Free Hall Effect Sensor Magnetic Flux & Trip Distance Tool

1. Magnetic Field Calculation for Cylindrical & Disc Magnets

Hall effect switches (such as the Allegro A1104, Texas Instruments DRV5023, or Honeywell SS400 series) respond to perpendicular magnetic flux density passing through their silicon die. For an axially magnetized cylindrical or disc permanent magnet of radius $R$ and thickness $T$, the on-axis magnetic field $B(z)$ at a distance $z$ from the pole face is given analytically by: $$B(z) = \frac{B_r}{2} \left[ \frac{z + T}{\sqrt{R^2 + (z + T)^2}} - \frac{z}{\sqrt{R^2 + z^2}} \right]$$

Where $B_r$ is the residual magnetic induction (remanence) of the magnetic alloy. Neodymium-Iron-Boron (NdFeB) magnets range from $B_r = 11,700\text{ Gauss}$ (N35) to over $14,500\text{ Gauss}$ (N52), while sintered ceramic ferrite magnets typically exhibit $B_r \approx 3,900\text{ Gauss}$. Note that $1\text{ Tesla} = 10,000\text{ Gauss} = 1,000\text{ mT}$, so $1\text{ mT} = 10\text{ Gauss}$.

2. Switching Thresholds ($B_{op}$ vs $B_{rp}$) & Mechanical Hysteresis

Digital Hall switches incorporate an internal Schmitt trigger comparator to ensure clean, bounce-free digital switching:

• Operate Point ($B_{op}$): As the magnet approaches the sensor, the magnetic field rises. When $B(z) \ge B_{op}$, the internal output transistor switches ON, pulling the digital output pin LOW.
• Release Point ($B_{rp}$): As the magnet moves away, the field diminishes. The output remains latched LOW until the field drops strictly below $B_{rp}$, at which point the transistor turns OFF and releases the line to HIGH.
• Mechanical Hysteresis ($\Delta z = z_{rp} - z_{op}$): Because $B_{op} > B_{rp}$, the physical position where the switch trips is closer than the position where it releases. This mechanical deadband is essential in robotics, tachometers, and limit switches to prevent chattering from mechanical vibration.

3. Open-Drain Pull-Up Resistor Sizing ($R_{pu}$)

Most Hall effect sensor ICs employ an open-collector or open-drain N-channel MOSFET output stage. When inactive, no current flows, and an external pull-up resistor $R_{pu}$ tied to $V_{cc}$ is required to define the logic HIGH state. The resistor value is governed by two boundaries: $$R_{min} = \frac{V_{cc} - V_{ol(max)}}{I_{sink(max)}} \approx \frac{V_{cc}}{20\text{mA}}$$ $$R_{opt} = \frac{V_{cc} - 0.2\text{V}}{I_{target}} \quad (\text{typically } 1.0\text{ mA to } 2.0\text{ mA})$$

For $3.3\text{V}$ logic, a $2.2\text{ k}\Omega$ to $4.7\text{ k}\Omega$ resistor provides an ideal compromise between low quiescent current when asserted and rapid charging of trace capacitance.