Ćuk Converter Designer

Design an inverting Ćuk converter: duty cycle, both inductors, the coupling capacitor’s voltage, ripple and RMS current, the output capacitor, switch and diode stresses, and the load below which it leaves continuous conduction.

Last updated 22 Sep 2026

Ćuk power stage

Vin, −Vout, Iout, fsw → L1, L2, C1, Cout

Input voltage (V)Design at the input you care most about; ripple in L1 and L2 both grow with the input.

Output voltage magnitude (V)Enter 5 for a −5 V output. The Ćuk output is always negative.

Output current (A)The full-load current.

Switching frequency (kHz)

L1 ripple (% of the input current)Peak to peak, as a share of L1’s average current, which is the input current.

L2 ripple (% of the output current)Peak to peak. 20–40% is the usual range, as for a buck.

Coupling capacitor ripple (% of its voltage)Peak to peak. A few per cent keeps the ripple from disturbing the loop.

Output ripple target (mV peak to peak)

Diode forward drop (V)0 = ideal. About 0.3–0.5 V for a Schottky at full current. Use the figures from your part’s datasheet; typical values vary widely between manufacturers.

Switch on-state drop (V)0 = ideal. For a MOSFET, current × R_DS(on).

Ćuk converter: L1 draws a steady current from the input, the coupling capacitor C1 passes energy across, and L2 feeds the load, so the output sits below ground. The dots show average currents: on average the switch carries exactly the input current and the diode exactly the output current. C1's average current is zero (it takes the input current while the switch is off and gives up the output current while it is on), so no dots cross it, but it carries the RMS current shown in the results.

56.47µHExample

12 V in, −5 V out at 1 A, 500 kHz, 30% ripple in both inductors, 5% coupling-capacitor ripple, 20 mV output ripple, ideal switches

Ćuk converter power stage (CCM)

D = (|V_o| + V_d) ÷ (V_in − V_sw + |V_o| + V_d); I_L1 = I_o·D/(1 − D); V_C1 = (V_in − D·V_sw)/(1 − D) − V_d; L1 = (V_in − V_sw)·D ÷ (f·ΔI_L1); L2 = (|V_o| + V_d)·(1 − D) ÷ (f·ΔI_L2); C1 = I_o·D ÷ (f·ΔV_C1); C_out = ΔI_L2 ÷ (8·f·ΔV); I_o,crit = (1 − D)·(ΔI_L1 + ΔI_L2)/2

D: duty cycle, from volt-second balance on both inductors; ideally |Vo|/(Vin + |Vo|)
VC1: average coupling-capacitor voltage; ideally Vin + |Vo|, which is also the switch and diode stress
ΔIL1, ΔIL2: peak-to-peak inductor ripples you allow
ΔVC1, ΔV: coupling-capacitor and output ripple, peak to peak
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, −5 V out at 1 A, 500 kHz, 30% ripple in both inductors, 5% coupling-capacitor ripple, 20 mV output ripple, ideal switches
D = 5 ÷ (12 + 5) = 29.41%; input current = 1 × 0.2941 ÷ 0.7059 = 416.7 mA
L1 = 12 × 0.2941 ÷ (500,000 × 0.30 × 0.4167) = 56.47 µH → 68 µH (E12)
L2 = 5 × 0.7059 ÷ (500,000 × 0.30) = 23.53 µH → 27 µH (E12)
V_C1 = 12 + 5 = 17 V; C1 = 1 × 0.2941 ÷ (500,000 × 0.05 × 17) = 692 nF → 1 µF; RMS 647.9 mA
C_out = 0.3 ÷ (8 × 500,000 × 0.020) = 3.75 µF; CCM down to 128.9 mA

How the Ćuk converter works and how to size it

The Ćuk converter (Ćuk and Middlebrook, 1977) puts an inductor on both sides and passes energy through a capacitor in the middle. With the switch on, L1 charges from the input while the coupling capacitor C1 discharges into L2 and the load; with it off, L1’s current recharges C1 through the diode while L2 keeps feeding the load. Both the input and the output current are continuous, which is its great advantage over the inverting buck-boost designer: small input and output capacitors and little conducted noise. Like the buck-boost it inverts, with the ideal ratio |V_out|/V_in = D/(1 − D). Set the diode and switch drops to 0 for an ideal design; enter them to see how they stretch the duty cycle.

The coupling capacitor. Volt-second balance on the two inductors puts C1 at V_in + |V_out| on average — 17 V in the example — and the switch and the diode both block this voltage. Charge balance on C1 sets the currents: it takes the input current while the switch is off and gives up the output current while it is on. That makes its RMS current large (647.9 mA here for a 1 A output), so choose a capacitor, usually a multilayer ceramic or film part, rated for that current and for its DC voltage with margin, and allow for a ceramic’s capacitance loss under DC bias.

Continuous and discontinuous conduction. In a Ćuk converter each inductor current can dip below zero without anything changing; what matters is the diode current, iL1 + iL2. The converter stays in CCM while the load is above (1 − D)(ΔI_L1 + ΔI_L2)/2, which is Erickson and Maksimović’s result with the two inductors in parallel. With the E12 parts in the example that is 128.9 mA. Below it the duty-cycle relation no longer holds.

How this was checked. Every formula on this page was compared against a time-stepped switching simulation of the four energy-storage elements, run to steady state for several designs, with and without drops. Control is harder than it looks: the Ćuk is a fourth-order converter with a right-half-plane zero and a C1–L resonance, so the loop needs care; coupling L1 and L2 on one core can steer the ripple away from the input or output. For switch losses use the MOSFET loss calculator; for a positive output, the buck converter designer.

Frequently asked questions

What is the output voltage of a Ćuk converter?

Negative: Vout = −Vin × D ÷ (1 − D) in the ideal case, so it can be above or below the input in magnitude. 12 V in at 29.41% duty gives −5 V.

How do you calculate the coupling capacitor in a Ćuk converter?

C1 = Iout × D ÷ (f × ΔVC1), where ΔVC1 is the ripple you allow on it. It sits at about Vin + |Vout|, and its RMS current is roughly Iout × √(D/(1 − D)). For the example, 692 nF at 17 V with 647.9 mA RMS.

What voltage do the switch and diode see in a Ćuk converter?

The coupling-capacitor voltage, about Vin + |Vout|: 17 V for 12 V in and −5 V out, before any ringing.

When does a Ćuk converter enter discontinuous mode?

When the diode current iL1 + iL2 reaches zero, at loads below (1 − D)(ΔIL1 + ΔIL2)/2: 128.9 mA in the example.

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References

Erickson RW, Maksimović D. Fundamentals of Power Electronics, 3rd ed. Springer, 2020. Ch. 2 (volt-second and charge balance, the Ćuk converter example), Ch. 5 (discontinuous conduction).
Ćuk S, Middlebrook RD. A new optimum topology switching DC-to-DC converter. IEEE Power Electronics Specialists Conference (PESC), Palo Alto, June 1977. doi:10.1109/PESC.1977.7070814.
IEC 60063:2015. Preferred number series for resistors and capacitors. The E6 and E12 series used for the suggested standard parts.