3. Discontinuous Conduction Mode - JoshSilver8/ENGR454_Buck_Converter GitHub Wiki
May 6, 2021
We have determined the goal of milestone is to better understand buck converters operating in discontinuous conduction mode. We did a fair amount of research from various sources listed below and have come to the realization that DCM control is not easy to implement. Our long-term goal is to be able to create a state space average model that allows us to control the buck converter in both CCM and DCM. Essentially this implies that we should be able to output a desired voltage across a wide range of load resistor values. In theory if one were to charge a phone or a laptop which both have very different load resistance, the controller could account for the variance accordingly.
To begin our investigation of varying load resistances we started with the output IV characteristics. The first equation we looked at was equation which gives us the maximum load resistance that will maintain CCM at various duty cycles. This left us with the following data.
| Duty Cycle | RMAX |
|---|---|
| 0.1 | 6.98E+01 |
| 0.2 | 7.85E+01 |
| 0.3 | 8.97E+01 |
| 0.4 | 1.05E+02 |
| 0.5 | 1.26E+02 |
| 0.6 | 1.57E+02 |
| 0.7 | 2.09E+02 |
| 0.8 | 3.14E+02 |
| 0.9 | 6.28E+02 |
Following this we attempted to graph the transition from DCM to CCM by increasing current. This was done in Python using numpy and Matplotlib libraries. We ran the Vout equations incrementing the duty cycle 9 times in order see the transition points at different duty cycles. The part we are still confused on is finding the correct Vout equation to model the DCM, we believe our next step will be to develop our own equations for Vout to correctly model this transition graph. We tried 5 different Vout equations from various sources and the best results which modeled the graph provided to us the best was equation 2 that can be seen in the code below. More research needs to be done here but the magnitudes of the graphs are concerning as we hit CCM at just 4mA which seems very low.
