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I have a question about the formula provided on the application notes of the HB100 sensor. It is: $$f_d = 2v \frac{f_t}c\cos(\vartheta)$$ where \$f_d\$ is the doppler frequency, \$v\$ the velocity of the object, \$c\$ the speed of light and \$\vartheta\$ is an angle formed between the intersection of the object axis and the axis of the observer (see image below).

The application note says

if the target is moving straight toward or away from HB100 the formula is simplified to \$f_d = 19.49v\$ (\$v\$ in km/h).

I can't derive this formula, in this condition theta angle is zero, so \$\cos(0) = 1\$ and the formula I derived is about:

$$f_d = 70.17v$$

Could someone explain how the formula reported in the application note is derived? enter image description here

The application note can be found here

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  • \$\begingroup\$ it might help to actually link to that application note. \$\endgroup\$
    – Marcus Müller
    Commented Dec 9, 2018 at 17:14
  • \$\begingroup\$ rfwireless-world.com/calculators/… \$\endgroup\$
    – Andy aka
    Commented Dec 9, 2018 at 17:25
  • \$\begingroup\$ yes you're right, I uploaded the post with the link. \$\endgroup\$
    – JDoe
    Commented Dec 9, 2018 at 17:26
  • \$\begingroup\$ What's Ft? .... \$\endgroup\$
    – Chu
    Commented Dec 9, 2018 at 17:33

1 Answer 1

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Without even trying to actually do the same calculation as you: there's a peculiar factor of 3.6 between your result and the application note.

Chances are, either one of you or the app note author forgot to convert km/h to m/s.

(1 km/h = 1000 m / (3600s) = 1/3.6 m/s)

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  • \$\begingroup\$ Marcus is exactly right! You forgot to divide by 3.6 to convert from km/h to m/s. The formula for \$f_d\$ assumes that \$v\$ is in the same (standard SI) units as \$c\$, i.e., m/s. \$\endgroup\$
    – Peter Paris
    Commented May 28, 2020 at 15:40

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