Pull-Up Resistor for Logic

Formula

Description

Open-drain and open-collector outputs require an external pull-up resistor to define the high-state voltage. The resistor value must be small enough that the sink current through it (when the output is low) does not cause the low-state voltage to rise above VOL_max. The formula gives the maximum pull-up resistance. Additionally, the pull-up must be large enough that the open-drain device can sink the current without exceeding its IOL rating. I²C bus pull-ups, interrupt lines, reset circuits, and wired-OR buses all require properly sized pull-up resistors.

Variables

• R — Pull-up resistor value (Ω)
• V_cc — Supply voltage (V)
• V_OL — Maximum acceptable low output voltage (V)
• I_sink — Current the open-drain output can sink (A)

Practical Notes

For I²C at 3.3 V standard mode (100 kHz): R = 1.5-4.7 kΩ. For I²C fast mode (400 kHz): R = 1-2.2 kΩ. Smaller R gives faster rise times but increases power consumption and IOL current. The rise time is determined by the RC time constant: t_rise ≈ 2.2 × R × C_bus. For multiple devices on the bus, the total bus capacitance C_bus is the sum of all device input capacitances plus trace capacitance.