AnasSarkiz/usb-c-pwm-pa25

docs/CALCULATIONS.md

# A1 calculations and intended bench limits

Revision A1, 2026-09-30. These are design calculations, not measured performance. Manufacturer references are registered in `references/README.md`.

## Motor and current regulation

The PA25-24126000-G23 drawing specifies 12 V, 250 mA rated current, 20 mA no-load current, 199/266 rpm geared rated/no-load speeds, 0.54 kg·cm rated geared torque and 22.56:1 ratio. Rated electrical input is 3 W. The separate 1.4 W entry is not electrical consumption. Torque × speed gives about 1.10 W geared output; the drawing does not reconcile these two mechanical figures. Starting/stall current, winding thermal limits and safe stall duration remain measurements to obtain.

DRV8874 uses 450 µA/A nominal IPROPI scaling. R30 || R31 = 10 kΩ || 820 kΩ = 9.8795 kΩ. With the LM4040 2.5 V reference, Itrip = 2.5/(9879.5 × 450e-6) = **0.5623 A**. Using ±7.5% scaling at 0.4–1 A, ±1% resistance, and a ±0.5% reference design allowance gives approximately **0.515–0.617 A**. The selected B-grade reference has ±0.2% initial tolerance; the wider allowance includes temperature/load effects over the intended 0–40 °C bench ambient. Dynamic overshoot, blanking and comparator delays are additional; reserve 0.65 A for budgeting and measure peaks. This is never a continuous motor rating.

At lower currents the driver specifies ±30 mA sensing error, before external and ADC errors. Firmware latches a fault when measured current is at least 350 mA for 100 ms. This verifies sustained-overload handling but cannot establish a safe intentional stall time. No locked-rotor test is authorized by this calculation. PWM is 12 MHz / 600 = 20 kHz; 2 permille/ms ramp steps take 500 ms from zero to full command.

## Regulated rail and PD budget

TPS54202 uses R16=191 kΩ and R17=10 kΩ: 0.596 × (1+19.1) = **11.9796 V**. Combining the 0.581–0.611 V feedback limits with independent 1% resistors gives **11.458–12.517 V** before load/line drops. Firmware accepts measured VM from 11.1 to 12.8 V; verify measurement error and transients physically. A typical 12 V label does not imply ±2% regulation.

Budget: output voltage 12.517 V; motor-path current 0.65 A; other 12 V current 0.02 A; minimum efficiency target 85%; input-side control/protection allowance 0.35 W; margin 25%.

Pinput = ((12.517 × 0.67)/0.85 + 0.35) × 1.25 = **12.77 W**. This is 0.851 A at 15 V and 0.946 A at the conservative 13.5 V board-input analysis point. The latter is an analysis point, not a USB-PD specification. U1 requests **1 A operating / 1.5 A maximum** at fixed 15 V. Firmware requires the actual source PDO to offer at least 1.5 A and verifies the active request. Reference supply: 30 W USB-C PD with fixed 15 V/2 A, a compliant 3 A C-to-C cable no longer than 1 m. No 12 V PDO, USB-A adapter or ordinary computer port is relied upon.

TPS259470L ILM=2.8 kΩ gives about 1.19 A, with approximately ±10% IC tolerance above 1 A plus resistor tolerance (about 1.06–1.33 A). This sits below the requested 1.5 A maximum. Initial bulk charge at 0.2 V/ms into 470 µF requires 94 mA plus load; firmware inhibits the bridge through settling. Both eFuses have 10 nF dVdt capacitors and latched fast-trip configuration. Q2/Q3 reset both paths. Nominal UV/OV thresholds: U2 13.2/16.8 V; U5 10.872/13.2 V. Threshold and resistor tolerances must be included in supply corner tests.

## Buck energy storage and compensation

L1 is Bourns SRP7050TA-150M: 15 µH ±20%, 3.5 A RMS, 6 A saturation, 92 mΩ maximum DCR. Nominal inductor ripple at 15 V → 12 V, 500 kHz is 0.32 A peak-to-peak. A conservative 16.8 V, 12 µH, 400 kHz corner gives 0.714 A peak-to-peak: approximately 1.007 A peak at the 0.65 A motor budget. The 6 A saturation rating also accommodates the regulator's much higher internal short-circuit peak-current threshold; it does not make this a 6 A board.

C15 is **Panasonic 25SVPF47M**, 47 µF ±20%, 25 V polymer, 30 mΩ maximum initial ESR, 2.8 A ripple rating. C16 is 100 nF ceramic. The polymer avoids using unverified MLCC DC-bias capacitance as the regulator's bulk output. Initial minimum is 37.6 µF; including the datasheet's 20% endurance change gives 30.08 µF. These are not a lifetime prediction. At 0.714 A ripple, capacitor RMS current is about 0.206 A. The estimated capacitive ripple at 400 kHz and 30.08 µF is 7.4 mV; initial ESR adds about 21.4 mV. Endurance ESR and temperature require measurement.

TI's small-ESR crossover estimate, 3.95/(Vout × Cout), gives 7.02 kHz nominal and 10.96 kHz at the above minimum, below its 40 kHz guidance. The ideal small-ESR feed-forward value is about 119 pF; TI instructs reducing it for medium ESR. C19=47 pF gives a zero at about 17.7 kHz with 191 kΩ. This is a starting compensation choice, not a measured phase margin. Bench acceptance requires stable startup, line/load steps and no sustained ringing; measure the loop if needed. The 500 kHz input bypass loop and SW area must be assessed on actual routed copper.

## Regeneration and thermal shutdown

The downstream reverse-blocking U5 prevents VM feeding the buck or USB source. A 470 µF capacitor alone stores only 12.22 mJ between 12 and 14 V. U7/U8 are powered from VM so the dissipative clamp can operate after USB removal.

R41=43.2 kΩ, R42=10 kΩ and R43=820 kΩ with a 2.5 V reference give about **13.432 V turn-on** at a low comparator output. With the gate limited near 9.1 V by D6, turn-off is about **12.95 V**. Component tolerances, comparator offset, output low voltage and zener operating current change these values. Target peak VM <14 V in initial bench tests; this is an acceptance target, not a guaranteed transient bound.

R70–R77 are eight Bourns CRM2512AJW-201ELF, 200 Ω ±5%, 2 W pulse-resistant parts in parallel: 25 Ω nominal. At 14 V the bank draws 0.56 A and dissipates 7.84 W, or 0.98 W each. The initial **≤0.5 J/event and ≤1 W average** test envelope is deliberately limited; 0.5 J corresponds to about 64 ms at 14 V. The CRM-A pulse curve provides substantial pulse headroom at this duration, but does not qualify the board's continuous thermal performance. No 16 W continuous board rating is claimed. Q1 switches this load with a protected gate; its transient safe operating area and temperature still need scope/thermal verification.

The 10 kΩ/B3380 NTC with a 27.4 kΩ pull-up gives a nominal hardware trip around 70 °C against the 0.250 V comparator threshold. Firmware trips earlier at 300 mV (about 65 °C) and treats >1.8 V as an open-sensor fault. Actual temperatures depend on tolerance and sensor placement. Board temperature does not represent winding temperature.

STOP or a direction change ramps PWM down, enters coast, waits at least 2 s, and requires deliberate STOP/zero re-arming. There is no speed sensor: the 2 s interval does not prove the shaft has stopped. Characterize stopping time for the actual mechanism before loaded use. External back-driving, suspended loads and continuous regeneration are outside this bench prototype's assigned scope.

## Copper basis and remaining measurements

Use four layers with specified 1 oz copper on every layer, 0.8 mm main power/motor routes where possible, ≥0.15 mm signals/clearance, 0.60/0.30 mm ordinary tented through vias, ≥0.5 mm edge clearance and 4 mm-radius mounting keepouts. Nominal copper resistivity at 20 °C is 1.724e-8 Ω·m: a 0.8 mm × 35 µm trace is about 0.616 mΩ/mm; at 0.65 A a 50 mm path loses about 20 mV and 13 mW. A 0.15 mm × 35 µm neck is 3.284 mΩ/mm; a 2 mm neck loses about 4.27 mV and 2.78 mW at 0.65 A. These electrical losses are not a thermal model or permission for arbitrarily long narrow power routes. Inner-layer thermal behavior must be reviewed separately; an external-layer ampacity assumption cannot be applied to an internal trace. The 1 oz inner-copper option is a fabrication requirement, not the default 0.5 oz stack.

For a 0.30 mm drill and assumed 20 µm finished plating, a 1.6 mm barrel is about 1.46 mΩ (0.62 mW at 0.65 A). Manufacturer-confirmed plating and actual via count are required. Ground pours, package escapes, physical neck lengths, drill/pad gaps and all power transitions must be measured from the routed output. Physical thermals remain pending. Configuration values alone do not pass copper validation.