The story is more complicated if pulse-width modulation (PWM) is used to operate the motor at less than full speed. Now switching losses, as well as conduction losses must be considered.

Each time the drive-stage MOSFETs switch on or off, there is a short period of time when the transistor is operated in the linear region, meaning the current is not zero, and the voltage across the channel is greater than when the transistor is fully on. During this time, the power dissipation in the transistor reaches a maximum. The circuit simulation in Figure 4-1 illustrates this as the transistor T1 switches from an off state with no current flowing to an on state. The power dissipation in the transistor is shown as PM1, and reaches a maximum when the current and voltage across the transistor are midway through the transition.

Figure 4-1 Simulation Showing Switching Power Dissipation

Note that before the transistor turns on, the power dissipation is essentially zero, since no current is flowing. After the transistor turns on, in the conduction phase of operation, the power dissipation is the product of the steady-state current and the voltage across the transistor, which is relatively low.

The instantaneous power dissipation in the drive transistors is a product of the voltage across the drain-to-source channel and the current through the channel. A simplified mathematical model of the instantaneous power assumes a linear slope on both the rising and falling transitions. With these simplifications, we can model the power dissipation as:

For an apples-to-apples comparison, we can calculate the power dissipation for equivalent 12V and 48V cases. In both cases we will deliver about 48 Watts to a load during steady-state operation, so the 12V system requires a current of 4A, and the 48V system requires a current of 1A. Select MOSFETs for each case so that during steady-state operation the drive delivers 99.7% efficiency to the load; thus about 160 mW is dissipated in the MOSFETs. So the 12V system uses MOSFETs with RDS(on) of 10mOhms, and the 48V system uses MOSFETs with RDS(on) of 160mOhms In both cases, the maximum instantaneous power dissipated in the MOSFETs is 12W, as shown in Figure 4-2

Figure 4-2 Instantaneous Power Dissipation for Equivalent 12V and 48V Systems

The key result is that for equivalent systems in terms of steady-state performance, if the slew rates are equal, the 48V system dissipates the switching power for a duration of 4 times as long as the 12V system. The total energy dissipation is the area under each of the curves in Figure 4-2. It is this energy that can significantly heat the transistors during PWM operation.

Figure 4-3 shows voltage transitions for integrated motor drivers with adjustable slew rates, the DRV8245-Q1 with a 12-V supply and the DRV8363-Q1 with a 48-V supply. Note that the slope is not constant during the rising edge, but the total transition time correlates to the inverse of the slew rate setting. As expected, the rise time of the 48-V device, with a slew rate setting of 19V/us, is about four times longer than the rise time of the 12V device with a slew rate of 20V/us.

Figure 4-3 Comparison of 12V and 48V Voltage Transitions with Various Slew Rate Settings

To reduce the power dissipation, we want to get through the transition phase quickly. Thus we want a fast slew rate, reducing the rise time and fall time for the drive stage transistors. Adjustable slew rate settings give this flexibility. However, as this document discusses later, fast slew rates impact electromagnetic emissions, due to the larger high-frequency content in fast signal edges.