The design of an efficient DC-DC converter is anything but simple.
DC-DC converters are circuits that can increase or decrease the supply voltage. They are particularly useful when using batteries to power a wide variety of devices. For this reason, they must make the best possible use of the energy provided by accumulators and, in fact, their efficiency can easily exceed 96%.
The design of a DC-DC converter, however, is anything but simple. To truly obtain maximum performance, many parameters must be calculated, and every use case and every operating condition is different. Unfortunately, it is not possible to generalize the equations and the efficiency values must be calculated for each application to find the best operating point, depending on the source and load resistance.
Internal battery resistance limits efficiency
All electronic components in a circuit involve a certain rate of dissipation. The friction of electrons in conductors and semiconductors converts part of the energy into heat, which is dissipated into the environment and therefore not used profitably.
Among the causes that lower the efficiency of a power circuit is the internal resistance of the generator, which cannot be completely eliminated. In addition, DC-DC converters are generally more efficient when the absolute value of the difference between the input voltage and the output voltage is smaller. Figure 1 below shows a generic example of an electrical circuit consisting of a voltage generator and a load.
The first circuit is ideal, and the generator has an internal resistance of 0 Ohm. An ideal converter has an efficiency of 100% and works at any input and output voltage. The second circuit is real, and the generator has an internal resistance of 0.3Ω.
The efficiency of the first circuit is 100% since all the generator’s energy is used by the load, a 10 Ohm resistor. The efficiency of the second circuit is lower at 97%, since 3% of the energy is wasted in unused heat. Let us examine the simple formulas below that lead to the above results:
As can be seen from the formulas, efficiency is a function of input voltage, output voltage, and current flowing on the output load. Dissipation also includes its effect on all other electronic components, such as the resistance of the PCB, the resistance of electrical wires and wiring in general, the impedance of the generator, the resistance of inductors, and so on.
As a result of these causes, the reduction in efficiency can easily exceed 10%, when all the individual reasons for it are added up. In relation to the above, it is useful to observe the graph in Figure 2, which shows that the internal resistance of the generator is one of the worst antagonists to the efficiency of a circuit.
Figure 2 shows that, whatever configuration is adopted, an increase in the resistance of the electrical source inexorably leads to a decrease in the efficiency of the entire system. It can also cause other less obvious, but equally problematic, effects on the circuit.
Such an occurrence is often difficult to detect, since the circuit operates smoothly and the output of the converter conforms to the design rules. It is the efficiency of the system that is drastically affected, and the designer must have excellent measuring equipment to detect such issues.
Challenges of a bistable circuit
One of the natural solutions would lead the designer to implement power supply systems with a lower internal resistance. But in practice, other methods are preferred because lowering the resistance is not always feasible, and the solution costs and circuit complexities would certainly outweigh the benefits received. One of the many solutions to these issues is to choose a higher input voltage to limit the input current demand, and thus reduce the need for a low source resistance.
Sometimes, it is more efficient with an even higher supply voltage, but each solution must be evaluated very carefully because results vary from case to case. Sometimes, in the presence of a very high load, the input of the converter can become bistable. Bistability is an uncertain condition in which the converter can work under two stable input conditions, each with its own efficiency.
The output of the converter is normal, but the efficiency of the entire system is very low. The probable presence of bistability in a generic circuit can be seen in Figure 3. The input voltage must respect a lower limit, below which the current is practically zero. This sub-voltage (called VL) ensures that the DC-DC converter is switched off for all input voltages below VL.
The fact that the converter does not draw current under these conditions prevents large input currents from being drawn during circuit start-up. When the voltage exceeds VL, the input current rises toward the maximum point. Designers must design the converter circuit in such a way that it never becomes bistable.
This problem is easily observed in I/V graphs, where the load line intersects the converter curve. In some rare cases, the occurrence of tristable conditions is also possible, depending on the position of the load line. Normally, the load line must not touch the tip of the DC-DC converter curve and, above all, must not lie below it.
The upper limit of the resistance of the source resistance (RS) load line is called R(bistable), and can be calculated using the following formula:
The RS should always be smaller than R(bistable), otherwise the converter’s operation becomes very inefficient, or it may even stop working. One of the most difficult tasks of the designer is to precisely know these ratios. The maximum overall efficiency of a converter is when the supply voltage is very close to the output voltage, as mentioned earlier. Maximizing efficiency can be achieved by bringing these two values closer together, but sometimes it is not necessary to take such precautions, which could increase costs. By working hard on load curves, high efficiency can be achieved, even while keeping costs lower.
Inductor quality (DCR)
The efficiency of a DC-DC converter is determined by every single component, even the relatively unimportant ones. Even the inductor in the circuit does not escape this rule. It is important to test the various efficiencies by using any DC-DC converter and trying out different inductor types while, of course, maintaining the inductive value of the component.
For this type of application, the most critical inductor parameter is the relative parasitic resistance. The lower the value of the parasitic resistance, the higher the efficiency of the DC-DC converter.
One of the most important parameters is the DCR (DC Resistance), which is the amount of resistance an inductor presents to signals with frequencies at or near 0 Hz. Inductors have very low resistance for low-frequency signals, while they exhibit very high resistance for high-frequency signals.
The DCR of an inductor is very low, usually between 0.01 Ohm and 4 Ohm. Larger inductors have a higher DCR value due to the longer length of the wire. Here again, the designer must be wise to implement a rather low inductance, which limits the effects of the DCR as much as possible. Figure 4 shows a simple DC-DC converter from 5 V to 3.3 V operating with non-ideal reactive components.
The results, therefore, are very close to the real thing. That is why it is important to try different types of inductors, all with a value of 47 uH but different resistance values, to see how efficiently the circuit responds.
The market makes many inductors available to designers with different DCR rates for the same inductance. Models with lower DCR cost more. Higher inductance corresponds to higher resistance (DCR), and vice versa. This parameter is useful for determining losses due to heating of the wire. The designer should therefore choose as low a DCR as possible. Only by improving this parameter will the efficiency of the converter increase significantly, as can be seen in the table below.
Inductors DCR | Output Power | Input Power | Efficiency |
0.03 | 1.63463 | 2.06405 | 79.1951 |
0.06 | 1.63486 | 2.06297 | 79.2479 |
0.09 | 1.6348 | 2.07033 | 78.9633 |
0.12 | 1.63474 | 2.07686 | 78.7121 |
0.15 | 1.63469 | 2.08437 | 78.4262 |
0.18 | 1.63465 | 2.09143 | 78.1591 |
0.21 | 1.6346 | 2.0986 | 77.8899 |
0.24 | 1.63455 | 2.10684 | 77.5828 |
0.27 | 1.6345 | 2.11309 | 77.3508 |
0.30 | 1.63446 | 2.12148 | 77.0432 |
0.33 | 1.63438 | 2.12743 | 76.8244 |
0.36 | 1.63435 | 2.13575 | 76.5233 |
0.39 | 1.63429 | 2.14223 | 76.2890 |
0.42 | 1.63424 | 2.14964 | 76.0239 |
0.45 | 1.63426 | 2.15297 | 75.9072 |
0.48 | 1.63426 | 2.157 | 75.7656 |
The simulation above involved the use of the same electronic components. The only difference between the various tests was to vary only the value of the DCR of the L1 inductor, using 16 examples of 47 uH inductors, with an intrinsic resistance between 30 milliohms and 480 milliohms. The results speak for themselves: a low DCR value results in a higher efficiency value and less heating of the converter.
The designer’s task is not only to design the converter, but also to choose the best electronic components on the market—for instance, inductors, even if they are more expensive. One must, therefore, be wary of devices that are sold at very low prices, as they almost certainly do not fully comply with all efficiency and safety regulations. High efficiency means that less energy is unnecessarily dissipated in the form of heat, and thermal management of the converter also becomes less problematic and simpler.
This article was originally published on EE Times.
Giovanni Di Maria has always been fond of electronics, maths and DIY. He is a computer programmer and a computer science and maths teacher. He loves figures and he’s always on the look out for big Prime Numbers. He has also written a book about PIC Microcontroller 16F84 programming with mikroBasic. He is the owner of Elektrosoft, a company that deals with electronics and information technology. He is a full time trainer and teacher.
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