电源内阻：扼杀DC-DC转换效率的元凶(SourceResistance:TheEfficiencyKillerinDC...-其他光电实用电路图

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 src="/data/attachment/portal/201007/ET29214201007211251206.gif">

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 converter.

We now have enough information to calculate the source's power dissipation and therefore its efficiency. Because the open-circuit value of source voltage (V_PS) is given, we need src="/data/attachment/portal/201007/ET29214201007211251208.gif">

I_IN can also be solved in terms of V_PS, V_IN, and R_S:



Equate the expressions from equations [6] and [7] and solve for V_IN:



To understand their implications, it is very instructive to visualize equations [6] and [7] graphically (Figure 3). The resistor load line is a plot of all possible solutions of equation [7], and the DC-DC I-V curve is a plot of all possible solutions of equation [6]. The intersections of these curves, representing solutions to the pair of simultaneous equations, define stable voltages and currents at the DC-DC converter's input. Because the DC-DC curve represents constant input power, (V_IN+)(I_IN+) = (V_IN-) (I_IN-). (The + and - suffixes refer to the two solutions predicted by equation [8], and correspond to the ± signs in the numerator.)


It's easy to get lost in the equations, and therein lies the value of the load-line analysis plot of Figure 3. Note, for example, that if the series resistance (R_S) equals zero, the resistor load-line slope becomes infinite. The load line would then be a vertical line passing through V_PS. At this point V_IN+ = V_PS and the efficiency would be 100%. As R_S increases from 0Ω, the load line continues to pass through V_PS but leans more and more to the left. Concurrently, V_IN+ and V_IN- converge src="/data/attachment/portal/201007/ET292142010072112512012.gif">
Figure 4. A standard DC-DC converter circuit illustrates the ideas of Figure 3.


Figure 5. Above V_MIN, the MAX1626 input I-V characteristic closely matches that of a 90%-efficient ideal device.

When V_IN exceeds V_L, the input current climbs toward a maximum that occurs when V_OUT first reaches the preset output voltage (3.3V). The corresponding input voltage (V_MIN) is the minimum required by the DC-DC converter to produce the preset output voltage. For V_IN > V_MIN, the constant-power curve for 90% efficiency closely matches the MAX1626 input curve. Variations from the ideal are caused primarily by small variations in DC-DC converter efficiency as a function of its input voltage.

The power-supply designer must also guarantee that the DC-DC converter never becomes bistable. Bistability is possible in systems for which the load line intersects the DC-DC converter curve at or below V_MIN/I_MAX (Figure 6).


Figure 6. A closer look at the intersection points indicates a possibility of bistable and even tristable operation.

Depending src="/data/attachment/portal/201007/ET292142010072112512015.gif"> The source resistance (R_S) should always be smaller than R_BISTABLE. If this rule is broken, you risk highly inefficient operation or a complete shutdown of the DC-DC converter.

It might be helpful to plot, for an actual system, the relationship shown in equation [9] between source efficiency and source resistance (Figure 7). Assume the following conditions:


Figure 7. This plot of source efficiency vs. source resistance indicates multiple values of efficiency for a given R_S.

V_PS = 10V Open-circuit power-supply voltage
V_MIN = 2V Minimum input voltage that ensures proper operation
P_IN = 50W Power to the DC-DC converter's input (P_OUT/EFF_DCDC).

Using equation [12], R_BISTABLE can be calculated as 0.320Ω. Subsequently, a plot of equation [9] shows that source efficiency drops as R_S increases, losing 20% at R_S = R_BISTABLE. Note: this result cannot be generalized. You must perform the calculations for each application. src="/data/attachment/portal/201007/ET292142010072112512017.gif">

Therefore,



A 5V/10A power supply with 1% load regulation, for example, would have only 5.0mΩ of output resistance- not much for a 10A load.

It's useful to know how much source resistance (R_S) can be tolerated and how this parameter affects system efficiency. R_S must be less than R_BISTABLE, as stated earlier, but how much lower should it be? To answer this question, solve equation [9] for R_S in terms of EFF_SOURCE, for EFF_SOURCE values of 95%, 90%, and 85%. R_S95 is the R_S value that yields a 95% source efficiency for the given input and output conditions. Consider the following four example applications using common DC-DC converter systems.

Example 1 derives 3.3V from 5V with a load current of 2A. For 95% source efficiency, be careful to keep the resistance between the 5V source and the DC-DC converter's input well under 162m½. Notice that R_S90 = R_BISTABLE, by coincidence. This value of R_S90 also implies that the efficiency could as easily be 10% as 90%! Note that system efficiency (as opposed to source efficiency) is the product of source efficiency, DC-DC converter efficiency, and load efficiency.

Example 1. Application Using a MAX797 or MAX1653 DC-DC Converter (I_OUT = 2A) V_PSV_OUTI_OUTV_MINEFF_DCDCP_OUTR_BISTABLER_S95R_S90R_S855V3.3V2A4.5V90%6.6W0.307Ω0.162Ω0.307Ω0.435Ω
Example 2 is similar to Example 1 except for outputcurrent capability (20A vs. 2A). Notice that the seriesresistance requirement for 95% source efficiency is 10 times lower (16mΩ vs. 162mΩ). To achieve this low resistance, use 2oz. copper PC traces.

Example 2. Application Using a MAX797 or MAX1653 DC-DC Converter (I_OUT = 20A) V_PSV_OUTI_OUTV_MINEFF_DCDCP_OUTR_BISTABLER_S95R_S90R_S855V3.3V20A4.5V90%66W0.031Ω0.016Ω0.031Ω0.043Ω
Example 3 derives 1.6V at 5A from a source voltage of 4.5V (i.e., 5V-10%). The system requirement of 111mΩ for R_S95 can be met, but not easily.

Example 3. Application Using a MAX1710 DC-DC Converter with Separate +5V Supply (V_PS = 4.5V) V_PSV_OUTI_OUTV_MINEFF_DCDCP_OUTR_BISTABLER_S95R_S90R_S854.5V1.6V5A2.5V92%8W0.575Ω0.111Ω0.210Ω0.297Ω
Example 4 is the same as Example 3, but with higher supply voltage (V_PS = 15V instead of 4.5V). Notice the useful trade-off: a substantial increase in the difference between input and output voltages has caused an efficiency drop for the DC-DC converter alone, but the overall system efficiency is improved. R_S is no longer an issue because the large R_S95 value (>1Ω) is easily met. A system with an input filter and long input lines, for example, can maintain a source efficiency of 95% or more without special attention to line widths and connector resistances.

Example 4. Application Using a MAX1710 DC-DC Converter with Separate +5V Supply (V_PS = 15V) V_PSV_OUTI_OUTV_MINEFF_DCDCP_OUTR_BISTABLER_S95R_S90R_S8515V1.6V5A2.5V86%8W3.359Ω1.149Ω2.177Ω3.084Ω

When looking at DC-DC converter specifications, it is tempting to maximize efficiency by setting the supply voltage as close to the output voltage as possible. This strategy, however, can increase costs by placing unnecessary limitations on elements such as the wiring, connectors, and trace layout. System efficiency may even suffer. The analytic tools presented in this article should make such power-system trade-offs more intuitive and obvious.

1. Erickson, Robert W. Fundamentals of Power Electronics. Chapman and Hall, 1997.
2. Lenk, Ron. Practical Design of Power Supplies. IEEE Press McGraw Hill, 1998.
3. Gottlieb, Irving M. Power Supplies, Switching Regulators, Inverters and Converters. Second Edition, TAB Books, 1994.
4. Wettroth, John. "Controller Provides Constant Power Load." EDN, March 14, 1997.

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