Relevant Theory

As noted, the aim of this class was to learn the basic methods of electric power analysis and design which includes learning the characteristics of various electronic power switches and learning about different switching topologies. We also covered MPPT tracking briefly in class as it was useful for a large portion of the class who chose to do a solar project.

Maximum Power Point Tracking

Maximum power point tracking (MPPT) utilizes the known fact that the maximum power from a source is determined from the load resistance used to extract that information. In this way, you can experimentally find the MPPT of a solar panel by creating a plot of resistance vs power from the solar panel and finding the peak power at a specified resistance. The I-V characteristics of the solar panel can make it difficult to find that load resistance, however, since the curve can continually change as the intensity of the sun on the solar panel changes. Since the power in a circuit can be found through P = V*I, one can see how having V at a maximum and I at a maximum produces the maximum amount of power. Unfortunately, the maximum point only occurs at a specific load resistance. Noting the characteristic of the curve, any slight deviation of the load resistance can greatly decrease the power produced. Ideally, having a variable resistor that changed simultaneously to match the ideal resistance corresponding the MPP would be the best option. This could be done very easily in an AC circuit by using a transformer where the resistance across a transformer is given by Rp = N^2*Rs, where Rp is the resistance on the primary side and Rs is the resistance on the secondary side.

Interestingly, buck converters are essentially DC transformers. The typical buck converter topology is shown below. In switching mode converters, there are switches that switch on and off at a given frequency, f, with a given duty cycle, D. this switch is typically implemented by the use of a mosfet. Assuming that the circuit is in steady state and that the inductor is always positive and the capacitor is very large, then the switching period is T. This implies that the time the switch is closed is DT, and the time it is open is (1-D)T.

The closed switch analysis yields (deltaIL)closed = [(Vs-Vo)/L]DT and the open switch analysis yields (deltaIL)open = -(Vo/L)(1-D)T.

If we write (deltaIL)closed + (deltaIL)open = 0 => [(Vs-Vo)/L]DT - (Vo/L)(1-D)T = 0 => Vo = DVs

Essentially, this implies that we can treat the Duty cycle as a turns ratio if we think of it in terms of an AC transformer with the equation: Vs = (TurnsRatio)Vp

With regards to impedance, we can make the assumpton that Pin = Pout so that it is analyzed as an "ideal transformer", and therefore we can derive the following: Vs^2/Rin = Vo^2/RL => Vs^2/Rin = Vs^2(D^2/RL) => Rin(D^2) = RL

This means that we can change the resistance that our solar panel sees just by changing the duty cycle of the buck converter.

Synchronous DC-DC Buck Converters

Two main factors influence the decision to use a synchronous MOSFET instead of a diode.

• Duty cycle
• and output current. When duty cycle is low, then the low side switch carries the current during most of the switching cycle. That improves the gains and efficiency you would get by using a MOSFET instead of a diode. Remember that the diode always drops around 0.5 volts whereas the MOSFET drop could be less than 50 millivolts. THis means that the switching is much more efficient. When output current is higher than three amps the synchronous MOSFET becomes a better design decision, because few diodes can handle more than 1.5 watts of dissipation which is significantly lower than the 2.5 watts expected from 3A. (notes take from https://microchipdeveloper.com/desanl:synchronous-buck-converter-overview)

It's also important to note that the two mosfets must NOT be on at the same time. Consequently, a "dead" time is usually programmed into the switching pattern. During this dead time, the body diode of the LOW fet provides a conducting path for the current in the inductor. It is typically operated in continuous-current mode because it would allow the inductor current to go negative, but a Discontinuous current mode is also possible.