Looking at average voltages, the following can be written:
and since the average voltage of VC1 is equal to VIN, VL1 = −VL2. For this reason, the two inductors can be wound on the same core. Since the voltages are the same in magnitude, their effects of the mutual inductance will be zero, assuming the polarity of the windings is correct. Also, since the voltages are the same in magnitude, the ripple currents from the two inductors will be equal in magnitude.
The average currents can be summed as follows:
When switch S1 is turned on, current IL1 increases and the current IL2 decreases (becomes more negative). The energy to increase the current IL1 comes from the input source. Since S1 is a short while closed, and the instantaneous voltage VC1 is approximately VIN, the voltage VL2 is approximately −VIN. Therefore, the capacitor C1 supplies the energy to decrease (more negative) the current IL2.
When switch S1 is turned off, the current IL1 becomes the same as the current IC1. Also, since inductors do not allow instantaneous changes in current, the current IL2 will continue in the negative direction. From Kirchoff's Current Law, it can be shown that ID1 = IC1 - IL2. It can then be concluded, that while S1 is off, power is delivered to the load from L2 and L1. C1, however is being charged by L1 during this off cycle, and will in turn recharge L2 during the on cycle.
The capacitor CIN is required to reduce the effects of the parasitic inductance and internal resistance of the power supply. The boost/buck capabilities of the SEPIC are possible because of capacitor C1 and inductor L2. Inductor L1 and switch S1 create a standard boost converter, which generate a voltage (VS1) that is higher than VIN, whose magnitude is determined by the duty cycle of the switch S1. Since the average voltage across C1 is VIN, the output voltage (VO) is VS1 - VIN. If VS1 is less than double VIN, then the output voltage will be less than the input voltage. If VS1 is greater than double VIN, then the output voltage will be greater than the input voltage.
SEPIC Equations and Component Ratings, Maxim Integrated Products. Appnote 1051, 2005.
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