GOAL: Reduce the Bulk Cap to the lowest capacitance allowing for proper functionality of the ESC (120F3[X]v2) used in the pegasus drone.
Due to the inductance of the conductor path from the battery to the ESC, load transients presented by the ESC will cause voltage to fluctuate at the ESC terminals. If this voltage drops below a certain value (need to find the optimal nominal voltage range, and characteristics of the motor’s load transients), also known as rail droop/collapse, for a long enough time, the motor/ESC functionality will be negatively affected. A Bulk capacitor can be used to compensate for this, and provide the demanded transient current.
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The length of the conductor path (8 gauge wire) from the positive battery terminal to the ESC is ~117cm. This might be useful for finding the inductance of the PDN (NOTE: Inductance strongly depends on the loop area. Since this loop area is not well defined, it might be fine to approximate it with straight wire inductance… need more research). From this resistance calculation tool, this segment of wire results in ~2.5 Ohms of resistance (though the PDB and other interconnects will increase this value).
From the Pegasus Overview, the maximum required current from all 4 motors “is anticipated to be 90Amps… Any individual motor will not draw more than 23 amps at a time, not including the path”. Can ESC control circuitry (3 Half bridge drivers, MCU, MOSFET gates, …) current be neglected?
(But the doc section below seems to indicate a max of 25A).
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In this scenario, the only source of current for the ESC is the capacitor, and given some general ESC ratings/requirements for good performance (need to figure out), an upper limit for the necessary capacitance can be found.
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Modelling in terms of load transient current as the input and capacitor voltage as the output results in a non-linear system. Can try to use Numerical methods to come up with a formula for finding capacitance.
It is an LC circuit, so current transients cause it to resonate. The higher the cap’s ESR, the more these oscillations are damped. Low ESR is better for efficiency and reducing voltage droop magnitude but worse for dampening oscillations!
Closer Upper-Bound Calculations
A slightly more accurate approximation of the ESC’s PDN is the following:
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or
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During a load transient, when the ESC suddenly sinks some current, we can employ AC analysis to see what happens at the input of the ESC (what will the voltage differebce/ripple at the ESC, caused by the transient look like?) and from there, we can add proper decoupling to compensate:
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This, from my understanding, is a part of PDN analysis, where the input impedance profile (of the D.U.T/ESC) is designed to be below a particular threshold: the target impedance.
To elaborate, we want to design our PDN such that, for the worst case load transient (at a rate/frequency of our concern; i.e. the fastest rate at which current can change through the BLDC motor coils), the rail collapse / voltage ripple doesn’t go beyond the ESC’s rated tolerance (need to find).
This means, for the maximum current IMAX (which gets drawn during the transient), the voltage difference across the PDN’s equivalent impedance must be below Vripple (maximum voltage ripple tolerable by the ESC).
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This equivalent impedance Z is called the target impedance.
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(Though, some PDN analysis guidelines use 50% of the transient current, as the other result may be too conservative - meaning that its unlikely that the worst case transient, at the worst case frequency, draws the ESC’s rated amount of current; the end of this article briefly discusses this).
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