I'm trying to model the ultrasonic sensor for a simulation and I need to somehow express in what angles and distances the object will be detected by the sensor.

What does sensitivity mean? It is set in dB values. I thought it is the amount of attenuation at which the sensor can still detect the object, but that would mean the lower number, the better, and the picture below shows that for the chosen frequency 40 kHz the sensitivity is around -75 dB, while other frequencies go to -95 dB. So what does this property mean and how should I understand the graph?

enter image description here

Another thing I can't figure out is the radiation graph (or directivity graph, if they are the same. They look the same, so I have no idea.) Examples of those graphs are shown below.

enter image description here enter image description here

What does the line represent? I'm thinking it's some kind of contour connecting the distances in all the angles which has something same. Maybe the attenuation or the Sound Pressure Level. But those graphs never state any specific value related to the line.

From what I read I think that the Sound Pressure Level (SPL) in R0 distance is measured at angle 0 (directly ahead of the sensor) at 30 cm distance and I can compute the SPL in any other distance R at 0 angle using the formula

\$SPL(R) = SPL(R0) -20 \log(R/R0) - \alpha R \$

where \$\alpha\$ is the attenuation. Now this SPL is in dB, so I thought I could directly compare it to the sensitivity and get the result. If \$SPL > \text{sensitivity}\$ then the sensor can detect the object. But that's probably totally wrong.

So how can I compute that?


The example datasheet here


So to sum the information up, I have learned, that the sensor datasheet should provide:

  • SPL (Sound Pressure Level, usually measured at \$30\, cm\$ at the angle 0°, where reference is \$ 20\, \mu Pa\$ which is the lowest sound pressure a human might hear)
  • Sensitivity (at \$30\, cm\$ at the angle 0°, where reference is either \$1\, V\$ or \$10\, V\$)
  • Directivity graph of the radiation
  • Directivity graph of the sensitivity

There is an example of those information taken from the datasheet provided by @Andyakka.

The SPL and Sensitivity:

enter image description here

And the graphs:

enter image description here

The relation between \$SPL\$ in \$dB\$ and pressure \$p\$ in \$Pa\$ is \$ SPL = 20\log(\frac{p}{p_{ref}})\$, where \$p_{ref} = 20\, \mu Pa\$

The \$SPL(r_0,\theta_0)\$ at \$30\, cm\$ right in front of the sensor (\$r_0=0.30\, m\$, \$ \theta_0=0°\$) is \$120\, dB\$, that means \$ p(r_0,\theta_0)= p_{ref}\cdot10^{\frac{SPL(r_0,\theta_0)}{20}}=20\,Pa\$

If I want the pressure at angle \$0°\$ in any other distance \$r\$, I compute it with following formula:

\$ SPL(r,0°) = SPL(r_0,0°)-20\log(\frac{r}{r_0})-\alpha r \$,

where \$\alpha\$ is the attenuation of the wave and can be approximated by formula

  • for frequencies \$f<50\,kHz\$: \$\alpha = 0.01f\$
  • for frequencies \$50\,kHz<f<300\,kHz\$: \$\alpha = 0.022f-0.6\$

If I want to know the \$SPL\$ at \$30\,cm\$ in any other angle, I look at the graph. I can see the \$SPL\$ decreases by about

  • \$4\,dB\$ at angle of \$30°\,\$
  • \$6\,dB\$ at angle of \$45°\,\$
  • \$11\,dB\$ at angle of \$60°\,\$

Since the \$SPL\$ is already in \$dB\$, I can simply subtract the value from the \$SPL(r_0,\theta_0)\$ and I get

  • \$SPL(r_0,30°)\,= 116\, dB\$ : \$p(r_0,30°)=12.6\, Pa\$
  • \$SPL(r_0,45°)\,= 114\, dB\$ : \$p(r_0,45°)=10\, Pa\$
  • \$SPL(r_0,60°)\,= 109\, dB\$ : \$p(r_0,60°)=5.6\, Pa\$

Then I can use the same formula as shown above to compute the SPL at any other distance.

\$ SPL(r,\theta) = SPL(r_0,\theta)-20\log(\frac{r}{r_0})-\alpha r \$,

Now I would need to compute the wave that gets reflected from an object at certain place depending on the object's size and surface. If I knew at which angle and with which pressure a wave gets back to the sensor, I could use the sensitivity graph to compute the voltage produced by the sensor.

The relationship between sensitivity value \$s\$ in \$dBV\$ and voltage value \$u\$ in \$V\$ is \$ s=20\log(\frac{u}{u_{ref}}) \$, where the \$u_{ref}\$ is in this case \$10 V\$.

So the voltage \$u\$ related to the sensitivity of \$-63\, dB\$ is \$u = u_{ref}\cdot 10^{\frac{s}{20}}=10\cdot 10^{-\frac{63}{20}} = 7.1\, mV\$

So if the sound wave travels into the sensor from angle \$0°\$ and at distance \$30\, cm\$ has a pressure of \$20\,Pa\$, the sensor produces a voltage of \$7.1\, mV\$.

If I use simple linear relationship, that would imply that for sound wave which has at the distance of \$30\, cm\$ pressure \$1\, Pa\$ at angle \$0°\$ would induce the sensor output of \$355\,\mu V\$

For the sensitivity in other directions I can read from graph, that the sensitivity decreases by about

  • \$5\,dB\$ at angle of \$30°\,\$
  • \$9\,dB\$ at angle of \$45°\,\$
  • \$14\,dB\$ at angle of \$60°\,\$

Than means

  • \$ s(r_0,30°)=-68\, dB\$ : \$u(r_0,30°)=4\, mV\$ for wave of pressure \$116\, dB\$
  • \$ s(r_0,45°)=-72\, dB\$ : \$u(r_0,45°)=2.5\, mV\$ for wave of pressure \$114\, dB\$
  • \$ s(r_0,60°)=-77\, dB\$ : \$u(r_0,60°)=1.4\, mV\$ for wave of pressure \$109\, dB\$

If I know the pressure of the wave at any other distance, I use the formula shown earlier to compute respective SPL at 30 cm and from there I compute the actual sensor output.

\$ SPL(r_0,\theta) = SPL(r,\theta)-20\log(\frac{r_0}{r})-\alpha r_0 \$,

Please somebody confirm or provide explanation of the error. Thank you!

  • 1
    \$\begingroup\$ You should keep in mind that this would vary A LOT depending on what object, the shape, direction and so forth you would try to detect and it will vary also vary significantly with temperature, humidity and air pressure. You might end up with totally different results than your calculations. It probably also vary a lot from part to part and there are no tolerances given on the datasheet. This is probably a case where a testing approach would yield better results than calculations. \$\endgroup\$
    – Damien
    Dec 12, 2018 at 13:48

2 Answers 2


What does sensitivity mean?

It tells you how much signal voltage is produced for a given sound pressure level at a certain distance. The dB value is usually quoted as: -

$$dBV/ Pa$$

So, an SPL of 94 dB is one pascal (Pa) of pressure and a figure of -75 dB would imply an output voltage of 0.18 mV RMS. But I've seen some that have a 10 volt reference and that would make -75 dB into 1.8 mV such as in this data sheet.

So how can I compute that?

More than likely, in the data sheet it will be revealed in the typical operating conditions table (as per the DS I linked on page 4).

  • \$\begingroup\$ "It tells you how much signal voltage is produced for a given sound pressure level at a certain distance" -- is it also dependent on the angle? Are the numbers in the datasheet only valid for the direction right ahead of the sensor? \$\endgroup\$
    – user828950
    Dec 6, 2018 at 15:32
  • \$\begingroup\$ Yes it's dependent on the angle as your 2nd picture shows. As for the DS, it's a bit hit and miss. For instance, they do define the sensitivity as -75dB/V/μbar but they make a mistake in saying "dB/V" when it should be dBV. This tells me that the supplier isn't very careful. Personally that would stop me buying from them. I have to have most of the boxes ticked and that error is plain stupidity on their part. \$\endgroup\$
    – Andy aka
    Dec 6, 2018 at 15:35
  • \$\begingroup\$ Can you please show me the formula you use to compute the voltage at different SPL? I can't figure it out from the description. \$\endgroup\$
    – user828950
    Dec 6, 2018 at 16:14
  • \$\begingroup\$ I think I understand how you got to 1.8 mV. If reference, i.e. 0 dB, is set to 10 V, then -75 dB from that is \$\frac{10}{10^{75/20}} = 1.8 \,mV\$. Then how is SPL related to that? It seems to me now that SPL is the pressure that sensor makes and sensitivity is some measure of sensors ability to detect ultrasound, but I miss the link between them. \$\endgroup\$
    – user828950
    Dec 7, 2018 at 9:54
  • \$\begingroup\$ If the sensitivity figure implies 1.8 mV RMS for a pressure of 1 Pa RMS then 1 Pa RMS equates to 94 dB SPL (by definition). \$\endgroup\$
    – Andy aka
    Dec 7, 2018 at 10:27

As to the directivity graph, it shows the relative sensitivity with respect to the angle. I.e., at 0° you have full sensitivity (0dB) as specified in the other graphs. At 60° the sensitivity is reduced by about 25dB.

So whatever sensitivity you get at your operating conditions from the other graphs, e.g. if you use 38kHz instead of 40kHz, you must (additionally) derate it by the given amount depending on angle.

  • \$\begingroup\$ So if I look at the directivity graph in my question, it means at 30 cm at angle 0° the SPL is 97 dB. At 30 cm at angle 30° it is about 89 dB and at 30 cm at angle 60° it is about 74 dB? It is still at 30 cm? And from there I can compute SPL at different distances in the respective direction. \$\endgroup\$
    – user828950
    Dec 6, 2018 at 16:20
  • \$\begingroup\$ So the directivity in sensitivity is different graph than the directivity in radiation? The two graphs I provided tells different things? It seems that the directivity in sensitivity relates to sensor ability to sense ultrasound and directivity in radiation relates to sensor ability to transmit sound of certain strength. Is that right? \$\endgroup\$
    – user828950
    Dec 7, 2018 at 11:57

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