Complete Ćuk DC-DC converter design tool. The Ćuk topology uses two inductors and an energy-transfer capacitor to produce a negative, regulated output at any voltage — step-up or step-down. Calculate duty cycle, both inductors, coupling and output capacitors, MOSFET and diode ratings, switching losses, and efficiency. CCM and DCM analysis included.
Ćuk Converter Designer
Negative output · Step-up/down · Dual inductor · CCM/DCM · Full loss analysis
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⚠Ćuk topology: Output is always negative w.r.t. input GND (e.g. +12 V → −15 V). The converter uses two inductors (L1 input, L2 output) and an energy-transfer capacitor C1. Both MOSFET and diode block Vin + |Vout|. Key advantage over inverting buck-boost: both input and output currents are continuous (lower ripple), making it ideal for noise-sensitive applications.
Input / Output Specification
V
V
A
Switching Parameters
kHz
%
%
%
Efficiency & Loss Parameters
%
mΩ
V
Switch & Capacitor Parameters
nC
V
mΩ
Key Results
Duty Cycle D
—%
Ideal D (no loss)
—
Practical D (with η)
—
Voltage Gain |M|
—
Output Voltage Vout
—
◆ CCM — Continuous Conduction Mode
L1 (Input)
—
μH recommended
L2 (Output)
—
μH recommended
C1 Transfer Cap
—
μF minimum
C2 Output Cap
—
μF minimum
IL1 Peak
—
A
IL2 Peak
—
A
Estimated Efficiency
—
%
Enter parameters
60%75%85%92%98%
Ćuk Converter Topology
L1 — Input Inductor
L1 Min (CCM)
—
μH
L1 Recommended
—
μH (×1.5 margin)
IL1 Average
—
A (= Iin)
IL1 Peak
—
A (sat. rating ≥ this)
ΔIL1 Ripple p-p
—
A
L1 RMS Current
—
A
L2 — Output Inductor
L2 Min (CCM)
—
μH
L2 Recommended
—
μH (×1.5 margin)
IL2 Average
—
A (= Iout)
IL2 Peak
—
A (sat. rating ≥ this)
ΔIL2 Ripple p-p
—
A
L2 RMS Current
—
A
Enter values to see inductor recommendations.
C1 — Energy Transfer Capacitor
C1 Voltage VC1
—
V (= Vin + |Vout|)
C1 Min Capacitance
—
μF
C1 Voltage Rating
—
V (≥1.3 × VC1)
C1 RMS Current
—
A
C1 Ripple Voltage
—
V p-p (target <2%)
Recommended C1
—
μF (×2 margin)
C2 — Output Capacitor
C2 for ΔVout
—
μF
ESR Ripple
—
V (ESR × ΔIL2)
Total Output Ripple
—
V peak-to-peak
C2 Voltage Rating
—
V (≥1.5 × |Vout|)
Target |ΔVout|
—
V
Recommended C2
—
μF (×1.5 margin)
MOSFET Requirements
VDS Blocking
—
V (= Vin + |Vout|)
ID Peak
—
A (= IL1,pk + IL2,pk)
ID RMS
—
A
Cond. Loss
—
W
Rec. VDS Rating
—
V (1.3×(Vin+|Vout|))
RDS(on) Budget
—
mΩ (entered)
Diode Requirements
VR Reverse Voltage
—
V (= Vin + |Vout|)
IF,avg Average
—
A
IF,peak
—
A
Diode Loss PD
—
W
Recommended Component Summary
Component
Parameter
Minimum
Recommended
Status
Loss Breakdown
Total Estimated Loss
—W
Input Power Pin
—
Output Power Pout
—
Calculated η
—
Power Density
—
MOSFET Conduction (I² × RDS)—
MOSFET Switching (Qg × V × f)—
Diode Conduction (Vf × Iout)—
L1 DCR Conduction (est.)—
L2 DCR Conduction (est.)—
Output Cap ESR—
Calculated Efficiency
—
%
Calculate to see result
60%75%85%92%98%
Detailed Loss Table
Loss Source
Formula
Value (W)
% of Total
Reduction Tip
Key Waveforms — One Switching Cycle
L1 Inductor Current iL1(t) — input inductor (continuous, rises during ON)
L2 Inductor Current iL2(t) — output inductor (continuous, falls during ON)
MOSFET Gate Signal Vgs(t)
C1 Capacitor Current iC1(t) — carries sum of L1 and L2 currents
Same DC transfer function as the inverting buck-boost. Output is always negative. At D=0.5 gain=1 (inverted). The Ćuk advantage is continuous current in both L1 and L2 — lower ripple than a simple inverting buck-boost.
Transfer Capacitor Voltage
V_C1 = Vin + |Vout| = Vin / (1 − D)
C1 carries the full bus voltage at all times. This is the highest voltage in the circuit. V_C1 = Vin + |Vout| regardless of operating point. Rate C1 at ≥ 1.3 × V_C1 for reliability.
L1 carries the average input current. Set ΔiL1 to 20–40% of IL1_avg for typical designs. L1 current rises during ON (MOSFET on) and falls during OFF (diode on).
L2 carries the average output current. L2 current falls during ON (C1 charges L2 and delivers to output) and rises during OFF (diode freewheels). Set ΔiL2 ≈ 20–40% of Iout.
Transfer Capacitor C1 Sizing
C1_min = D × Iout / (fsw × ΔV_C1)
ΔV_C1 target: 1–2% of V_C1
I_C1_rms ≈ sqrt(IL1_rms² + IL2_rms²)
C1 must handle the combined RMS current of both inductors — the most stressed component. Use film or high-ripple-rated polymer caps. Keep ΔV_C1 < 2% for good regulation.
Because L2 current is continuous, output ripple is very low — a key Ćuk advantage. The ESR term often dominates. Use low-ESR polymer or ceramic capacitors.
Same as the inverting buck-boost — both switches block V_C1 = Vin + |Vout|. For 12V → −15V: 27V stress. Rate devices at ≥ 1.3 × (Vin + |Vout|) and add TVS snubber for transients.
The MOSFET carries both L1 and L2 currents during the ON phase — peak current is the sum of both inductor peaks. This is higher than in a single-inductor topology at the same power.
How a Ćuk Converter Works
The Ćuk converter (invented by Slobodan Ćuk at Caltech in 1976) is an inverting DC-DC topology that produces a regulated negative output voltage from a positive input. It uses two inductors (L1 and L2), an energy-transfer capacitor (C1), a MOSFET switch, and a diode. The DC transfer function is identical to the inverting buck-boost — Vout = −Vin × D / (1 − D) — but the fundamental advantage is that both the input and output currents are continuous, dramatically reducing ripple on both sides.
During the ON phase (MOSFET closed): L1 charges from Vin; C1 discharges through L2 to the output. During the OFF phase (MOSFET open): L1 charges C1 through the diode; L2 freewheels through the diode to maintain output current. The energy-transfer capacitor C1 sits at a DC voltage of Vin + |Vout| and must handle the combined RMS current of both inductors.
Ćuk vs Inverting Buck-Boost: Same DC gain equation, but the Ćuk has continuous current in both inductors (lower EMI, smaller filter caps), while the inverting buck-boost has pulsed input and output currents. Disadvantage: more components (two inductors, extra capacitor) and C1 is a high-stress part. The Ćuk is preferred in noise-sensitive designs such as audio, instrumentation, and precision analog circuits.
Inductor and Capacitor Selection
The two inductors can be designed independently or wound on a single coupled core (a coupled-inductor Ćuk). For independent inductors: L1 carries the average input current IL1_avg = Iin and L2 carries the average output current IL2_avg = Iout. Each inductor’s ripple is set independently — 20–40% of average current is typical. Both L1 and L2 must not saturate at their respective peak currents, and both should have low DCR to minimise conduction loss.
The transfer capacitor C1 is the most critical component. It must handle the full V_C1 = Vin + |Vout| DC voltage and the combined RMS current of both inductors. This is a demanding combination — use film capacitors or high-grade polymer electrolytics with good ripple-current ratings. The output capacitor C2 benefits from the continuous L2 current and is much smaller than in a simple buck-boost. ESR is typically the dominant ripple contributor.
Frequently Asked Questions
What is the voltage gain formula for a Ćuk converter?
Ideal: Vout = −Vin × D / (1 − D). Practical: Vout = −Vin × D × η / (1 − D). The duty cycle is D = |Vout| / (Vin × η + |Vout|). This is identical to the inverting buck-boost transfer function. At D = 0.5, |Vout| = Vin (inverted). The Ćuk differs from the buck-boost only in its internal waveforms and component count, not in its I/O relationship.
Why does the Ćuk have lower ripple than an inverting buck-boost?
In a standard inverting buck-boost, the input current is pulsed (zero during OFF phase) and the output current is also pulsed (zero during ON phase). The Ćuk uses two inductors to make both input current (through L1) and output current (through L2) continuous. This dramatically reduces the required filter capacitance and EMI on both input and output rails — important in noise-sensitive systems.
What is the voltage on the transfer capacitor C1?
In steady-state, V_C1 = Vin + |Vout| = Vin / (1 − D). For 12 V in and −15 V out, V_C1 = 27 V. C1 also carries the RMS current sum of both inductors, making it the most stressed passive component in the circuit. It must be rated for both the DC voltage (with margin) and the ripple current — use film or high-grade polymer caps, not standard aluminium electrolytics.
Can the Ćuk be used with coupled inductors?
Yes — the coupled-inductor Ćuk winds L1 and L2 on the same core. With a turns ratio of 1:1 and tight coupling, the ripple in both inductor currents can be made exactly zero in theory (complete ripple cancellation). In practice, residual ripple exists due to leakage inductance, but the ripple reduction is significant. This is one of the unique advantages of the Ćuk topology over all other non-isolated converters.
Calculations are theoretical estimates. Actual performance depends on component parasitics, PCB layout, thermal management and control loop design. Always validate with bench measurement and thermal imaging.
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