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Even though a motor driver IC is thought of as a switch or set of switches, it is not a perfect switch. Power is dissipated in the motor driver IC, primarily due to resistive losses which are proportional to drive current, as well as from other sources such as internal quiescent power and switching losses.
The precise calculation of this power loss is complex and a subject of its own (refer to Calculating Motor Driver Power Dissipation, application note). For the purposes of this discussion, we will simplify the power loss to that which is dissipated in the FET ON-resistance of the power stage, called RDS(ON).
Since the power switch is resistive when it is conducting current, it dissipates power according to Ohm's law: P = I2R, where I is the DC or RMS current flowing to the load and R is the sum of the RDS(ON) of the output switches. In an H-bridge motor driver, when driving current, there are two switches dissipating power; the high-side switch to the supply, and the low-side switch to ground. Note that stepper motor drivers normally have two full H-bridges in the same IC.
This power dissipation causes the temperature of the device to rise. How much the temperature rises is estimated by multiplying the power dissipated (in watts) by the junction-to-ambient temperature, referred to as θJA. The θJA value is variable, as it depends on how well the PCB design can dissipate the heat conducted from the IC. Data sheets typically indicate some value for θJA based on a standard PCB construction.
If too much current is driven, the device heats up to a point that can endanger the reliability of the device. All motor driver ICs from TI have a thermal shutdown circuit disabling the outputs when the die temperature reaches a predefined threshold (typically around 150°C).
The maximum die temperature before overtemperature shutdown is a limiting factor for how much DC or RMS current a motor driver IC can deliver. Maximum die temperature is not typically a limitation of the short-term peak current.
In most cases, the thermal limit is the dominant factor in determining the maximum current a motor driver can provide.
This current level is not simple to calculate, as it depends greatly on conditions that the IC manufacturer does not control, like PCB design and ambient temperature.
For further information about thermal considerations, refer to PCB Thermal Calculator.