Electrical – Why are shunt resistors in BLDC motor drivers placed betweent MOSFETs and ground and not MOSFETs and the motor

You are right in that they are not switching losses. If they were, the current would go up with frequency, not down.

You said it yourself. Your controller implements a dead time. At higher frequency the dead time is a larger fraction of the PWM period, so the effective time the motor is on is reduced.

Just to avoid some confusion, I want to point out that what you are seeing has nothing to do with the induction of the motor coils. The inductance of the coils only serves to smooth out the individual pulses. These decreases the ripple current in the coils and makes the current closer to the average. That's actually a good thing.

Depending on how exactly you are driving the motor, it is possible that too little inductance of the coils causes problems at low frequencies by causing back and forth current even though it averages to the desired amount. The losses in the coils are proportional to the square of the current which is higher with ripple imposed on the slow desired signal than just the average. Unless you have a unusual or badly designed setup (I have seen both), this is probably not the problem. Again, the dead time explains your symptoms very nicely.

Added:

I just realized that maybe by "PWM" you are talking about the motor phase drive frequency (how fast you are trying to rotate the magnetic field), not the PWM frequency used to modulate the effective drive voltage the motor sees. Your question is badly worded in that this major distinction is not clear. If in fact you are wondering why the motor takes less current when it is run faster, then that is because of the back EMF it generates. You can think of a motor as something that makes torque proportional to voltage with a variable voltage source in series. This voltage source apposes the voltage you apply proportional to how fast the motor is spinning in the direction you are trying to drive it in. The faster it goes, the less efective voltage is presented to the "driving" part of the motor, and it takes less current.

Most micro-controllers with ADC's have an internal bandgap reference with a voltage of ~1V (see datasheet for more precise values and tolerances; ex.: the STM32F415xx series has a bandgap reference of 1.21V). This effectively increases your resolution to 1253 steps full scale by flipping a software switch.

If you want to do even better, you have a few options:

1. Use an op-amp to amplify the output of your current sensor
2. Use a higher resolution external ADC
3. Use a lower voltage external reference (for example, something like this). Note that a simple voltage divider directly into the vref pin is almost never a good idea.

In none of these cases do you need to change the voltage supply to your microcontroller.

As a side note, I don't understand your aversion to using a shunt resistor. For moderately low currents (few amps) it is the most accurate way to measure currents. For example, the ACS712 chip you've listed has an accuracy of 1%. That means you get an accuracy of 6.64 bits (~100 steps). It is very easy to get shunt resistors with 0.5% accuracy, giving an accuracy of 7.64 bits (~200 steps). Using a 0.1% accurate shunt gives you 9.97 bits of accuracy (~1000 steps).

If you use a very small shunt resistor with an instrumentation amplifier the burden voltage will be negligible. For example, say you have an in-amp with a gain of 100x (very do-able). An appropriate shunt resistor to get 0-1.21V full scale needs a shunt resistor of 6.05mOhms, and will have a burden voltage of 12.1mV. For all intensive purposes this is negligible. You can reduce this even more by using a 1000x in-amp circuit (also very do-able).