Question: Is the power consumption of brush motor drivers calculated by:
(LSI Circuit Current x Motor Current) x Supply Voltage?
Answer: With the (Motor Current x Supply Voltage) calculation, since the power consumption of the motor itself is included, determining the driver power consumption Pc when operating at a constant voltage becomes basically:
Pc = (Small-Signal Circuit Current x Source Voltage) + [Motor Current x (Low-Side Output Voltage + High-Side Output Voltage)].
Figure 1. Equivalent Circuit Example
In the equivalent circuit in Fig. 1 above we have a Small Signal Circuit Current Icc, Supply Voltage Vcc, and Motor Current Io. Since the MOS output is often represented by resistance values, given an ON resistance at the high-side output RonH and a low-side ON resistance of RonL, the High Side Output Voltage VH is determined by Io x RonH and, similarly, the Low Side Output Voltage VL by Io x RonL. This makes it possible to calculate the power consumption Pc by: Icc x Vcc + Io x (VH + VL) → Icc x Vcc + Io2 x (RonH + RonL).
Figure 2. PWM Operation
As an example, during current regeneration operation with the 2 outputs leading to the motor, consider the case of ON operation of the output transistor at the ground side as in Figure 2b above.
In one period of PWM operation (tpwm), at output OUT1 we define:
tr: Time to transition from Low to High
tdr: Current supply time to maintain High
tf: Time to transition from High to Low
trc: The time for current regeneration in order to maintain Low, which is divided into 4 parts; the other output OUT2 is in continuous Low operation.
An easy way to think of this operation and how to calculate power consumption is that the voltage change from output high to low and vice versa are constant and in a straight line between currents. The current change during regeneration and voltage supply is also in a straight line.
The energy consumption of the voltage change component is the product of the voltage time constant and current time constant integrated at each time, while the power consumption of the current change component is determined by the product of the resistance and square of the current time constant, integrated at each time.
The energy consumption Er of the tr component is:
Er ≒ • ip1 • VM･tr + (ip1)2 • RonL • tr
The energy consumption Ef of the tf component is:
Ef ≒ • ip2 • VM • tf + (ip2)2 • RonL • tf
The energy consumption Edr of the tdr component is:
Edr ≒ • {(ip1)2 + ip1 • ip2 + (ip2)2} • (RonH + RonL) • tdr
The energy consumption Erc of the trc component is:
Erc ≒ • {(ip1)2 + ip1 • ip2 + (ip2)2} • (2 • RonL) • trc
The output power consumption Pc_ot is calculated from the sum of these 4 components divided by the total time:
Pc_ot ≒ (Er + Edr + Ef + Erc)/tpwm
To arrive at the total power consumption Pc we need to add the circuit current Icc and supply voltage Vcc:
Pc ≒ Pc_ot + Vcc • Icc
In the case that tr and tf are sufficiently smaller than tpwm with virtually no current change and ip1=ip2, the power is determined by:
Pc ≒ (ip1)2 • {(RonH + RonL) • tdr/tpwm + (2 • RonL) • trc/tpwm} + Vcc • Icc
which is the sum of the ratios of the drive time and regenerative time with respect to a single PWM period of generated power based on the changed current pathway during drive operation.
