Wheel speed sensor math

Here resides the math used to calculate constants which relate the output voltage of the LM2907 on the FS-3 peripheral board to a linear speed of the car

• Assuming $V_{max}=\frac{80}{3600}mps$
• Assuming $T=62$ (Number of teeth per revolution)
• Assuming $R_w=8in$ (inches per mile: 63360)

$${\nu }_{max}=\frac{63360\cdot V_{max}\cdot T}{2\pi R_w}$$

The datasheet for the LM2907

The only things that actually matt er are:

$$R_1=\frac{V_{Omax}}{180\mu A}$$ $$f_{max}=\frac{I_2}{C_1\cdot V_{CC}};I_2=180\mu A$$

In our application ($V_{Omax}$ = 5), $R_1$:

$$\frac{5V}{0.00018A}=27.7k\Omega$$

In our application (${\nu }_{max},V_{CC}$)

$${\nu }_{max}=\frac{180\mu A}{C_1\cdot 5}$$ $$C_1=\frac{180\mu A}{{\nu }_{max}\cdot 5}$$

Expanding..

$$C_1=\frac{180\mu A}{\frac{63360\cdot V_{max}\cdot T}{2\pi R_w}\cdot 5}$$

Yields:

$$C_1=2.0728983785\times 10^{-8}F$$ $$C_1=20nF$$