Resistor Sizing and the MOSFET Heat Ledger

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

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Ada ADA · CALCULATION AUDIT

Resistor Sizing and the MOSFET Heat Ledger

The chapter sizes an LED driver — 2.8 V across a 28-ohm collector resistor at 100 mA — and argues a power MOSFET barely warms, dissipating just 5.5 mW of conduction loss plus a little switching loss. Both claims are load-bearing for the hardware. This audit checks the resistor values and the MOSFET heat ledger line by line, showing where heat would grow with current squared and frequency.

Companion to the chapter From Electricity to Electronics — every number here comes from that chapter.

Ada: This chapter sizes an LED driver with Ohm’s law and then argues a power MOSFET barely warms up. Both claims are load-bearing for the hardware, so let me audit the resistor values and the dissipation ledger line by line.

  • LED collector resistor. With 5 V - 2.0 V LED - 0.2 V Vce(sat) = 2.8 V across the resistor at 100 mA, R = 2.8 V / 0.1 A = 28 ohms. The nearest 33-ohm standard part then passes 2.8 V / 33 ohms = 0.084848 A = 84.8 mA, safely under the 100 mA limit.
  • Base resistor. R = (3.3 V - 0.7 V) / 0.002 A = 2.6 V / 0.002 A = 1,300 ohms, rounded down to a 1 kohm part.
  • MOSFET conduction loss. P = I^2 x Rds(on) = (0.5 A)^2 x 0.022 ohms = 0.0055 W = 5.5 mW.
  • MOSFET switching loss. P = Qg x Vgs x f = 63e-9 C x 3.3 V x 1,000 Hz = 0.0002079 W = 0.208 mW, for a 1 kHz total of 5.5 + 0.208 = 5.71 mW. Raising the PWM to 20 kHz lifts switching to 63e-9 x 3.3 x 20,000 = 0.004158 W = 4.16 mW, a total of 5.5 + 4.16 = 9.66 mW.

The dissipation stays in single-digit milliwatts because Rds(on) is tiny and the gate charge is small, so no heatsink is needed at either frequency. But the same ledger shows exactly where heat would grow — conduction rises with the square of current and switching rises linearly with frequency — so it is the early-warning tool before a bigger motor or a faster PWM crosses the heatsink threshold.

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