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# SEPIC converter

A SEPIC (single ended primary inductor converter) is a DC-DC converter which allows the output voltage to be greater than, less than, or equal to the input voltage. The output voltage of the SEPIC is controlled by the duty cycle of the control transistor. The largest advantage of a SEPIC over the buck-boost converter is a non-inverted output (positive voltage). SEPICs are useful in applications where the battery voltage can be above and below the regulator output voltage. For example, a single lithium ion battery typically has an output voltage ranging from 4.2 volts to 3 volts. If the load requires 3.3 Volts, then the SEPIC would be effective since the battery voltage can be both above and below the regulator output voltage. Other advantages of SEPICs are input/output isolation provided by C1 and true shutdown mode: when the switch is turned off output drops to 0 V.

## Circuit operation

The basic schematic for a SEPIC is shown in Figure 1. As with other Switched mode power supplies, the SEPIC exchanges energy between the capacitors and inductors in order to change energy from one voltage to another. The amount of energy exchanged is controlled by S1, which is typically a MOSFET. MOSFETs are used instead of BJTs due to the extremely high input impedance and the low voltage drop across the MOSFET when turned on.

### Continuous mode

A SEPIC is in continuous mode if the current through the inductor L1 never falls to zero. In a SEPIC, during steady-state operation, the average of VC1 is Vin. Since C1 blocks DC current, the average of IC1 is zero. Since average IC1 is zero, the only source of the average load current is IL2. Therefore, the average current through L2 is the same as the average load current and is independent of the input voltage.

Looking at average voltages, the following can be written: $V_\left\{IN\right\} = V_\left\{L1\right\} + V_\left\{C1\right\} + V_\left\{L2\right\}$

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:

$I_\left\{D1\right\} = I_\left\{L1\right\} - I_\left\{L2\right\}$

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.

## Non-ideal circuit

The voltage drop and switching time of the diode (D1) is extremely critical. The switching time needs to be extremely fast in order to not generate high voltage spikes across the inductors, which could cause damage to components. Fast silicon or Schottky diodes can be used. The resistances in the inductors and the capacitors can also have large effects on the converter efficiency and ripple. Lower series resistance in the inductors allows for less energy dissipated as heat, which results in a large portion of the energy being transferred to the load. Low ESR capacitors should also be used for C1 and C2 to minimize ripple and prevent heat build up, especially in C1 where the current is changing direction frequently.

Excellent Design Guidelines from National Semiconductor in Application Note 1484

## References

Maniktala,Sanjaya. Switching Power Supply Design & Optimization, McGraw-Hill, New York 2005

SEPIC Equations and Component Ratings, Maxim Integrated Products. Appnote 1051, 2005.

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