# Slope Compensation for Mild Inductor Saturation

Aug. 1, 2006
Peak current control has long been a popular PWM method in switching power supplies and has the equally well-known characteristic that when operating in continuous conduction mode

Peak current control has long been a popular PWM method in switching power supplies[1] and has the equally well-known characteristic that when operating in the continuous conduction mode, for duty cycles greater than 50%, slope compensation is needed to ensure stability.[2] That is, an extra compensating slope must be added to the normal current upslope to prevent instability in the switching cycle.

Slope compensation is a function of both upslope and downslope. For linear inductance, the minimum amount of slope compensation is half the difference between the magnitude of the current downslope and the current upslope.

For example, if the duty cycle (D) is 66.7%, or D = 2/3, then:

giving a slope compensation of 0.5. This is shown in Fig. 1.

For D = 0.8, the downslope is 4 times the upslope, so the minimum slope compensation is then 1.5 times the current upslope. These numbers are the absolute minimum slope compensation needed to assure stability. This means that any PWM disturbance will not grow with time, but conversely, neither will any disturbance die down. However, if slope compensation is always more than needed, any disturbance will die down; the more the slope compensation, the quicker disturbances die down.

In the design of switching converters, great effort is usually taken to assure that the inductance never gets anywhere near saturation because of the fear of nonlinear anomalies. This usually means that the inductor is designed for absolute maximum load current, the lowest input voltage (where current is the greatest) and maximum core temperature (where the saturation flux density is the lowest). The result of this worst-case design is that the inductor is often substantially larger than otherwise needed.

Concern about inductor saturation may be appropriate if the core's air gap is small or nonexistent, because the core can rapidly enter saturation and inductor current can have an abrupt and enormous peak. However, if the core has a large air gap, which is often the case, it enters saturation in a gradual manner. If this is the case, then some small amount of saturation might be acceptable and the inductor can be smaller.

The whole purpose of the inductor in a switching converter is to store and release energy as efficiently as possible. When the inductor enters saturation, the upslope of the current ramp increases, which means that the inductance is decreasing. However, a partly saturated core continues to store energy, the majority of which can be recovered during the downslope.

The increase in current upslope at the onset of saturation might appear to reduce its slope compensation requirements because it seems to be peforming the same function as slope compensation. However, the rule for figuring the amount of slope compensation for slightly saturated inductors is the same as for linear inductors: Minimum slope compensation is half the difference between the downslope and upslope at the point where the inductor current crosses the current threshold.

Suppose, for example, the duty cycle is 66.7% (D = 2/3), but the inductor core is entering gentle saturation such that its incremental inductance is half of its linear inductance at the current threshold level. Both the upslope and downslope of the current in the vicinity of the current threshold will then be twice their respective slope values, as shown in Fig. 2.

For these higher slopes, the minimum required slope compensation is equal to 1, or twice that required for a linear inductor. This may not be such a big disadvantage because the slope compensation can be set to the minimum needed for this mild saturation case, which is rarely encountered. Then this slope compensation is much greater than needed for the usual linear current ramps and any transient disturbances die out very rapidly.

Permitting mild saturation in rare worst-case situations and using this compensation scheme allows a smaller and possibly lower-cost inductor core. To account for real-world tolerances, an inductor core with mild saturation might be defined as having a linear or constant inductance up to a specific current level, and if ramp time needed to reach that current is extended by an additional 10% to 15%, then the incremental inductance drops to half.

### References

1. Deisch, Cecil. Patent #4148097, “DC to DC Converter Utilizing Current Control for Voltage Regulation,” April 3, 1979.

2. Deisch, Cecil. “Simple Switching Control Method Changes Power Converter into a Current Source,” Power Electronic Switching Conference (PESC), 1978.

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