AD2S1210 Equation 5 (LOS angular latency) missing square root?

Thanks @skowalik , but isn't that the no-fault case? My understanding is that Equation (5) applies when one channel is lost.

Thanks, rehfi . I think you're onto something, although I can't see where the arctan term comes from when I try to derive it myself.

Let's assume the cosine channel fails and remains at zero, while the sine channel continues operating normally. In that case, the cosine channel is always below the threshold, whereas the sine channel only falls below the threshold at arcsin(Threshold/Amplitude).

If LOS detection is triggered only when both channels are simultaneously below the threshold, then the resulting blind-zone width becomes:

2 × arccos(LOS Threshold / Amplitude)

This derivation seems to support Equation (5) being correct, although for a different reason than I originally assumed. My initial assumption was that LOS was based on the monitor signal, whereas this result follows from individual SIN/COS threshold comparisons combined with an AND condition. However, with this approach and no faults (both cosine and sine channels nominal), LOS would repeatedly be triggered at e.g.: 45, 135, degrees if the LOS threshold would be set lower than A x sin(45) = A x 1/sqrt(2), which seems odd.

To rephrase my question: Is LOS detected by comparing the monitor signal's values against the threshold, or by comparing the SIN and COS channels individually using an AND condition? Could you confirm which method is actually implemented?



Regards,
David

Thanks @skowalik , but isn't that the no-fault case? My understanding is that Equation (5) applies when one channel is lost.

Thanks, rehfi . I think you're onto something, although I can't see where the arctan term comes from when I try to derive it myself.

Let's assume the cosine channel fails and remains at zero, while the sine channel continues operating normally. In that case, the cosine channel is always below the threshold, whereas the sine channel only falls below the threshold at arcsin(Threshold/Amplitude).

If LOS detection is triggered only when both channels are simultaneously below the threshold, then the resulting blind-zone width becomes:

2 × arccos(LOS Threshold / Amplitude)

This derivation seems to support Equation (5) being correct, although for a different reason than I originally assumed. My initial assumption was that LOS was based on the monitor signal, whereas this result follows from individual SIN/COS threshold comparisons combined with an AND condition. However, with this approach and no faults (both cosine and sine channels nominal), LOS would repeatedly be triggered at e.g.: 45, 135, degrees if the LOS threshold would be set lower than A x sin(45) = A x 1/sqrt(2), which seems odd.

To rephrase my question: Is LOS detected by comparing the monitor signal's values against the threshold, or by comparing the SIN and COS channels individually using an AND condition? Could you confirm which method is actually implemented?



Regards,
David