# Benefits of a coupled-inductor SEPIC converter

**Abstract**

The single-ended primary-inductor converter—the SEPIC converter—is capable of operating from an input voltage that is greater or less than the regulated output voltage. Aside from being able to function as both a buck and boost, the SEPIC design also has minimal active components, a simple controller, and clamped switching waveforms which provide low noise operation.

It is often identified by its use of two magnetic windings. These windings can be wound on a common core, in the case of a single dual-winding coupled inductor, or they can be two independent inductors. Designers are often unsure of which approach is best and whether there is any real difference between the two. This article looks at each approach and discusses the impact each has on a practical SEPIC converter design.

**Circuit operation**

** Figure 1** shows the basic SEPIC converter with a coupled inductor. When the FET (Q1) turns on, the input voltage is applied across the primary winding. Since the winding ratio is one-to-one, the secondary winding is also imposed with a voltage equal to the input voltage.

*Figure 1: The basic coupled inductor SEPIC converter. *

But because of the polarity of the windings, the anode of the rectifier (D1) is pulled negative and reversed bias. With the rectifier biased off, the output capacitor is now required to support the load during this on-time period. Additionally, this forces the AC capacitor (C_ac) to be charged to the input voltage.

While Q1 is on, current flow in both windings is through Q1 to ground, with the secondary current flowing through the AC capacitor. The total FET current during the on time is the sum of the input current and the output secondary current.

When the FET turns off, the voltage on the windings reverses polarity to maintain current flow. The secondary winding voltage is now clamped to the output voltage when the rectifier conducts to supply current to the output. Through transformer action, this clamps the output voltage across the primary winding. The voltage on the drain of the FET is clamped to the input voltage plus the output voltage. Current flow during the FET off time for both windings is through D1 to the output, with the primary current flowing through the AC capacitor.

**Balancing volt-microseconds**

The circuit operates similarly when the coupled inductor is replaced with two discrete inductors. For the circuit to operate properly, volt-microsecond balance must be maintained across each magnetic core. That is, the product of the inductor’s voltage and time must be equal in magnitude and opposite in polarity during the FET on and off times.

It can be algebraically shown that the AC capacitor voltage, for separate inductors, is also charged to the input voltage (**Reference 1**). If we consider the output-side inductor first, it is clamped to the output voltage during the FET off time, as was the secondary winding of the coupled inductor. During the FET on time, the AC capacitor imposes a potential equal to the input voltage but opposite in polarity across the inductor.

With defined voltages clamped across the inductor for each interval, balancing the volt-microseconds determines the duty cycle (D). This is simply:

D = Vo / (Vo + V_{IN}),

for continuous conduction mode (CCM) operation. The voltage imposed across the input side inductor is equal to the input voltage when the FET is on.

When the FET is off, volt-microsecond balance is maintained by clamping Vout across it. It is easy to remember that when the FET is on, the input voltage is applied across both inductors and when the FET is off, the output voltage is imposed across both. The voltage and current waveforms of the two discrete inductor SEPIC converters are quite similar to that of the coupled inductor version. So much so, that it would be difficult to tell them apart.

**Two versus one?**

If there is little difference in circuit operation, does it matter which one to use? A single coupled inductor is often selected due to its reduced component count, better integration, and lower inductance requirement compared to using two single inductors.

However, the limited selection of higher-power off-the-shelf coupled inductors poses a problem for power-supply designers. If they choose to design their own inductor, they must specify all pertinent electrical parameters as well as deal with longer lead times. Coupled inductors can benefit from leakage inductance, which is beneficial in reducing ac current losses (**Reference 2**). Coupled inductors must have a 1:1 turn ratio for volt-microsecond balance.

Choosing to use two separate inductors typically offers a much broader selection of off-the-shelf components. Since the currents and even the inductance for each inductor are not required to be identical, different component sizes can be selected for each, providing greater flexibility.

** Equations 1 through 3** show the calculations for inductance for both coupled and separate inductors. The equations determine the minimum inductance necessary for CCM operation at maximum input voltage and minimum load. Comparing these equations at 50 percent duty cycle operation (which occurs when V_{IN} equals V_{OUT}) and unity efficiency, the value calculated for the coupled inductor in **Equation 1** is twice that of separate inductors.

Since the converter will certainly have losses and most input-voltage sources vary quite a bit, this simplified inductance generalization is usually false, but it’s often adequate for all but extreme cases. It usually means that the converter will enter DCM operation slightly sooner (or later) than expected, which in most cases, is still acceptable.

As previously mentioned, with separate inductors, it is not necessary that the output-side inductor be the same value as the input-side inductor, as is often assumed, but can certainly be done for simplicity sake. The output-side inductor’s value can simply be determined by scaling the input-side inductor by V_{OUT}/V_{IN}. The benefit of using a lower-value output-side inductor is that it is typically smaller and lower cost.

**Example design**

The specifications shown in **Table 1** are the basis for a design comparison. The first design uses a coupled inductor and the second uses two separate inductors. This design is typical of an automotive input voltage range with an output power of 64 W.

*Table 1: Prototype SEPIC electrical specification*

** Equation 1** determines the coupled inductor requires an inductance of 12 μH, with a combined current rating of 13 A (based on I_{IN} plus I_{OUT}). This design poses a particular challenge because of the limited selection off-the-shelf inductors. Therefore, a custom inductor from RENCO was specified and designed.

This inductor was wound on a split-bobbin to intentionally introduce leakage inductance to minimize circulating currents which can induce losses. These losses are due to the AC capacitor ripple voltage being imposed across the leakage inductance. For designs of lower power, coupled inductors from Coilcraft (MSS1278 series) and Coiltronics® (DRQ74/127 series) offer good off-the-shelf alternatives. For the separate inductor design, a 33 μH Coilcraft SER2918 was used for L1 and a 22 μH Coiltronics HC9 was selected for L2.

Each was chosen based on winding resistance, current rating and size. Care must be taken when selecting the inductors because core and AC winding losses must also be considered. These losses reduce the inductor’s allowable DC current, but not all vendors provide adequate information to calculate this. Failure to properly calculate this could greatly increase core temperature beyond the typical 40°C rise, decrease efficiency, and hasten premature failure.

** Figure 2** show the prototype SEPIC schematic with a coupled inductor. To implement the separate inductors in the design, the coupled inductor was simply replaced with two inductors on the same PWB. **Figure 3** shows both prototype circuits, with L1 occupying the space of the coupled inductor and L2 in the upper right corner.

** **

*Figure 2: A 16V/4A SEPIC converter schematic with coupled inductor*** **

*(click here to enlarge).*

*Figure 3: Coupled inductor (left) and dual-inductor (right) *

*SEPIC converter prototypes.*

As expected, both circuits operated in a nearly identical fashion, with the switching voltage and current waveforms being essentially the same. But there were several key differences in performance. While the control loop for the coupled inductor design was quite benign, the separate inductor design was initially unstable.

Measurement of the loop gain determined that a high-Q, low-frequency resonance was the culprit, requiring the addition of a damping R/C filter in parallel with the AC capacitor. The resonant frequency, while greatly simplified, appeared to be approximately 1/2π√[Cac×(L1+L2)]. The SEPIC circuit has a quite complex control loop characteristics, necessitating the use of mathematical tools for detailed analysis because the analytical results are often difficult to interpret. Adding this R/C damping filter (220 μF/2 Ω) adds cost, circuit area, and losses.

This is in addition to the 10% area premium that two inductors require over a single, coupled inductor. **Figure 4** shows the measured efficiency for both circuits. It can be seen that there is an across the board boost in efficiency of up to 0.5% for the coupled-inductor design.

This is likely due to lower overall core losses in the coupled inductor design, since its DC wiring losses were actually higher than that of the dual inductor design. L2 uses a powered iron core material, which tends to have higher losses than the ferrite material used for L1 and the custom coupled inductor (**Reference 3**). While ferrite material for L2 could have been used, it would have resulted in a larger area.

** **

*Figure 4: Both coupled and separate Inductors *

*achieve good efficiency.*

**Summary**

The SEPIC converter can be successfully implemented with either dual inductors or a single coupled inductor. Improved efficiency, reduced circuit area, and more benign control loop characteristics are benefits realized in the prototype hardware when using a properly wound, custom-coupled inductor. While custom components are less desirable than off-the-shelf parts, many coupled inductors are readily available, albeit in smaller sizes. If time-to-market is critical, separate inductors provide greater flexibility to the designer.

**References**

1. Balance volt-microseconds for L1 and L2:

L1: DVin = (1-D)(Vcap+Vout-Vin)

L2: (1-D)Vout = DVcap

Vout = VcapD/(1-D)

Substitute L2 equation into L1 equation:

DVin = (1-D)(Vcap+VcapD/(1-D)-Vin)

DVin = (1-D)Vcap+VcapD -(1-D)Vin

DVin = (1-D)Vcap+VcapD -Vin+DVin

Vin = (1-D)Vcap+VcapD

Vin = Vcap-DVcap+VcapD

Vin = Vcap

2. John Betten, “SEPIC Converter Benefits from Leakage Inductance,” *PowerPulse.Net*, Design Features, May 27, 2010.

3. Robert Kollman, “Don’t get burned by inductor core loss,” *Power Management Designline*, July 13, 2009.

To learn more about this SEPIC converter and other power solutions, visit: www.ti.com/power-ca.

**About the Author**

** John Betten** is an Applications Engineer and Senior Member of Group Technical Staff at Texas Instruments, and has more than 25 years of AC/DC and DC/DC power conversion design experience. John received his BSEE from the University of Pittsburgh and is a member of IEEE. You can reach John at ti_johnbetten@list.ti.com.