SEPIC Converter Designer
SEPIC Converter Designer
Design a SEPIC: the one switching topology that steps up or down from the same circuit and keeps the output the right way up. Duty cycle, both inductors for separate or coupled windings, the coupling capacitor and the RMS current that decides its part number, the output capacitor, and every switch and diode stress.
SEPIC power stage
12 V in, 15 V out at 1 A, 500 kHz, 30% ripple in both inductors, 5% coupling-capacitor ripple, 50 mV output ripple, separate inductors, ideal switches
SEPIC power stage (CCM)
- D
- duty cycle from volt-second balance on both inductors; ideally Vo/(Vin + Vo)
- VCs
- average coupling-capacitor voltage. It is the INPUT voltage — the same balance that gives D also puts both inductors at Vin − Vsw while the switch is on
- ΔIL1, ΔIL2
- peak-to-peak inductor ripples you allow. With one 1:1 coupled inductor each winding needs half the value shown for two separate ones
- Cout
- the diode feeds the output in pulses, so the output capacitor supplies the whole load for the on-time — Io·D/f of charge, which is why it is large
- Io,crit
- load at which the diode current iL1 + iL2 just reaches zero; below it the converter is in DCM
Worked example
12 V in, 15 V out at 1 A, 500 kHz, 30% ripple in both inductors, 5% coupling-capacitor ripple, 50 mV output ripple, separate inductors, ideal switches
D = 15 ÷ (12 + 15) = 55.56%; input current = 1 × 0.5556 ÷ 0.4444 = 1.25 A
Both inductors see Vin while the switch is on, so L1 = 12 × 0.5556 ÷ (500,000 × 375 mA) = 35.56 µH → 39 µH (E12)
L2 = 12 × 0.5556 ÷ (500,000 × 300 mA) = 44.44 µH → 47 µH (E12)
VCs = Vin = 12 V; Cs = 1 × 0.5556 ÷ (500,000 × 0.60) = 1.852 µF → 2.2 µF, carrying 1.122 A RMS
Cout = 1 × 0.5556 ÷ (500,000 × 0.050) = 22.22 µF → 33 µF, with an ESR below 19.51 mΩ and 1.12 A RMS through it
Switch and diode both block 27 V and see a peak of 2.563 A; CCM holds down to 139 mA
SEPIC against Ćuk, at identical conditions
| SEPIC | Ćuk | |
|---|---|---|
| Output polarity | Positive — the same way up as the input | Inverted |
| Coupling capacitor sits at | Vin | Vin + |Vout| |
| Second inductor L2 goes | from the capacitor to ground | from the capacitor to the load |
| Diode goes | from the capacitor to the load | from the capacitor to ground |
| Output current is | pulsed — the diode feeds the capacitor | continuous — L2 feeds the load |
| Output capacitor for 20 mV at 12 V → 5 V, 1 A, 500 kHz | 29.41 µF | 3.75 µF |
| Output capacitor RMS current, same conditions | 645.5 mA | 86.6 mA |
| Switch and diode block | Vin + Vout | Vin + |Vout| |
| Duty cycle | Vout/(Vin + Vout) | the same |
How a SEPIC works, and how it differs from a Ćuk
A SEPIC — single-ended primary-inductance converter — is the fourth-order cousin of the buck-boost. The input feeds L1; a switch pulls L1’s far end to ground; a coupling capacitor passes that node on to a second node where L2 goes to ground and a diode goes to the load. Its output can be above or below the input from the same circuit and the same duty cycle relation, D = Vout/(Vin + Vout), and — unlike the inverting buck-boost and unlike the Ćuk — the output comes out positive. That is why it is the standard answer for a 12 V rail from a lead-acid battery that sags to 9 V and rises to 15 V while charging.
The coupling capacitor sits at Vin. This surprises people who know the Ćuk, where it sits at Vin + |Vout|. The reason is simple: L2 goes to ground, so its DC voltage is zero and the node beyond the capacitor has no DC offset, while L1’s DC drop is also zero, so the node before it is at Vin. Volt-second balance then puts Vin − Vsw across both inductors while the switch is on — which is why L1 and L2 take the same formula, and why equal ripple targets give equal inductors. The capacitor carries the output current one way while the switch is on and the input current the other way while it is off, so its RMS current is Iout·√(D/(1−D)) — 1.122 A here for a 1 A load. Undersize it and it will run hot, lose capacitance under DC bias if it is a ceramic, and eventually fail; this is the commonest way a SEPIC that works on the bench dies in the field.
Coupled or separate inductors. Both windings see the same voltage at every instant, so they can be wound 1:1 on one core. When they are, the mutual inductance means each winding only needs half the value two separate inductors would, for the same ripple — that result comes straight out of solving v = L·di/dt + M·di’/dt for the two windings with M = L, and it is checked that way in this page’s own proof. A coupled part is smaller and cheaper, and the ripple can be steered towards one winding by deliberately mismatching the turns. What it adds is a coupling of the capacitor’s ripple voltage into the leakage inductance, which produces a circulating current the ideal equations do not predict — so measure the real ripple rather than trusting the calculation. Use the toroid turns calculator if you are winding your own.
Where SEPIC pays for its convenience. The output capacitor. In a Ćuk, L2 sits between the coupling capacitor and the load, so the output current is continuous and the output capacitor only absorbs a triangular ripple — 3.75 µF is enough for 20 mV in that page’s example. In a SEPIC, L2 goes to ground and the diode feeds the load, so the output capacitor supplies the entire load current for the whole on-time and then takes a pulse back: 29.41 µF for the same 20 mV, with 645.5 mA of ripple current instead of 86.6 mA. Its ESR usually decides the ripple before its capacitance does. The switch and diode stresses are the same in both — Vin + Vout blocking, and a peak current of IL1 + IL2 — so the MOSFET loss calculator and the diode power loss calculator apply unchanged. Compare with the Ćuk converter designer if an inverted output is acceptable, and with the boost or buck designers if the input never crosses the output.
How this was checked. Every formula above was compared against an exact solution of the switched power stage: each sub-interval is linear, so the cycle map is a pair of matrix exponentials and the periodic steady state is the fixed point of that map, solved directly rather than waiting for a simulation to settle. Duty cycle, coupling-capacitor voltage, both ripples, both capacitor ripples, all four RMS currents and the peak switch current were read off that solution at two operating points — one stepping up with ideal devices and one stepping down with a 0.45 V diode and a 0.15 V switch drop — and agree with the equations to better than 1%. Control is not easy: like the Ćuk this is a fourth-order converter with a right-half-plane zero and an L–C resonance between the coupling capacitor and the inductors, so the loop needs real compensation and damping.
Frequently asked questions
What is a SEPIC converter used for?
Any supply where the input voltage crosses the output voltage — a 12 V rail from a lead-acid battery that runs from 9 V to 15 V, a 5 V rail from a lithium cell that starts at 4.2 V and ends at 3.0 V, or a 3.3 V rail from an unregulated wall adapter. It steps up and down without changing mode and without inverting.
What is the difference between a SEPIC and a Cuk converter?
Two components swap places. In a Ćuk the diode goes from the coupling capacitor to ground and L2 carries the output; in a SEPIC L2 goes to ground and the diode carries the output. The consequences are that the Ćuk inverts and the SEPIC does not, that the coupling capacitor sits at Vin + |Vout| in a Ćuk but at Vin in a SEPIC, and that the SEPIC’s output current is pulsed, so it needs a far bigger output capacitor.
What voltage does the coupling capacitor in a SEPIC see?
The input voltage. L2’s DC drop is zero because it goes to ground, and L1’s DC drop is zero, so the capacitor bridges Vin and 0 V. Rate it for the maximum input voltage with margin, and remember a ceramic loses most of its capacitance near its rated voltage.
Can I use a coupled inductor in a SEPIC?
Yes, 1:1, and it is usually the better choice. Both windings see the same voltage at every instant, so the mutual inductance halves the inductance each winding needs for a given ripple. Watch the leakage inductance, which carries a circulating current driven by the coupling capacitor’s ripple.
Why does a SEPIC need such a large output capacitor?
Because the diode feeds the load in pulses: for the whole on-time the output capacitor supplies the load on its own, which is Iout × D/f of charge. At 1 A, 29.4% duty and 500 kHz that is 588 nC, and holding it inside 20 mV takes 29.41 µF against 3.75 µF for the equivalent Ćuk.
What is the duty cycle of a SEPIC converter?
D = (Vout + Vd)/(Vin + Vout + Vd), the same relation as a buck-boost or a Ćuk. 12 V in and 15 V out gives 55.56%, and the input current is then Iout·D/(1−D) = 1.25 A for a 1 A load.
Related calculators
References
- Texas Instruments (National Semiconductor). AN-1484: Designing A SEPIC Converter, SNVA168E, May 2006 (revised April 2013). D = (VOUT + VD)/(VIN + VOUT + VD); inductor and peak-current equations for separate and coupled windings; the coupling capacitor’s RMS current IOUT·√((VOUT + VD)/VIN(min)) and ripple IOUT·Dmax/(Cs·fsw); MOSFET and diode stresses of VIN + VOUT.
- Coilcraft. Selecting Coupled Inductors for SEPIC Applications. When two windings are closely coupled on one core the ripple current is shared between them and the required inductance is halved — two 22 µH single inductors are replaced by one coupled inductor of 11 µH per winding.
- Erickson RW, Maksimović D. Fundamentals of Power Electronics, 3rd ed. Springer, 2020. Volt-second and charge balance, the SEPIC and Ćuk converters, and discontinuous conduction in fourth-order converters.
- IEC 60063:2015. Preferred number series for resistors and capacitors. The E6 and E12 series used for the suggested standard parts.