Ćuk Topology Schematic
(Images sourced from Microchip)
Derivation Steps
Step 1: Write inductor‑voltage equations for both switch states
| State | Voltage across L1 | Voltage across L2 |
|---|---|---|
| Q1 ON (D·T) | VL1 = VIN | VL2 = −VOUT − VC1 |
| Q1 OFF ((1−D)·T) | VL1 = VIN − VC1 | VL2 = −VOUT |
(Images sourced from Microchip)
Q1 ON
(Images sourced from Microchip)
Q1 OFF
For circuit analysis of Q1 ON / OFF, refer to:
Cuk Converter: Energy Flow Breakdown & Component Functions during Switch ON/OFF
Step 2: Apply Volt-Second Balance to L_1
Under steady-state conditions, the net volt-second product over one switching cycle equals zero:
V_{IN}\cdot D + (V_{IN}-V_{C1})\cdot(1-D)=0
Expand and simplify:
V_{IN}\cdot D + V_{IN}(1-D) - V_{C1}(1-D)=0
V_{IN}=V_{C1}(1-D)
Therefore:
\boxed{V_{C1}=\frac{V_{IN}}{1-D}}
Step 3: Apply Volt-Second Balance to L_2
(-V_{OUT}-V_{C1})\cdot D + (-V_{OUT})\cdot(1-D)=0
Expand and simplify:
-V_{OUT}\cdot D - V_{C1}\cdot D - V_{OUT}(1-D)=0
-V_{OUT}-V_{C1}\cdot D=0
Therefore:
\boxed{V_{OUT}=-V_{C1}\cdot D}
Step 4: Eliminate V_{C1} to Obtain the DC Transfer Function
Substitute
V_{C1}=\frac{V_{IN}}{1-D}
into the equation for V_{OUT}:
V_{OUT}=-\frac{V_{IN}}{1-D}\cdot D
Thus, the DC voltage conversion ratio of the Ćuk converter is:
\boxed{\frac{V_{OUT}}{V_{IN}}=-\frac{D}{1-D}}
Interpretation
Output Polarity
The negative sign indicates that the output voltage polarity is inverted relative to the input. Although the input and output share the same ground reference, the Ćuk converter produces a negative output voltage.
Output Voltage Magnitude
|V_{OUT}|=\frac{D}{1-D}\times V_{IN}
Depending on the duty cycle D:
-
D < 0.5 → Step-down operation
|V_{OUT}| < V_{IN}
-
D = 0.5 → Equal magnitude
|V_{OUT}| = V_{IN}
-
D > 0.5 → Step-up operation
|V_{OUT}| > V_{IN}
Related Products
Additional References
More Cuk Converter Articles
Cuk Applications
- Cuk Converter: Analysis of Cuk LED Driver Implementation (MOSFET Version)
- Cuk Converter: Analysis of Cuk LED Driver Implementation (GaN Version)
- Cuk Converter: How to Resolve Current Overshoot During Cuk PWM Dimming?
Cuk Operating Principles
- Cuk Converter: Energy Flow Breakdown & Component Functions during Switch ON/OFF
- Cuk Converter: Comprehensive Analysis of Typical Operating Waveforms
- Cuk Converter: Derivation of Negative‑Output‑Voltage Formula
- Cuk Converter: Cuk vs SEPIC Topology – Pros, Cons and Differences in Coupling Capacitor Operation