upd: explanation of efficiency change with PWM frequency and damping
About an year ago I’ve found that braking of motors in BHeli_S firmware significantly reduces efficiency. If damping is removed with modified BHeli_S firmware flight time can be increased by up to 30%. Later it was found that 0802 motors in contrast to 0603 motors do not show negative current (braking) with regular firmware and that is why flight time is longer.
Recently RPM filtering was introduced and new ESC firmware was developed by joelucid, see rcgroups.com discussion and JFlight.net. And most recently the author added new variations of firmware working at 48kHz and undamped versions of both 24kHz and 48kHz. Many people noticed that 48kHz version significantly increases flight time without negative effects caused by undamped versions.
Here I’m measuring performance of all JESC 2.2 versions with my test stand. The motor is Happymodel 19kV, FC is Mobula7 F4 version, ESC FW S-H-50. 4 blade betaflight 31 mm prop. RPM filtering is not involved in this measurements, just driving the motors with JESC (free firmware).
Figure below shows voltages and currents at one of the motor’s coils measured with home-made Hall-effect based sensor. As expected we can see negative current caused by braking for both 24 kHz and 48 kHz versions.
Fig. 1 Voltages and currents at the motor’s coil for 24kHz, 24 kHz undamped, 48 kHz and 48 kHz undamped versions of JESC firmware. Note, shape of the voltage curves is different from that we discussed earlier (here and here) it happens because this FC has Xcom MOSFETs at the low side.
And thrust, rpm and current (total, measured at the battery) are:
Fig. 2 Thrust vs throttle position
Fig. 3 RPM vs throttle
RPM curve vs throttle (Fig.3) gets more nonlinear with 24kHz undamped and 48 KHz version. This effect is expected, it means that with undamped FW and 48kHz FW (weak damping) the ESC-motor gets out of closed-loop feedback of RPM vs throttle; and reminds more free rotation curve of pure PWM regulation see more here and here. Curves are between ESC with full closed-looped control (hard braking) and open-loop with just PWM control .
Fig.4 Total current (including FC) vs throttle
It may seem that about the same current of 24 kHz and 24 kHz undamped versions is in contradiction with better efficiency of undamped version, but actually is not, because thrust is determined by RPM (and mechanical power), and undamped version has higher rpm at the same throttle. Total effect of flight efficiency is complex: it depends on 1) lost current while braking 2) rpm at the same current 3) overall higher efficiency at higher throttle.
Sure all FW versions have the same performance at high throttle, because at duty cycle close to 100% there is no PWM at all.
Here is the efficiency, expressed as current vs thrust. 48 kHz and 48 kHz undamped versions show best efficiency at hovering point (~4g) and current consumption is up to 30-40% less compared to 24 kHz version). 48 kHz version is even better than undamped 24 kHz version.
Fig.5. Total current vs thrust.
Conclusions:
1. At low throttle JESC 48 kHz version has better efficiency compared to 24 kHz version. Current may be lower at hovering by 30-40%.
2. Maximum thrust is the same for all versions.
3. This may not work for bigger motors, higher inductance may reduce overall efficiency of PWM . It may be roughly modeled with online graphing tool (there are inductance and frequency inputs under “throttle PWM” checkbox).
4. It is hard to predict theoretically what will happen in real life, because overall performance depends on many different factors. For example, the same 19kV motor used in previous measurements shows drastically different results for both lack of negative current and curves shapes. That time another FC (F3) and ESC FW (Bheli_S) were used. To be honest, currently I have no clue why it happens.