# Selecting Your Boost Converter Inductance

January 3, 2014

A battery alone may not be capable of supplying complex systems with all the voltage rails necessary to function properly. Applications such as automotive LED drivers, audio amplifiers, and telecommunications, to name a few, require boost converters to create a higher output voltage from a lower input. To the boost converter designer, it may not be obvious whether or not the converter should be designed to operate in continuous conduction mode (CCM), discontinuous conduction mode (DCM), or a combination of both.

Boost converters come in many shapes and sizes, with a wide range of power levels and boost ratios. These requirements determine whether the boost is best designed to operate in CCM or DCM. In DCM, the inductor current ramps up from zero when the FET is on and fully discharged back to zero again before the next switching period. But in a non-synchronous CCM boost, the inductor's current is always greater than zero when current is ramping up, as well as when ramping down and discharging the inductor's stored energy into the output capacitor and load.

In CCM, the duty cycle is constant with loading, but varies with input voltage. In most CCM designs, below a certain minimum load, the operating mode transitions to DCM because the inductor current eventually decreases to zero before the next switching cycle.

In most cases, high-power boost converters are designed to operate in CCM, and low-power boosts operate in DCM. This is because CCM allows lower peak currents throughout the entire circuit, which typically results in lower circuit losses. One exception may be in the output rectifier for high-voltage boosts, such as in a PFC where reverse-recovery currents can induce additional losses. Generally these losses can be handled with a high quality (fast) rectifier.

If operating in DCM, expect to see peak inductor currents that are two times larger than in CCM, but could be much higher if the inductance value is purposely reduced. These higher currents increase the rms currents in the input and output capacitors and can add to the switching losses in the FET, which results in larger (or more) components to handle the additional stresses. This disadvantage alone often outweighs the other advantages DCM offers at high power.

While the inductor's rms current is higher in DCM, its wire resistance is usually much lower, so the copper losses tend to be the same or less than CCM. But the core losses in DCM are greater at high-power levels. Sometimes this can make the often hyped benefit of reduced inductor size invalid because a larger core may be necessary to handle these added losses. But where DCM really shines is at lower power levels, where the added stresses in the capacitors and FET don't necessarily require larger components and a smaller inductor can work.

An added benefit of DCM is when operating at high boost ratios, where CCM operation requires large on-times; the inductance can be decreased in value to allow a reduced on-time (along with higher peak currents). This is desirable because controllers often run into their maximum controllable on-time (or minimum off-time) limits and skip pulses. This way, the designer can fine tune the on and off times to the controller's workable range. Additionally, the control loop behavior in DCM is better than that of CCM because of the lack of a right-half plane zero, which can translates into superior transient performance.

Sometimes the effects of the RHPZ can be minimized by reducing the inductance value, which pushes it to a higher frequency where it has less of an impact. All CCM boosts operate in DCM under some conditions, whether it is at light loading, startup, or during a transient condition. This is perfectly acceptable, but it's a good idea to know the conditions where this occurs.

Figure 1 is a graph of the inverse boost ratio (VIN/VOUT) versus the duty cycle terms (Dx(1-D)^{ 2}) in the inductance equation (Equation 1). This term is directly portional to the required inductance in a CCM boost. The peak of this plot occurs when the ratio of VIN/VOUT is 2/3, or when the boost ratio (VOUT/VIN) is 1.5 [1]. This may be a somewhat non-intuitive result. What this means is that in designs using a varying input voltage, there's a band of VIN/VOUT ratios that the circuit must operate between. If the range is wide and this band includes the peak for Figure 1, then the inductance should be calculated at the VIN/VOUT ratio of 2/3. If the band does not encompass the 2/3 point, then it should be designed at its relative peak ratio.

Figure 2 is an automotive LED driver application and uses a controller to regulate the output current rather than fixing the output voltage. This design operates over a band of 0.27 to 0.97 as shown by the dashed lines in Figure 1. Its inductance is calculated at the ratio of 2/3. Since the LED load current is constant, to select the necessary inductance, choose a design load current that's less than the actual load current. As long as the actual load current is greater than this chosen level, the converter operates in CCM.

In this example the LED current is 0.22A, and a critical conductional level of 0.15A was selected, which means that the converter should always operate in CCM. This level is a good balance between minimizing the required inductance and guaranteeing CCM operation. For this design, this equates to a calculated inductance of 68 uH. To verify that this inductance is correct, assign the constant K as equal to the term D(1-D)^{ 2} from the graph [2]. Substituting into Equation 1 and solving yields K in Equation 2. We can use the calculated value of K to determine our operational boundaries.

Figure 3 is a slight variation of Figure 1, with the horizontal axis converted to duty cycle rather than VIN/VOUT. It shows the calculated value of K for the design example using a 68-uH inductor and the reduced load current of 0.15A. This illustrates that the circuit's operation is always above the curve, indicating that it will operate in CCM under all input voltages. But, the circuit actually regulates the current at 0.22A, so the typical value for K is closer to 0.23. This is significantly higher on the curve and deeper into CCM, providing the margin intended.

As an example of another design point to visualize an unexpected operating condition, consider what would happen if a 33-uH inductor were used instead. This value could be selected, if it was calculated at VIN max or VIN min rather than the VIN related to the peak of Figure 1. With 33 uH, the corresponding value of K is 0.11 and is shown on Figure 3. Between operating duty cycles of 0.16 and 0.55 (28 VIN and 15 VIN, respectively), the circuit operates in DCM unintentionally, but operates in CCM outside those duty cycles. Since both modes have the different control loop characteristics, possible instabilities may result, if operating in multiple modes.

Boost converters can operate in CCM, DCM, or both with major dependencies on the input voltage and load. Calculating the required inductance to guarantee CCM operation involves knowing what input voltage (or duty cycle) to use in the calculation. For designs with a wide input range, use a VIN/VOUT ratio of 2/3 (D = 0.33). Existing designs can utilize the calculated value of K from Equation 2 to determine the operating mode from the D(1-D)^{ 2} curve. By properly sizing the inductor, unexpected issues may be avoided as well as having a better understanding of which mode or modes in which the boost is operating.

John Betten is an applications engineer and senior member of group technical staff at Texas Instruments, and has more than 28 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.

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