In the following thesis the operation of power converters is showed and demonstrated by both steady-state analysis and Fourier-method. In the simplest case of a Buck converter, the use of the Fourier method is possible, but much more complicated. Using steady-state analysis, key attributes of the converter are detailed, such as its operation modes, dynamics and output fluctuations. This model was supported by Matlab Simscape circuit oriented simulations. Since Simscape is limited in terms of parameter freedom (as an example, realizing closed feedback would be hard), the converter’s Variable Structure State Space Model is thoroughly derived and detailed - first in continuous case, later discretized using Finite Difference Method. This approach could also handle both the steady and the transient state of the system. It is also possible to drive the system with a stair signal and map the non-ideal Duty Ratio to Output Voltage characteristics. The control methods are mentioned and briefly detailed, with exceptional attention to the Discrete PI Control. The rising problems during discretization are fully detailed, as among others the inability to accurately reach a certain duty ratio and the importance of the increment buffer.
A two channel Buck Boost converter was built on a prototyping board which was our main goal. Although during the process, several problems occurred, most of them were solved. The inverting output was limited, as the driver could not handle negative voltages. Another channel was built by cascading a Buck and a Boost converter together, this was capable of consistently producing a voltage from 12 V to 25 V.
One problem of our model that remains unsolved, is the non-linearity of the measured output voltage. The control was implemented by using a PIC24FJ128GA010. A microcontroller Analog Digital Converter (ADC) requires a voltage of 0-3.3V, but the converter produced either from 0-(-8V) or 0-25V by their respective channels. The conversion between the two voltage levels was achieved by a parallel voltage division branch, and the divided voltage was further processed using an operational amplifier. The inversion of this circuit was corrected by the controller using fixed value, by dividing the output voltage and the ADC input. When the voltages varied (such as the supply voltage), this transfer ratio changed as well. The occurring error is not drastic, for example when the supply voltage changed from 16.6 V to 12V, it resulted in 3%.. The PI control was supplemented by saturation to the maximum duty ratio (so that it can never go beyond the tipping point of the D-Vo), it may achieve an adaptive tolerance based on the actual duty cycle. According to our experiments during measurements at low loads the losses were high due to the diode voltage drops, while increasing the load and using Schottky diodes greatly enhanced efficiency. As the modelling methodologies grew in complexity and the diode losses were reduced, the results converge.