# Understanding the workings of an ultrasonic sensor

I am trying to simulate an ultrasonic sensor using a ray-based approach. For that, my current process can roughly be described as such:

• approximate wavefront using rays that mimic the shape of the sensor's beam form
• subtract angle-dependent SPL loss for each ray
• calculate sound pressure level that gets reflected back to the sensor at each hit point, track Δt the ray needs to get back to the receiver
• subtract angle-dependent transmitter SPL loss
• aggregate SPL at the sensor given tuples of SPL and Δt from each ray (e.g. overlaying different echos arriving at the same time)

My calculated SPL always refers to the reference sound pressure of 20μP.

My problem is as simple as it is impossible for me to understand: I now have SPL values at the receiver ("measured" at 30cm distance from the sensor, as in most datasheets like here). However, I'm not sure how to determine whether the receiver can register an echo or not, which is where the sensitivity comes into play. As far as I understand from here and here, that value from the spec sheet describes how the receiver can translate sound pressure into a voltage.

This is not what I need, I just want to decide whether an echo is registered or not - can I just assume that the sensor can pick up any sound pressure impulse above the reference, i.e. 20μP or an SPL of 0dB? I feel like I am missing something very obvious here, but I cannot seem to be able to figure it out. Any help would be greatly appreciated!

• The echo will, at some point, be fainter than the noise level of your circuit & sensor so you can no longer be reasonably sure it's actually an echo. For other reasons you won't be able to detect something too close. Jun 22, 2020 at 14:49
• Thank you for your reply! Do you happen to know what I could look into to figure out where I could reasonably draw the line? I can't seem to find datasheets of fully integrated ultrasonic sensors (e.g. automotive) that detail how they evaluate their data. Thank you for the hint regarding the minimum distance, I've included that using a user option to set the minimum (and also maximum) distance in the ray tracing program. Jun 22, 2020 at 14:59
• Ray tracing in the same sense as rendering 3D models to 2D images doesn't work with ultrasonics. That's because the transmitter sends a coherent sinewave and the received signal should be summed with right phase angles in every point of the receiving transducer to get the total signal. Microwave radars have the same problem. Radar engineers overcame the complexity by considering the echoes as statistical phenomenas.
– user136077
Jun 22, 2020 at 16:58