Once all the slaves are assigned to the appropriate slave channels and bus voltages are identified, the pull-up resistors, R_p, for each of the buses need to be selected appropriately. The minimum pull-up resistance is a function of the reference voltage of the specific I²C channel (V_DPUX), V_OL,(max), and I_OL as shown in Equation 1.

Equation 1.

The maximum pull-up resistance is a function of the maximum rise time, t_r (300 ns for fast-mode operation, f_SCL = 400 kHz) and bus capacitance, C_bis given by Equation 2.

Equation 2.

The maximum bus capacitance for an I²C bus must not exceed 400 pF for fast-mode operation. The bus capacitance can be approximated by adding the capacitance of the PCA9548A, C_io(OFF), the capacitance of wires, connections, traces, and the capacitance of each individual slave on a given channel. If multiple channels are activated simultaneously, each of the slaves on all channels contribute to total bus capacitance.