between the peak amplitude and the TODT is about 99.92%, which means the TODT method could gain high measuring performance by the time measurement. The biggest advantage of the TODT digitizing method is its high integration, which is strongly demanded by today's nuclear imaging detectors.