# Switch Mode Power Supplies - The Cúk SMPS.

In 1978, the US Patent Office granted Dr Slobodan Cúk of CalTech (pronounced Chook) a patent for the design of a new SMPS topology. The benefits of his new topology include increased efficiency, low input and output current ripple, minimal RFI and small size and weight.

The series of diagrams below shows how the Cúk circuit is derived.

Firstly, consider a boost converter followed by a buck converter:

If the diodes are thought of as switches, then the two switch-and diode sets could be replaced with a DPDT switch:

The DPDT switch and shunt capacitor can be replaced with an SPST switch and series capacitor, providing that a reverse of output polarity is accepted:

The circuit is an example of a Cúk SMPS. A practical realisation could be as follows:

The DC voltage transformation ratio M is M=D/D', where D is the duty ratio (fractional on-time) of the transistor switch operated at a switching frequency 1/Ts, and D'=1-D is the complementary duty ratio (fractional offtime). For a DC input voltage Vi, the output voltage is Vo=MVi. The converter thus has a step down ratio for D < 0.5 and a step-up ratio for D > 0.5. The other principal feature is that both the input and output currents are non-pulsating, both being smoothed by the input and output inductors. These inductors also eliminate current surges in the transistor switch at power-on and power-off, which is often a difficult problem to solve.

Theoretically, the output capacitance C2 is not needed, but is usually included to absorb the load current fluctuations. The Cúk converter is unique because energy transfers capacitively from the input to the output, instead of inductively as in all previous converters.

A capacitor of 1uF charged to 50V has a stored energy of 1.25mJ, equal to an inductor of 2.5mH passing 1A. The size of a 1uF 50V capacitor, however, is considerably smaller than a 2.5mH 1A choke. Therefore capacitive energy transfer is more effective on a per unit size or weight basis than inductive energy transfer.

Because the input and output inductor currents are essentially constant, the switching current is confined entirely within the converter in the transistor-coupling capacitor-diode loop. With careful layout, this loop can be made physically small, which will reduce the radiated RFI from the magnetic field. In addition, the voltage and current waveforms in this converter are particularly clean, with very little ringing or overshoot; very little snubbing is needed.

Cúk References

• S. Cúk and R.D. Middlebrook, "A New Optimum Topology Switching DC-to-DC Converter", IEEE Power Electronics Specialist Conference 1977 pp 160-179.
• S. Cúk and R.D. Middlebrook, "Coupled Inductor and Other Extensions of a New Optimum Topology Switching Converter", IEEE Industrial Applications Society Annual Meeting, 1977 pp 1110-1126.
• S. Cúk and W.M. Polivka, Analysis of Integrated Magnetics to Eliminate Current Ripple in Switching Converters, Power Conversion International Proceedings, 1983 pp 361-386.

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