ELEC 87 Power electronics Study of flyback stepdown converter and comparison with buck converter Edmond Gheury Jonathan Goldwasser th May Abstract i D This paper will focus on the study of a flyback stepdown converter, operating in continuous and discontinuous current conduction modes and at the boundary between them. The influences of both the control variable D and the load resistance R load will be stressed out. A simple PSpice model will help us understand those concepts with explicit plots. N : N v C R load Nomenclature D Switch duty ratio Figure : Flyback converter η f s i o I o Efficiency of the converter Switching frequency Output current Average output current t off t on v Switch off-time Switch on-time Primary voltage i D Diode current Input voltage I D Average diode current v o Output voltage L L N N P d P load R load Primary inductance Secondary inductance Primary coil turns Secondary coil turns Average input power Average output load power Load resistance Average output voltage Introduction The purpose of this project is to study the flyback converter. The flyback converter is a stepdown switching DC power supply. Flyback converters are derived from buck-boost converters by adding a secondary winding to achieve electrical isolation, as shown in Fig..
Symbol Value Unit / /. Vdc L /L /.87 µh Coupling.999 / R load Ω t on /t off / µs f s khz.7.6 Table : Parameter values of our flyback converter.7.88 First, we will focus on continuous and discontinuous conduction modes. We will describe those modes and find the boundary between them. Next, we will compare our flyback converter with a buck converter, built from the components of the flyback converter, and determine which is more efficient. The parameter values of our flyback converter are gathered in Tab. v (V)..8.6.8.98.98.98.986.988.99.99.99.996.998. Figure : Continuous conduction mode v and v o Vo (V) Continuous current conduction mode In the continuous current conduction mode of operation, energy is stored in the magnetic field of the core and air gap during t on. However, not all of the stored energy is transferred to the secondary when the switch turns off and therefore the diode current never falls to zero during t off. So, the conduction is said to be continuous only when the demagnetization of the inductance core is incomplete. The voltage and current waveforms for the continuous current conduction mode are shown in Fig. and Fig.. During t on, the voltage applied to the primary equals and the diode is reverse biased. Hence, the current flowing in the load resistance is provided only by the capacitor. Next, the switch is turned off causing the current to flow in the secondary winding through the diode. This current decreases linearly during t off but never reaches zero during that time interval resulting in the trapezoidal waveform of Fig.. The voltage and current I o remain approximatively constant due to the peak detector effect of the Diode-RC circuit. The efficiency of the flyback converter can be determined using power dissipation markers in PSpice. The first marker is connected to the voltage source and the second one to the load resistance. The re- ID (A) 9 8 7 6.98.98.986.988.99.99.99.996.998 Figure : Continuous conduction mode i D
.98.98.986.988.99.99.99.996.998 9 Power dissipated in the load Power injected in the flyback converter 8 7 6 Power (W) Amplitude (V) Temps (s).... Frequency (Hz) Figure : Flyback converter efficiency η = 8.8% Figure : Fourier analysis of voltage v sults are shown in Fig.. The efficiency η is defined by η = P load P d For the flyback converter with D =. and R load = Ω, the average powers are D =.6 D =. P d =.9 W P load = 9.6 W D =. so the efficiency is D =. D =. D =. η flyback = 8.97% D =. D =. D =. D =. Figure shows a Fourier analysis performed on voltage v. As expected, harmonics around the switching frequency f s and its multiples are present in v. Boundary between continuous and discontinuous conduction modes In this section, we ll try to find the boundary between continuous and discontinuous current conduction mode. In order to achieve this, we first vary the switch duty ratio D while maintaining the load resistance at a value of Ω. Next, we vary the load resistance R load and keep the switch duty ratio at a constant value. In both cases, we plot the diode current waveforms. D =..98.98.98.98.98.98.98.98.98.98.98 Figure 6: Switch duty ratio variation. Switch duty ratio variation As the switch duty ratio decreases, the conduction is getting closer to discontinuous mode. Figure 6 shows diode current waveforms for several switch duty ratios. To determine an accurate value of the switch duty ratio that leads to a discontinuous current conduction mode, it s more suitable to rescale Fig. 6, as shown in Fig. 7. By looking attentively Fig. 7, we see that the boundary value of the switch duty ratio is between. and.. Further computations show that the value D B =.6 is the exact boundary between the two conduction modes of operation if R load = Ω.
.986.987.987.988.988.989.989.98.....8. D =...6 Rload =.7..... D =.. Rload =.8.98.98.98.98.98.98.98.98.98 Figure 7: Zoom on Fig. 6 Figure 9: Zoom on Fig. 8 Rload = 9 Rload =.. 8 D =. Rload =. Rload =. 7 6 Rload =. Rload =. Vo (V) Rload =.6 Rload =.7. Boundary Rload =.8 Rload =.9 Rload =.98.98.98.98.98.98.98.98.98.98.98 D =...... Io (A) Figure 8: Load resistance variation Figure : Output voltage versus output current. Load resistance variation In Fig. 8, the discontinuous current conduction occurs when the load resistance increases and, hence, the output load power decreases. This power reduction lowers the average diode current and results in a discontinuous mode of operation. A zoom of the area of interest of Fig. 8 is shown in Fig. 9. An accurate value of R LB can be found using a smaller step size in the parametric sweep simulation of PSpice. The value R LB =.7Ω was found using this technique. The boundary can also be visualized in a I o plane, as shown in Fig.. Here, we see that for higher output currents, the output voltage is independent of the current. Indeed, in a continuous mode of operation, the DC conversion ratio is = N D N D which is not a function of I o. When the output power becomes smaller, the output voltage does not remain constant, meaning that the mode of operation is now discontinuous. The variation in the output voltage can be avoided using a control loop to adjust the switch duty ratio.
.98.98.986.988.99.99.99.996.998..7.7.. v (V). Vo (V).88...6 ID (A).98.98.98.986.988.99.99.99.996.998.. Figure : Discontinuous conduction mode v and v o Discontinuous current conduction mode..98.98.986.988.99.99.99.996.998 Figure : Discontinuous conduction mode i D Typical waveforms of the discontinuous current conduction mode are shown in Fig. and Fig.. In this mode of operation, the inductor core flux reaches zero during t on so there is no current flow in either secondary or primary. Those dead-times lead to the sawtooth current waveform shown in Fig.. The flyback converter operating in the discontinuous conduction mode has the advantage of lower inductance requirement caused by lower peak current. This makes the converter smaller and cheaper. Another advantage of the discontinuous conduction mode is the elimination of the right half plane zeros which cause the system to be unstable []. i D i L i o Comparison with buck converter The basic circuit of Fig. constitutes a buck converter. To build a buck converter from the components of the flyback converter, we must choose which winding of the transformer to use. A greater inductance leads to a better low-pass filter and we therefore chose L to build the buck converter. Choosing L would have been cheaper. Now, we need to adapt D so that it results in the same DC-DC conversion as the one studied previously. Theoretically, the conversion ratio of a buck v oi L C Figure : Buck converter R load
.8.8.86.88.9.9.9.96.98. Power dissipated in the load Power injected in the buck converter.8 Power (W) 8.8 6.88.8 voi (V).8 vo (V).89 Temps (s).8 Figure : Buck converter efficiency η = 6.%.86 converter is = D which leads to D =. =.7. However, using PSpice, we found that the correct value of D should be D buck =. The efficiency of the buck converter was found using the same power dissipation markers technique. The value η buck =.78.66 = 8.9% is a little bit greater than one found for the flyback converter. Thus, the buck converter is cheaper for two reasons: reduced power losses and less components. Voltage and current waveforms for the buck converter are shown in Fig. and Fig. 6 6 Conclusion This project helped us understand the basic concepts of the flyback converter. Using PSpice, the voltage and current waveforms were easily obtained, especially for parametric sweep simulations. Continuous and discontinuous current conduction modes were clearly described and the influences of both the switch duty ratio and the load resistance were physically explained. io (A).8.8.8.86.88.9.9.9.96.98..8 Figure : Buck converter v oi and v o.8.7.6.....8.8.86.88.9.9.9.96.98. Figure 6: Buck converter i L 6
After having compared the flyback and buck converters, we conclude that, for a given DC-DC conversion ratio, the buck converter is more efficient and cheaper than the flyback converter. Nevertheless, the buck converter doesn t offer the advantage of electrical isolation, which is almost always required. Further steps in the study of a flyback converter will involve designs of control loops in order to avoid any voltage variation at the output. References [] K. I. Archask and B. Almukhtar. The design and development of a novel flyback planar transformer for high frequency switch mode DC DC converter applications. Microelectronics Journal, (-):99 9, December. [] P. Dananjayan, V. ShRam, and C. Chellamuthu. A flyback constant frequency ZCS ZVS quasiresonant converter. Microelectronics Journal, 9(8):9, August 998. [] Ned Mohan, Tore M. Undeland, and William P. Robbins. Power electronics. Converters, applications and design. John Wiley & Sons, Inc., third edition,. [] P. C. Sen. Principles of electric machines and power electronics. John Wiley & Sons, 996. 7