Board power tree

Source — USB, an adapter or PoE is a voltage with a series resistance (the cable there and back) and a current or power limit. A battery is its open-circuit voltage at the state of charge, from the chemistry’s discharge curve, minus the current through its internal resistance.

LDO — the input current is the load current plus the quiescent (ground) current, so its loss is (V_in − V_out)·I + V_in·I_q. Dropout is a fixed part plus a resistance times the current: bipolar parts like the AMS1117 need about 1.1 V at any load, CMOS parts like the MCP1700 (178 mV at 250 mA) almost nothing at light load. Below V_out + dropout the output follows the input down.

Switcher — loss = V_in·I₀ + k·P_out + R·I_out²: a no-load loss (quiescent current and the pulse-skipping losses that dominate at microamps), a part proportional to the power (switching, gate drive, a catch diode’s forward drop) and conduction loss. The three numbers for each preset are fitted by hand to the efficiency curves in its data sheet; the inspector draws the curve and marks where the converter sits at the lightest and heaviest moments of the period. A buck cannot raise the voltage and a boost cannot lower it (it passes the input through its diode); below its minimum input a switcher turns off.

Switches and diodes — R·I² plus V_f·I plus its own quiescent current.

Temperature — T_j = T_a + P·θ_JA, from the package’s θ_JA in the preset (on modest copper; check the data sheet and your layout). Small packages reach their steady temperature in seconds to tens of seconds, so the loss used is the larger of the period average and any stretch lasting 10 s or more. Open in Thermal design takes the loss and θ_JA to the thermal tool to try a heatsink or more copper.

Warnings — overcurrent against each part’s rating (and a boost’s switch-current limit), input above the maximum or below the minimum, LDO dropout, a buck or boost that cannot regulate, LDOs that burn more than they deliver, junction temperatures within 25 °C of the limit or over it, a load’s supply outside its range, a battery peak above what the cell gives comfortably, and cable drop.

Battery life — the battery is discharged in ½ % steps of charge. At each step the whole period is solved again at that open-circuit voltage, so a switcher draws more current as the cell runs down and every converter is at its real light-load efficiency during sleep; the self-discharge is added as a steady drain. It stops when the cell falls to its cut-off under the peak load, a converter switches off, or a load’s supply drops below its minimum — the Uno example stops at about 20 % charge, when the AMS1117/NCP1117 can no longer hold the ATmega above 4.5 V.

Loads are constant currents. A resistor-fed LED or a motor draws less at a lower voltage; a constant-power load (a downstream converter you have not drawn) draws more.

The switcher model is a three-term fit, good for comparing parts and finding where the power goes, not a replacement for the data sheet’s curve at your input voltage. Light-load modes differ a lot between parts and settings (PFM, power-save, forced PWM).

The battery curve is at light load and 20–25 °C. Capacity falls at high currents (Peukert) and in the cold, and the internal resistance rises with age; the battery-life estimator applies temperature and ageing derating.

Inrush and start-up surges (a motor’s stall current, capacitor charging) are not modelled: give the load its surge current for a short active time if it matters.