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Maximising the coupled inductor technology

Posted: 12 Dec 2014 ?? ?Print Version ?Bookmark and Share

Keywords:Coupled inductors? current-ripple cancellation? MOSFETs? capacitors? magnetics?

Coupled inductors are typically utilised in multi-phase topologies to take advantage of the current-ripple cancellation from magnetic coupling between the phases. Normally, current-ripple cancellation happens only at the output of the multi-phase buck converter when typical discrete inductors are used. When these inductors are magnetically coupled, the current-ripple cancellation is applied to all elements of the circuit: MOSFETs, inductor windings, PCB traces.[1-6] Thus, the switching from all the phases affects each single phase, so the current ripple is reduced in amplitude and multiplied in frequency. Reduction in the RMS of the waveforms can improve the efficiency of the power converter or be traded for smaller magnetics, faster transient and, therefore, smaller output capacitance.

Coupled inductors vs. traditional inductor designs
The peak-to-peak current ripple in a traditional uncoupled buck converter can be expressed as Equation 1, where VIN is input voltage, VO is output voltage, L is the inductance value, D is a duty cycle (D = VO/VIN for a buck converter), and Fs is a switching frequency.

Equation 1

The current ripple in a buck converter with coupled inductors changes to Equation 2, for D [6] This particular equation is limited to D IN = 12V to core (0.5V to 2.5V). Equation 2 allows you to easily see how circuit and magnetics parameters affect current-ripple cancellation.

Equation 2

The additional multiplier in Equation 2, as compared to Equation 1, depends on application conditions. It changes due to duty cycle, coupling, and the number of coupled phases. Figure 1 shows normalized current ripple in discrete and coupled 210nH inductors in a 4-phase buck converter. The current ripple is normalized by a maximum current ripple: ripple in discrete inductor at D = 0.5 (so the normalized current ripple in a discrete inductor is 1 at D = 0.5). A typical application of 12V to 1.8V relates to the D = 0.15, as marked on the plot.

 Normalized current ripple for a 4-phase buck converter

Figure 1: Normalized current ripple for a 4-phase buck converter: discrete 210nH and coupled 210nH inductors with different coupling coefficient Lm/L.

 Normalized current ripple for a 4-phase buck converter

Figure 2: Normalized current ripple for a 4-phase buck converter: discrete 210nH and coupled 50nH inductors with different coupling coefficient Lm/L.

Figure 1 illustrates the dramatic current-ripple cancellation in all the power circuitry due to the coupled inductors. Notice that there are duty-cycle values where the benefit is significantly larger than around D = 0.15. Several plots for the coupled inductor illustrate the impact of the coupling coefficient Lm/L: for the practical coupling in Lm/L = 37 range, and some idealized and not realistic values Lm/L as 10 and 100. Assuming that the initial design with discrete inductors was reasonable and had acceptable current ripple, it makes sense to decrease the inductance value for the coupled inductor to achieve approximately the same current ripple around the targeted area D = 0.15. A value of 50nH/phase provides a similar current ripple as a discrete 210nH in this condition (figure 2).

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