A Risk-Free Path to Power System Design - Building Power Design Success

A single battery may not be able to provide all the voltage rails needed for a complex system to function properly. Applications such as automotive LED drivers, audio amplifiers, and telecommunications require a boost converter to convert a lower input voltage to a higher output voltage. It can be unclear to boost converter designers whether 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 a variety of shapes and sizes, supporting a wide range of power levels and step-up ratios. These requirements determine whether the boost converter is best suited to operate in CCM or DCM. In DCM, the inductor current starts to rise from zero when the FET turns on and is fully discharged to zero before the next switching cycle arrives. But in the case of non-synchronous CCM boost, the inductor current is always greater than zero, whether the current is rising, falling, or releasing the energy stored in the inductor to the output capacitor and load.

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

In most cases, high power boost converters operate in CCM, while low power boost is done in DCM. This is because CCM allows lower peak current to flow through the entire circuit, which usually results in lower circuit losses. However, there may be exceptions in the output rectifier of high voltage boost conversion, such as in PFC, where reverse recovery current causes more losses. This loss can usually be handled by using a high quality (fast) rectifier.

If operating in DCM, you will see twice the peak inductor current of CCM, but if the inductance value is intentionally reduced, the current can be much higher. These higher currents not only increase the RMS current in the input and output capacitors, but also increase the switching losses in the FETs, thus requiring larger (or more) components to handle the additional stress. This disadvantage alone often overshadows the other advantages that DCM provides at high power.

Although the inductor RMS current is higher in DCM, its wire resistance is typically much lower, so copper losses tend to be the same or lower than in CCM. However, core losses in DCM are greater at high power levels. Sometimes a larger core may be required to handle these increased losses, which can overshadow the often-excited “smaller inductor size” advantage. Where DCM really shines is at lower power levels, where the increased stress in capacitors and FETs does not necessarily require larger components, but a smaller inductor can do just that.

An additional benefit of DCM is that when operating at high step-up ratios (where CCM operation requires a lot of on-time), the on-time can be reduced (with higher peak current) by reducing the inductor value. This is very good because the controller will often reach the maximum controllable on-time (or minimum off-time) limit and skip pulses. This allows the designer to fine-tune the on- and off-times based on the controller's operable range. In addition, the control loop performance of DCM is better than CCM because there is no right-half-plane zero, which translates into excellent transient performance.

Sometimes the effect of RHPZ can be minimized by reducing the inductor value, and we can push RHPZ to a higher frequency where it has less effect. All CCM boosts can operate in DCM under certain conditions, whether at light load, startup, or in transient conditions. This is perfectly acceptable, but the conditions under which this occurs should be understood.

Figure 1 is a graph comparing the reverse boost ratio (VIN/VOUT) and duty cycle (D×(1-D)²) in the inductor equation (Equation 1). This term is proportional to the required inductance in a CCM boost converter. The peak in this graph occurs at a VIN/VOUT ratio of 2/3 or a boost ratio (VOUT/VIN) of 1.5[1]. This can be a bit counterintuitive. What it means is that in a design with a varying input voltage, the circuit must operate within a range of VIN/VOUT ratios. If that range is very wide and that range includes the peak in Figure 1, then the inductor should be calculated at a VIN/VOUT ratio of 2/3. If that range does not include the 2/3 point, then it should be designed at its relative peak ratio.

Figure 1. The maximum inductance required for CCM occurs when VIN/VOUT = 2/3

Equation 1

Figure 2 is an automotive LED driver application that uses a controller to regulate the output current instead of fixing the output voltage. The design circuit operates in the 0.27 to 0.97 range, as shown by the dotted line in Figure 1. Its inductance should be calculated at the 2/3 ratio. The LED load current is constant, so to select the required inductance, you have to choose a design load current that is lower than the actual load current. As long as the actual load current is greater than this selected level, the converter will operate in CCM.

Figure 2. Example of LED boost converter design always operates in CCM with constant load.

In this example, the LED current is 0.22A and a critical conduction level of 0.15A is chosen, which means the converter should always operate in CCM. This level provides a good balance between minimizing the required inductance and ensuring CCM operation. For this design, this equates to a calculated inductance of 68uH. To verify that this is the correct inductance, the D(1-D)2 term in Figure [2] can be assigned to the constant K. Substituting this constant into Equation 1 and performing the calculation, the value of K can be calculated using Equation 2. We can use the calculated value of K to determine the operating boundary.

Equation 2

Figure 3 is slightly different from Figure 1, with the abscissa being duty cycle instead of VIN/VOUT. The figure shows the calculated value of K for the design example (with a 68uH inductor) and a reduced load current of 0.15A. We can see that the circuit operates above the curve, indicating that the circuit will always operate in CCM at all output voltages. However, the circuit can actually regulate the current to 0.22A, so the typical value of K is closer to 0.23. This is significantly higher than the curve and deeper into CCM, so it provides the required margin.

Figure 3. Duty cycle affects the operating mode of a boost converter.

As another example of a design point that can illustrate unexpected operation, it is important to consider what happens when a 33uH inductor is used instead. This value can be chosen if it is calculated by VIN max or VIN min, rather than by VIN relative to the peak of Figure 1. Since the inductor is 33uH, the corresponding value of K is equal to 0.11, as shown in Figure 3. Between operating duty cycles of 0.16 and 0.55 (corresponding to 28VIN and 15VIN, respectively), the circuit will inadvertently operate in DCM, and outside these duty cycles it will operate in CCM. Since the two modes have different control loop characteristics, proper instability may result if operating in multiple modes.

The boost converter can operate in CCM, DCM, or both, depending on the input voltage and load. When calculating the required inductance to ensure CCM operation, it is important to know the input voltage (or duty cycle) value used in the calculation. For designs with a wide input range, a 2/3 VIN/VOUT ratio (D = 0.33) should be used. Existing designs can determine the operating mode using the D(1-D)² curve using the K value calculated from Equation 2. By properly sizing the inductor, you can avoid unexpected problems and gain a better understanding of which mode or modes the boost converter is operating in.

John Betten is an application engineer at Texas Instruments and a senior member of TI's Technology Council. He has over 28 years of experience in AC/DC and DC/DC power conversion design. John graduated from the University of Pittsburgh with a bachelor's degree in electrical engineering and is a member of the IEEE.