The MOSFET Switch Numbers

Ada audits the MOSFET switch numbers — current, heat, gate timing, and pull-down safety

ADA · CALCULATION AUDIT

Foundations · optional mathematics and physics

The MOSFET Switch Numbers

The chapter chooses a switch for a 2 A motor: a BJT would need 20 mA of base drive, above the ESP32’s 12 mA GPIO limit, so a MOSFET wins — dropping 0.10 V, dissipating 0.20 W, and rising just 12.5 C to a 37.5 C junction. This audit makes each MOSFET switch number explicit, from GPIO limits to gate timing, before the motor is connected.

Companion to the chapter Electronics Concepts and Calculators — every number here comes from that chapter.

Current, heat, gate timing, and pull-down safety, ~4 minutes

A transistor switch is a physics problem before it is a code problem: the GPIO only commands the gate, while motor current, heat, capacitance, and inductive kick decide whether the circuit survives.

The working

1. The BJT comparison fails on base current. The chapter's motor can draw 2 A. With a rough current gain of 100, the base drive would be:

I_base = I_collector / β = 2 A / 100 = 0.020 A = 20 mA

The ESP32 GPIO limit in this worked example is 12 mA, so the base-current estimate is already above the pin budget. That is why the voltage-controlled MOSFET is the better switch for this load.

2. The MOSFET heat check uses the running current and the on-resistance. The chapter uses 2 A and a conservative 0.050 ohm at the available 3.3 V gate drive:

V_DS = I × R_DS(on) = 2 A × 0.050 ohm = 0.10 V

P = I² × R_DS(on) = 2² × 0.050 = 4 × 0.050 = 0.20 W

The thermal estimate then turns electrical power into temperature rise:

ΔT = 0.20 W × 62.5 °C/W = 12.5 °C

T_junction = 25 °C + 12.5 °C = 37.5 °C

3. The gate resistor is a transient-current limiter, not a steady load. A 100 ohm resistor and 1200 pF gate capacitance give:

Review question	Arithmetic shown	Audit result
Peak gate-charge current	I = 3.3 V / 100 ohm	0.033 A = 33 mA, brief only while the gate charges
RC charge time constant	τ = R × C = 100 ohm × 1200 pF = 100 × 1200 × 10-12 s	1.2 × 10-7 s = 120 ns
Pull-down off-state margin	V = 10 µA × 10 kohm = 10 × 10-6 × 10000	0.1 V, below the 1-2 V threshold range
Pull-down power when driven high	P = V2 / R = 3.32 / 10000	0.001089 W = 1.1 mW

What the audit buys you: the same switch decision checks GPIO limits, MOSFET conduction loss, package temperature, gate timing, and boot/reset safety before the motor is connected.

Every number above is taken from the chapter's own MOSFET switch example and re-derived step by step.