Frequency-response-associated delay-dispersion issue in time-delay measuring sensors

We investigated the extent of the measurement error of a time-delay measuring sensor caused by the frequency-response-associated delay-dispersion issue. We considered the possible shapes of the frequency response of stable linear circuits and the possible shapes of a step signal. In general, systems with wider input bandwidth and whose input frequency response has a smaller peak are more accurate. The maximum potential amount of error caused by this issue is related to the 10-90% transition time of the system's input step response. For measurements referenced to the 50% level of the input signals' step size, this will be ~1/3× and closer to 1× the transition time in the case of systems without and with significant ringing, respectively.