# Doppler frequency formula (for HB100)

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?

The application note can be found here

• it might help to actually link to that application note. Commented Dec 9, 2018 at 17:14
• rfwireless-world.com/calculators/… Commented Dec 9, 2018 at 17:25
– JDoe
Commented Dec 9, 2018 at 17:26
• What's Ft? ....
– Chu
Commented Dec 9, 2018 at 17:33

• 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. Commented May 28, 2020 at 15:40