Junctions and Switch Losses

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

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Ada ADA · CALCULATION AUDIT

Junctions and Switch Losses

This chapter mixes microscopic carrier physics with everyday IoT switch choices — picking a diode, BJT, or MOSFET for a microcontroller load. It shows that under-driving a standard MOSFET’s 5V gate instead of using a logic-level part can waste about 0.49W of continuous heat and 5.9Wh/day on a 2A load. This audit checks whether the chapter’s numbers are physically consistent, reading the junctions and switch losses before you choose a part.

Companion to the chapter Semiconductors, Doping, and Diodes — every number here comes from that chapter.

Ada: Semiconductor chapters mix microscopic carrier physics with everyday IoT switch choices. The numbers already in this chapter are enough to check whether the story is physically consistent before you pick a diode, BJT, or MOSFET.

  • Doping multiplies carriers by millions, not infinitely. Silicon has about 5 x 10^22 atoms/cm3; at one dopant per million atoms that is 5 x 10^22 / 10^6 = 5 x 10^16 dopant carriers/cm3. Against the intrinsic 1.5 x 10^10 carriers/cm3, the ratio is 5 x 10^16 / 1.5 x 10^10 = 3.33 x 10^6 – the chapter’s “roughly three million times” conductivity claim is the right order of magnitude.
  • Electron mobility beats hole mobility by about 3x. mu_n / mu_p = 1400 / 450 = 3.11. That is why N-channel devices tend to switch faster – higher carrier mobility, not the absence of holes.
  • A forward diode dissipates real heat; a reverse diode barely does. The 1N4007 forward case: P = V x I = 0.9 x 1 = 0.9 W. Reverse leakage at 12 V and 0.5 uA: P = 12 x 0.5 x 10^-6 = 0.000006 W = 6 uW – five orders of magnitude smaller, so forward conduction is the thermal design case, not reverse leakage.
  • Schottky’s “8% efficiency” claim is a voltage-drop fraction. Swapping a 0.7 V silicon drop for a 0.3 V Schottky drop saves 0.7 - 0.3 = 0.4 V. On a 5 V rail that is 0.4 / 5 = 0.08 = 8% – correct, but only when the diode drop is a dominant series loss on that specific rail.
  • MOSFET beats BJT loss by 27x on the 12 V fan example. BJT: P = 0.3 x 0.5 = 0.15 W. MOSFET: P = 0.5^2 x 0.022 = 0.0055 W. 0.15 / 0.0055 = 27.3 – a different worked example from the chapter’s separate “2 A motor, 12x” comparison elsewhere, and both are internally consistent because they use different currents and Rds(on) values.
  • The GPIO mis-drive story checks out arithmetically – but this audit page’s own header used to misstate the gate voltage. The IRF540N example: rated Rds(on) = 77 mOhm @ Vgs = 10 V gives an expected (2 A)^2 x 0.077 = 0.308 W, which the chapter rounds to 0.31 W. Under-driven so Rds(on) rises to about 200 mOhm: (2 A)^2 x 0.2 = 0.8 W. The waste is 0.8 - 0.31 = 0.49 W continuous, and at 50% duty on a 2 A load: 0.49 x 0.5 x 24 = 5.88 Wh/day, rounding to the chapter’s “5.9 Wh/day.” Both figures reconcile exactly against the chapter. CORRECTED: the chapter’s own worked example runs this from a 5 V gate – its text says “IRF540N driven from 5V Arduino” and “with 5V gate drive: Rds(on) ~ 200 mOhm” – but this audit page’s header previously (and incorrectly) attributed the same numbers to a 3.3 V gate. The 0.49 W and 5.9 Wh/day numbers were always correct as computed; only the gate voltage attached to them on this page needed fixing, and the header above now reads 5 V to match the chapter.

The one-line rule survives the audit: verify Rds(on) at the gate voltage you can actually supply. The 0.49 W the chapter measures is not a 3.3 V number – it is what a 5 V gate still leaves on the table when the part wants 10-12 V to reach its rated Rds(on). A 3.3 V gate would sit even further from full enhancement and waste more, not the same amount.

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