电源内阻：扼杀DC-DC转换效率的元凶

Abstract: DC-DC converters, common in battery-driven, portable, and other high-efficiency systems, can deliver efficiencies greater than 95% while boosting, reducing, or inverting supply voltages. Resistance in the power source is one of the most important factors that can limit efficiency. This application note describes the effects of source resistance, how to calculate efficiency, real-world considerations, design considerations, and shows a real-world example.

DC-DC converters are commonly used in battery-operated equipment and other power-conserving applications. Like a linear regulator, the DC-DC converter can regulate to a lower voltage. Unlike linear regulators, however, the DC-DC converter can boost an input voltage or invert it to create a negative voltage. As an added bonus, the DC-DC converter boasts efficiencies greater than 95% under optimum conditions. However, this efficiency is limited by dissipative components. The main cause is resistance in the power source.

Losses due to source resistance can lower the efficiency by 10% or more, exclusive of loss in the DC-DC converter! If the converter has adequate input voltage, its output will be normal and there may be no obvious indication that power is being wasted.

Fortunately, testing the input efficiency is a simple matter (see the Source section).

A large source resistance can cause other, less obvious effects. In extreme cases, the converter's input can become bistable, or its output can decrease under maximum load conditions. Bistability means that the converter exhibits two stable input conditions, each with its own efficiency. The converter output is normal, but system efficiency may be drastically affected (see How to Avoid Bistability).

Should this problem be solved simply by minimizing the source resistance? No, because the practical limits and cost/benefit trade-offs posed by the system may suggest other solutions. A prudent selection of power-supply input voltage, for example, can considerably minimize the need for low source resistance. Higher input voltage for a DC-DC converter limits the input current requirement, which in turn lessens the need for a low source resistance. From a systems standpoint, the conversion of 5V to 2.5V may be far more efficient than the conversion of 3.3V to 2.5V. Each option must be evaluated. The goal of this article is to provide analytic and intuitive tools for simplifying the evaluation task.

As shown in Figure 1, any regulated power-distribution system can be divided into three basic sections: source, regulator(s) (a DC-DC converter in this case), and load(s). The source can be a battery or a DC power supply that is either regulated or unregulated. Unfortunately, the source also includes all the dissipative elements between the DC voltage and load: voltage-source output impedance; wiring resistance; and the resistance of contacts, PC-board lands, series filters, series switches, hot-swap circuits, etc. These elements can seriously degrade system efficiency.


Figure 1. A regulated power-distribution system has three basic sections.

Calculation and measurement of the source efficiency is very simple. EFF_SOURCEequals (power delivered to the regulator)/(power provided by V_PS) multiplied by 100%:



Assuming that the regulator draws a negligible amount of current when unloaded, you can measure source efficiency as the ratio of V_INwith the regulator at full load to V_INwith the regulator unloaded.

The regulator (DC-DC converter) consists of a controller IC and associated discrete components. Its characterization is described in the manufacturer's data sheet. Efficiency for the DC-DC converter (EFF_DCDC) equals (power delivered by the converter)/(power delivered to the converter) multiplied by 100%:



As specified by the manufacturer, this efficiency is a function of input voltage, output voltage, and output load current. It's not unusual for the efficiency to vary no more than a few percent over a load current range exceeding two orders of magnitude. Because the output voltage is fixed, we can say the efficiency varies only a few percent over an "output-power range" exceeding two orders of magnitude.

DC-DC converters are most efficient when the input voltage is closest to the output voltage. If the input variation is not extreme with respect to the data sheet specifications, however, the converter's efficiency can usually be approximated as a constant between 75% and 95%:



This discussion treats the DC-DC converter as a twoport black box. For those interested in the nuances of DC-DC converter design, see References 1-3. The load includes the device to be driven and all dissipative elements in series with it, such as PC-trace resistance, contact resistance, cable resistance, etc. Because the DC-DC converter's output resistance is included in the manufacturer's data sheet, that quantity is specifically excluded. Load efficiency (EFF_LOAD) equals (power delivered to the load)/(power delivered by the DC-DC converter) multiplied by 100%:



The key to optimum system designs is in analyzing and understanding the interaction between the DC-DC converter and its source. To do this we first define an ideal converter, then calculate the source efficiency, then test our assumptions against measured data from a representative DC-DC converterµin this case, the MAX1626 buck regulator.

An ideal DC-DC converter would have 100% efficiency, operate over arbitrary input- and output-voltage ranges, and supply arbitrary currents to the load. It would also be arbitrarily small and available for free! For this analysis, however, we assume only that the converter's efficiency is constant, such that input power is proportional to output power:



For a given load, this condition implies that the input current-voltage (I-V) curve is hyperbolic and exhibits a negative differential-resistance characteristic over its full range (Figure 2). This plot presents I-V curves for the DC-DC converter as a function of increasing input power. For real systems with dynamic loads, these curves are also dynamic. That is, the power curve moves farther from the origin as the load demands more current. Considering a regulator from the input port instead of the output port is an unusual point of view. After all, regulators are designed to provide a constant-voltage (sometimes constant-current) output. Their specifications predominantly describe the output characteristics (output-voltage range, output-current range, output ripple, transient response, etc.). The input, however, displays a curious property: within its operating range it acts as a constantpower load (Reference 4). Constant-power loads are useful in the design of battery testers, among other tasks.


Figure 2. These hyperbolas represent constant-power input characteristics for a DC-DC