Resistor Sizing and the MOSFET Heat Ledger

Resistor Sizing and the MOSFET Heat Ledger

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

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.

See the relationship before changing it

The figure reads from left to right. The blue card is pwm frequency. The middle card applies the page rule. The green card is total mosfet loss. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

Walk the arrows. Conduction loss stays fixed here while switching loss grows with frequency.

Derive the baseline in four named moves

1. 1

   Name the input. The chapter baseline is 20 kHz.

2. 2

   Name the relationship. loss = 5.5 mW + 63 nC x 3.3 V x frequency

3. 3

   Substitute with units. 5.5 + 63e-9 x 3.3 x 20,000 x 1000 = 9.66 mW

4. 4

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

Predict, then change pwm frequency

Try Predict the direction of loss = 5.5 mW + 63 nC x 3.3 V x frequency. Test another pwm frequency, then compare total mosfet loss.

PWM frequency

20 kHz

Chapter baseline

Total MOSFET loss

Observe Conduction loss stays fixed here while switching loss grows with frequency. Reset pwm frequency to 20 and compare total mosfet loss.

Explain Conduction loss stays fixed here while switching loss grows with frequency.

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 pwm frequency moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only pwm frequency. It is not a field prediction.

TryThe 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. Use Check derivation.

ObserveThe displayed ledger resolves 2.8 V, 28-ohm, 100 mA, 5.5 mW at full precision. This audit checks the resistor values and the MOSFET heat ledger line by line, showing where heat would grow with current squared and frequency. Check derivation shows this.

ExplainMOSFET conduction heat rises with current squared through Rds(on), while switching heat rises linearly with PWM frequency through gate charge; that is why the same part can stay cool here yet cross a thermal limit at a larger motor or faster PWM. Check derivation confirms it.

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.

Technical boundaries
The resistor and MOSFET ledger deliberately does not simulate load transients, switching loss, gate charge, component tolerance, thermal coupling, or inductive kick; it checks the chapter's nominal DC operating 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.