The MOSFET Switch Numbers

The MOSFET Switch Numbers

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

foundations
math-foundations
electronics
mosfet
intermediate
Ada 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.

See the relationship before changing it

The figure reads from left to right. The blue card is motor current. The middle card applies this page's rule. The green card is mosfet conduction loss. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only motor current, so the numeric fixture does not switch without explanation.

Motor current changes mosfet conduction loss An input card leads through the rule loss = current^2 x 0.050 ohm to the mosfet conduction loss result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. Conduction loss rises with current squared, so a modest overload creates disproportionate heat.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 2 A.

  2. 2

    Name the relationship. loss = current^2 x 0.050 ohm

  3. 3

    Substitute with units. 2^2 x 0.050 = 0.20 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 motor current

Try Predict the direction of loss = current^2 x 0.050 ohm. Test another motor current, then compare mosfet conduction loss.

2 A
Chapter baseline
MOSFET conduction loss

Observe Conduction loss rises with current squared, so a modest overload creates disproportionate heat. Reset motor current to 2 and compare mosfet conduction loss.

Explain Conduction loss rises with current squared, so a modest overload creates disproportionate 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 motor current moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only motor current. It is not a field prediction.

TryThe 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. Use Check derivation.
ObserveThe displayed ledger resolves 2 A, 20 mA, 12 mA, 0.10 V, 0.20 W at full precision. This audit makes each MOSFET switch number explicit, from GPIO limits to gate timing, before the motor is connected. Check derivation shows this.
Explainthe same switch decision checks GPIO limits, MOSFET conduction loss, package temperature, gate timing, and boot/reset safety before the motor is connected. Check derivation confirms it.

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:

Ibase = Icollector / 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:

VDS = I × RDS(on) = 2 A × 0.050 ohm = 0.10 V
P = I2 × RDS(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
Tjunction = 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.

Technical boundaries
The MOSFET check deliberately does not simulate motor inrush, switching loss, gate-charge dynamics, inductive clamp transients, thermal coupling, or parameter spread; it evaluates the chapter's nominal running-current point.

Work the audit first, then check the displayed derivation.

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