Junctions and Switch Losses

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.

See the relationship before changing it

The figure reads from left to right. The blue card is rds(on). The middle card applies the page rule. The green card is conduction heat. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

Rds(on) changes conduction heat An input card leads through the rule heat = (2 A)^2 x Rds(on) / 1000 to the conduction heat result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. Current is squared, so resistance that looks small can still make real heat.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 200 mOhm.

  2. 2

    Name the relationship. heat = (2 A)^2 x Rds(on) / 1000

  3. 3

    Substitute with units. 4 x 200 / 1000 = 0.80 W

  4. 4

    Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change rds(on)

Try Predict the direction of heat = (2 A)^2 x Rds(on) / 1000. Test another rds(on), then compare conduction heat.

200 mOhm
Chapter baseline
Conduction heat

Observe Current is squared, so resistance that looks small can still make real heat. Reset rds(on) to 200 and compare conduction heat.

Explain Current is squared, so resistance that looks small can still make real heat.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only rds(on) moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only rds(on). It is not a field prediction.

TryThis chapter mixes microscopic carrier physics with everyday IoT switch choices — picking a diode, BJT, or MOSFET for a microcontroller load. Use Check derivation.
ObserveThe displayed ledger resolves 5V, 0.49W, 5.9Wh/day, 2A at full precision. This audit checks whether the chapter’s numbers are physically consistent, reading the junctions and switch losses before you choose a part. Check derivation shows this.
ExplainMOSFET conduction loss follows current squared times Rds(on); a 5 V gate leaves the IRF540N near 200 mOhm instead of its 10 V rated resistance, producing the extra 0.49 W and 5.9 Wh/day. Check derivation confirms it.

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.

Technical boundaries
The device comparisons deliberately do not simulate temperature-dependent curves, switching transients, reverse recovery, package thermal impedance, manufacturing spread, or gate-drive dynamics; they evaluate the chapter's stated steady-state points.

Work the audit first, then check the displayed derivation.

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