Thermal efficiency and power
When a single phase is energized at 0° electrical angle (so-called full-step), one phase current is I_target and the other 0A. Power is simply I_target^2 * R.
When the electrical angle is at a multiple of 45° (or so-called half-step) we assume each phase is commanded sqrt(2)/2*I_target from trig sin(45°). Since power is related to the square of that, each phase (chip/coil) dissipates only half of the power ((sqrt(2)/2*I_target)^2*Rdson = 0.5(I_target^2)*Rdson) compared to if the same target was commanded at 0°. Since the power is more spread out, the temperature raises less locally.
Additionally, having single phases energized continuously is rare - only when the motor is hard locked. Any motor movement and phase current will switch from one phase to another following FOC's sinusoidal waveform. The DC equivalent of alternated sinusoidal current is called RMS and is expressed by sqrt(2)/2*I_target RMS. So the same kind of half-power advantage as above but now also applies to a single phase over time.
The whole point of RMS current is to allow power calculation as if we were dealing with DC.
When a motor is rotating not one but both phases experience a sinusoidal current waveform. To get RMS, we multiply I_target by sqrt(2)/2. Then from motor control fundamentals and/or FOC we know that phase control waveforms are shifted by 90° between each other or in other words one is sine and the other cosine. Since, sinx+cosx = sqrt(2)*sin(x+phi) the combined RMS current consumption for both phases is (sqrt(2)/2*I_target) * sqrt(2), which evaluates to just I_target. This allows us to say that the controller is capable of 3.3A combined RMS current or simply 3.3A. Note that the current is not physically combined until it is converted at the DC link, at which point its value can be lower depending on the input voltage.
Current:
| Scenario | Single phase current | Combined currents (non-physical) | Input current* |
|---|---|---|---|
| Standstill 0° |
I_target and 0
|
I_target |
I_target^2 * R / Vin |
| Standstill 45° | 0.7*I_target |
1.4*I_target |
I_target^2 * R / Vin |
| Rotating** |
0.7*I_target RMS |
I_target RMS |
I_target^2 * R / Vin |
Power:
| Scenario | Single phase power | Total power |
|---|---|---|
| Standstill 0° |
I_target^2 * Rand 0
|
I_target^2 * R |
| Standstill 45° | 0.5*I_target^2 * R |
I_target^2 * R |
| Rotating** | 0.5*I_target^2 * R |
I_target^2 * R |
R = Rdson + Rsense + Rmotor. Replace R with Rmotor (about 3ohm) or Rdson (up to 1ohm) to only estimate motor or chip power dissipation.
*Note Input current conversion will be lower due to efficiency and variable depending on duty cycle and mixed decay ratios
**Note, at higher speeds, the actual current will be even lower than the target due to BEMF.
To summarize, the A4950 driver will reach the highest temperature if the single phase is energized and the motor is stationary. If both phases are energized (45° electrical angle), or if the motor is rotating, half of the power is generated in each chip on average and it is dissipated easier and so the temperature will be lower.
A4950 Hardware overtemperature protection kicks in at 150°C after. Condition - no thermal paste, 12V supply, 3ohm motor - worst case scenario, i.e. in a standstill.
Times until hardware protection limits current:
Different board version / driver model.
Example thermal snapshot:
