RMS Current of a PWM Pulse Calculator (Trapezoid, Rectangle, Triangle)
Every hard-switched device carries the same waveform: a pulse that ramps from one current to another for a fraction of the period, then stops. Conduction loss goes with its RMS squared, device ratings with its peak, and the input capacitor with the difference between the two. One closed form covers the trapezoid and both of its limits - the rectangle and the triangle - so there is no need for a table of waveform factors.
Choosing something to solve for makes RMS current an editable target and computes the chosen input from it.
Formula
| Ia, Ib | current at turn-on and turn-off (A) |
| D | conduction duty cycle |
| Iac | AC (ripple) component of the waveform (A) |
What this model assumes, and where it stops
Assumptions
- Linear ramp between the two corner currents - true when the inductor voltage is constant during conduction, which is the CCM steady state.
- Instant switching: rise and fall transitions contribute nothing to the RMS. At normal switching speeds they are far too short to matter for conduction loss.
- Zero current outside conduction - this is one device's slice, not the inductor waveform. The inductor itself never stops conducting in CCM; use the inductor ripple page for it.
- Periodic steady state.
Limitations
- Conduction loss in a MOSFET is Irms^2 x Rds(on), but for diodes and IGBTs with a threshold voltage the average matters as much as the RMS: P = Vf Iavg + r Irms^2. This page gives both terms; the split is yours.
- The waveform factor says nothing about switching loss, which scales with frequency, voltage and current at the switching instants rather than with RMS.
- Rds(on) and Vf are temperature dependent, so the loss this feeds is the start of an iteration, not the end.
- For current-sense resistors and shunts the RMS here is exactly right; for capacitors carrying this pulse, subtract the DC first - that is the AC component output.
When you need a 3D field solution instead
Closed-form models like the one above hold on idealised geometry. These are the cases where they stop being good enough and a full 3D electromagnetic and thermal solution is the only way to get a trustworthy answer:
- Current sharing between paralleled devices, where layout inductance decides which device carries how much of this pulse.
- Skin and proximity effect at the switching harmonics in busbars and wide traces carrying these pulses - the trapezoid is rich in harmonics well beyond the fundamental.
- Shunt resistor self-heating with its own thermal time constants against millisecond pulse groups.
Common questions
Why does a pulsed current heat a resistance more than DC of the same average?
Because heating goes with the square of the instantaneous current, and squeezing the same charge into a shorter window raises the instantaneous value. A rectangular pulse at duty D heats 1/D times more than the DC equivalent - four times at 25% duty. This page reports that factor directly; it is why current-sense shunts and connector ratings care about the waveform, not just the average.
Do I use the RMS or the average for conduction loss?
Both, depending on the device. A MOSFET is resistive: P = Irms^2 x Rds(on). A diode or IGBT has a threshold plus a slope: P = Vf x Iavg + r x Irms^2. This page gives both numbers for exactly that reason - and at low duty cycles the difference between the two conventions is large.
Do the switching rise and fall times change the RMS?
Not measurably. A 50 ns transition in a 5 us period shifts the RMS by well under a percent, so treating the edges as instant is safe for conduction loss. What the edges do control is switching loss and EMI spectrum, which are entirely different calculations - the trapezoid corner frequencies at 1/(pi t_rise) decide the harmonic envelope.
References
- Erickson & Maksimovic - Fundamentals of Power Electronics, 3rd ed. - RMS values of commonly observed converter waveforms, Appendix A
- Infineon AN2019-05 - Conduction loss calculation from device datasheet parameters