# SEPICs

### Overview

SEPIC (single-ended primary inductance converter) is a topology of switch-mode power supply (SMPS) which can both up and down-convert, similar to a buck/boost. It can be viewed as a boost converter followed by a buck-boost converter.

Like a [^Ćuk Converter], a SEPIC has one switch and two inductors. It’s advantages over a buck-boost alone is that is has a non-inverted output voltage, DC decouplement from input to out (through a series power-transferring capacitor), which makes it easier to handle things such as short circuits on the output, and true turnoff of the output (when the switch is off, the output truly goes to 0V).

Like other SMPS, the SEPIC converter uses a switching element of control the output. The power transferring capacitor between input and output is sometimes called the AC capacitor.

### Output Voltage

In continuous-conduction mode (CCM), the equation linking the input voltage $V_{IN}$, output voltage $V_{OUT}$ and duty cycle $D$ of a SEPIC is:

\begin{align} V_{OUT} = \frac{D}{1-D} V_{IN} \end{align}

Like before, this equation assumes all components are ideal. This equation is identical to the one for a inverting buck-boost except for the negative sign (a buck-boost inverts the output, while a SEPIC does not).

### Inductor(s)

The SEPIC has two inductors, just like the [^Ćuk Converter]. They can either be wound on separate cores and not share any magnetic field (uncoupled inductors), or be wound on the same core and share a magnetic field (a coupled dual-winding inductor). Using a coupled dual-winding inductor has the advantages of reducing the component count, and lowering the total inductance requirements, but can be hard to find for high-power requirements. Coupled inductors used in a SEPIC also benefit from some leakage inductance, which reduces the AC losses.

The equations are different for coupled and un-coupled inductor designs. For a coupled inductor, the equation to calculate the inductance $L$ is:

\begin{align} L = \frac{V_{IN}^2 d_{min}^2}{2f_s P_{OUT(min)}(1 + d_{min}\frac{1 - n}{n})} \end{align}

And for two uncoupled inductors:

\begin{align} L_1 = \frac{d_{min} V_{IN(max)}^2 n}{2f_s P_{OUT(min)}} \end{align} \begin{align} L_2 = \frac{(1 - d_{min}) V_{OUT}^2}{2f_s P_{OUT(min)}} \end{align}

The above equations determines the minimum inductance required for CCM operation at maximum input voltage and minimum load (the worst-case scenario for a SEPIC).

### Capacitor

Sometimes the AC capacitor needs a series RC snubber circuit to make the SEPIC stable. A low resistance between 1-10R and a large capacitance between 50-1000uF can sometimes fix this.

### Examples

The LT from Linear Technology can be used in a SEPIC configuration to control a series of high-power LEDs.