Ada Audits the Regulator Trade

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

Ada Audits the Regulator Trade

A linear regulator (LDO) passes the full load current through and burns the leftover voltage as heat, while a switching buck trades that voltage for current instead. The chapter’s worked rail delivers 100 mA at 3.3 V from a full 4.2 V Li-ion cell, where the LDO runs at about 79% efficiency and, active five minutes an hour, wastes enough to cost roughly 29 mAh a day against a 90% buck. This audit carries both converters through the full duty cycle to weigh the regulator trade: which choice actually wastes less?

Companion to the chapter Hardware Optimization Strategies — every number here comes from that chapter.

Ada: A regulator choice is a conservation-of-energy check. Use the load power, then carry the converter and quiescent losses through the full duty cycle before deciding which part is efficient.

1. Heavy-load rail: compare battery current, not only efficiency. The chapter's worked rail is 3.3 V at 100 mA from a full 4.2 V Li-ion cell.

P_load = 3.3 V x 100 mA = 330 mW

LDO input = 4.2 V x 100 mA = 420 mW; waste = 420 - 330 = 90 mW; efficiency = 330 / 420 = 0.785714 = 78.6%

90% buck input = 330 mW / 0.90 = 366.667 mW; battery current = 366.667 / 4.2 = 87.302 mA; loss = 36.667 mW

The buck therefore draws 100 - 87.302 = 12.698 mA less from the battery during this phase, or 12.7% less current after final rounding.

2. Daily active loss: integrate the rail over time. The chapter's rail is active for 5 minutes/hour, which is 2 hours/day.

LDO daily waste = 90 mW x 2 h = 180 mWh/day

Buck daily loss = 36.667 mW x 2 h = 73.333 mWh/day; saving = 180 - 73.333 = 106.667 mWh/day

Cell-equivalent saving = 106.667 mWh / 3.7 V = 28.829 mAh/day, which rounds to about 29 mAh/day

3. Sleep rail: quiescent current can reverse the decision. The sleep example uses a 10 uA load, a buck controller drawing 15 uA, and a low-Iq LDO drawing 1 uA.

Buck sleep draw = 10 + 15 = 25 uA; effective light-load efficiency = 10 / 25 = 40.0%

Low-Iq LDO sleep draw = 10 + 1 = 11 uA; effective light-load efficiency = 10 / 11 = 90.9%

For 23.76 h asleep: buck = 25 x 23.76 = 594.0 uAh; LDO = 11 x 23.76 = 261.36 uAh; saving = 332.64 uAh/day

The physics lesson is why the chapter separates heavy-load and light-load regimes: the best active regulator can be the wrong sleep regulator when its own controller current is larger than the load.

Every number above is taken from the chapter’s own material and re-derived step by step.