# Critical Current Control (C3) and Modeling of a Buck Based LED Driver with Power Factor Correction

ABSTRACT

Buck converter has a good aptitude for LED driver application. Here a new technique introduced to control and model a buck converter in the closed loop condition using Lagrange equation. To improve the final model accuracy, parasitic elements of the converter are taken into account. The main advantage of this method is its novelty and simple implementation. Also, the converter power factor has improved under critical current control (C3) technique. Frequency response and step response of the small signal model are derived and analysed. The theoretical predictions are tested and validated by means of PSIM software. Finally, precise agreement between the proposed model and the simulation results has obtained.

INDEX TERMS:

1. Power factor correction
2. LED driver
3. Buck converter
4. Small signal model.
5. critical current

CIRCUIT DIAGRAM Fig. 1. Converter overall circuitry by C3 method in the PFC mode

SIMULATION RESULTS  Fig. 2. Converter source current and voltage along with each other Fig. 3. Reference current, input voltage and current after the bridge Fig.4. Harmonic contents of the converter input current Fig.5. Output voltage at the start-up moment Fig.6. Output capacitor current Fig.7. Load change effect on the converter input current

CONCLUSION

This paper analyses a buck based LED driver with improved power factor. Power factor correction is done using critical current control (C3) or borderline conduction mode (BCM). Also, the Lagrange differential equations are employed here as an efficient tool for switching converter modeling in the closed loop condition. The proposed modeling technique gives the designer better intuition about the circuit under study rather than traditional state space averaging (SSA) method. SSA is a tedious and fully mathematical tool for switching converters modeling. In addition, parasitic elements of the converter have taken into account so it helps to select the circuit parts value correctly before manufacturing process. Dynamic behaviour of the converter is analysed in both frequency and time domain such as transfer functions and step response. A PI compensator is employed in the closed feedback loop to stabilize and modulate the reference current amplitude corresponding to the demanded power. Since this method relying on the averaging method, then the final model is reliable from 0 Hz up to half of switching frequency according to the Nyquist theorem. Finally, the simulation results confirm the proposed model exactness and indicate the rapidity of system step response under compelling conditions.

REFERENCES

• Jardini J.A. et al., Power Flow Control in the Converters Interconnecting AC-DC Meshed Systems, Przegląd Elektrotechniczny, 01(2015), 46-49.
• Gajowik T., Rafał K., Bobrowska M., Bi-directional DC-DC converter in three-phase Dual Active Bridge Topology, Przegląd Elektrotechniczny, 05(2014), 14-20.
• Kazmierczuk M.K., Pulse Width Modulated DC-DC Power Converters, Wiley, Ohio, 2008.
• Ben-Yaakov S., Average simulation of PWM converters by direct implementation of behavioural relationships, IEEE Conf. , APEC, 1993, San diego, CA., 510-516.
• Shepherd W., Zhang L., Power Converter Circuits, Marcel & Dekker Inc., New York, 2004.