Design Feature: December 7, 1995

Operating dc/dc converters seems simple enough: You just connect a source and load, and they convert, right? This easy operation is true in most cases. If you’re operating the converter at some distance from the input source, however, the simple “plug-and-play” operation of the converter doesn’t automatically result. You need to follow some simple design guidelines to ensure that the converter will operate properly over long lines, that is, with a large source resistance. Fortunately, using a dc/dc converter with a large source resistance is an easy design exercise when you apply the maximum-power theory and make some simple design trade-offs.

Three predominant and diverse application areas require the operation of dc/dc converters at great distances from their input sources. The first application area is a secure-telephone arrangement, integrated-services digital-network (ISDN) feature phone, or call-box phone system. The second popular application is a remote-sensor data-collection system, such as one that collects undersea data. The third system is a central-office-to-rooftop radio or microwave-link setup. In these systems, both the data stream and dc power routes up to the roof-mounted transmitter in the same coaxial cable to keep installation costs reasonable.

Regardless of the end application, the basic problem of connecting a dc/dc converter to the end of a long cable boils down to analyzing the circuit in Figure 1. This circuit models the combined source and line resistances, R_S, which includes both feed and return wires, and the equivalent resistance of the dc/dc converter, R_L. Unfortunately, you may have little control over R_S. The application’s allowable cord size or the undersea cable that is on hand often fixes the value of R_S. After all, you don’t want to buy 5 miles of 50-conductor undersea cable if the cable you used on the last job is still available.

Determining the line resistance is fairly straightforward. You can either look at the manufacturer’s data—the preferred method—or you can roughly calculate the resistance if you know the wire AWG size by using the following formula:

(1)

For example, AWG 31 wire (diameter=0.66 mm) has a resistance per centimeter of 0.0044. The resistance of 1000m of this wire is 440V. Because a power supply needs a feed and a return line, the total supply-line resistance would be twice this number, or 880V at 20°C. The line temperature also affects the resistance of the wire. For instance, copper has a temperature coefficient of approximately +0.4%/8C. So, if you install a 1000m line in a warm climate, such as California, that line’s temperature could reach 1208C, and the resistance could increase by 40% to 1230V. As these examples show, line resistance can increase quickly, especially if the cable encounters high temperatures.

Based on Figure 1’s circuit, which comprises a simple source-and-load voltage divider, you can plot the power delivered to the load as a function of the source-to-load resistance ratio. As Figure 2 shows, the system delivers no power to the load at both extremes of load resistance (zero and infinity). Between these extremes is a bell-shaped curve that clearly shows a peak at R_S/R_L=1.

This peak is the maximum-power point. RF-circuit designers have long known about this maximum-power condition; thus, they always match all source and load impedances. If the sources, feed lines, and antennae have matched impedances, then the source will deliver the maximum power to the load. The losses will also be 50% in the source resistance, but the system transfers the maximum power. The preferred operation is on the left side of the maximum-power curve. On the right side of the curve, the converter has multiple operating points.

If you differentiate the voltage-divider equation at the load and find the limiting power, the following equation results:

where R=R_S=R_L. Thus, for a given situation, only the source voltage and source and load resistances affect the maximum power. The cable usually fixes the source resistance—at least preliminarily—which then determines the load resistance for maximum power. The only independent variable left is the source voltage.

Consider what Eq 2 means in the earlier example, for which the worst-case line resistance over temperature is about 1230V. If the application is a phone installation, the source voltage might be 48V. Thus, the maximum power is equal to or less than 0.47W. This maximum power is the theoretical limit. The actual power available to your remote electronics must in practice be less than the theoretical limit, because setting the nominal power at the maximum-power point doesn’t leave any room for component/circuit variations.

To properly apply maximum-power theory, you also need some understanding of the input characteristics of the dc/dc converter and its corresponding R_S. Modeling a dc/dc converter as a fixed resistor is inaccurate, even for small-signal analysis. You can classify dc/dc converters into two types for this analysis. The more common type is the PWM converter. You can identify these types by their large input-voltage range of 2-to-1 and greater. The other type is the fixed-pulse-width chopper converter, which usually requires a following linear regulator without feedback to the chopper.

Most modern converters are PWM types, which are constant-power devices at their input terminals. That is, for a constant output power, they draw constant power from the input source, even as the source voltage changes. The only exception to this operation is that changes in input voltage cause changes in efficiency, which ultimately changes the input power. Ignore this effect, however, for purposes of this discussion. As the input rises, the current that the converter needs to operate decreases. This relationship constitutes a negative resistance, even for a small-signal analysis. At a given operating point, the value of this negative resistance is

Thus, the minimum value of the input resistance is at low line input, V_S, and maximum input power, P_IN.

Fixed-pulse-width chopper converters exhibit a more constant-current input characteristic and a narrow input-voltage range of less than ±15% around the nominal voltage. Because of its narrow input voltage range, the straight-chopper type is now rare. Most applications rely on the PWM method to get wider input ranges.

The curves in Figure 3 show the input current and resistance of a typical 20W-output PWM dc/dc converter. This example converter is fairly typical of what is available today. The converter has an efficiency of 80%, a 20-to-60V (3-to-1) input range, and 25W input power at a full-output load. The input current in Figure 3a follows a basically parabolic curve as the input voltage decreases. At some point, the input current reaches a maximum. After this maximum, the input current then decreases as the duty-cycle-limiting circuitry inside the converter prevents the pulse-width modulator from regulating at lower input voltages. The input current then decreases rapidly as the output voltage collapses. At this point, the converter is in unstable, or dropout, mode and does not correctly regulate the output voltage.

With this background on the basic system and the converters themselves, you can appreciate the design subtleties of connecting a dc/dc converter to a long line (a high source resistance). At first analysis, you might think to use the highest source voltage available, say 60V dc for the converter of Figure 3. Because there is a significant voltage drop on the cable leading to the converter, you might then think that a 3- or 4-to-1 input-range converter would maximize the permissible cable length. However, maximum-power theory states that the system delivers maximum power when the source and load resistances match. In this matched condition, the input to the converter is exactly half of the no-load source voltage.

Thus, operating the converter with greater than a 2-to-1 input-voltage range doesn’t help the situation and can actually make it worse; a load-line analysis explains why. For the converter-input characteristics of Figure 3, the maximum line resistance for 25W using Eq 2 is

Thus, maximum power transfers to the load when both the source and load resistances equal 36V. Plotting a 36V load line with the input-current curve (Figure 4) shows that the load line intersects the converter’s input current at 30V, which is exactly one-half the predicted source voltage.

In this example, you can see that, as the source resistance increases, the load line rotates counterclockwise around the 60V source point in the graph’s lower right corner. When the source resistance increases beyond 36V, the load line intercepts the 25W input-current curve at around 16V, which is outside the converter’s 20-to-60V operating range. Under this condition, the converter is in dropout and simply fails to operate properly.

Figure 4 also shows what happens when the source resistance decreases. When R_S is less than 36ž, the load line rotates clockwise and now intersects the input-current curve at three points. These multiple intersecting points mean that the converter has two stable operating points and a third point in dropout at an input of about 18V.

Multiple operating points are scary, because they mean that the system may not power up as you planned. Two of the operating points in Figure 4 when R_S. is less than 36V happen to be stable and allow the converter to operate and regulate the output normally, albeit at two different input voltages. However, the third operating point is unstable.

You must take precautions to force operation at one of the two stable operating modes to ensure that, when given a chance, the converter doesn’t always find the unstable operating point. The converter finds this unstable point because the input voltage usually increases from zero as the source powers up. As the input voltage increases, you can follow the input current curve from left to right on Figure 4. The unstable operating point is the first one on this curve’s path, and the input voltage doesn’t increase further beyond this point.

These multiple operating points are unnecessary, however, and are solely the result of having a greater than 2-to-1 input-voltage range. If you limit the input range to exactly 2-to-1, only one stable operating point can exist, and the converter will start and operate at the same point every time.

Because a greater than 2-to-1 input range doesn’t allow the converter to transfer more power than is allowed by maximum-power theory, you might wonder why manufacturers design wide-input-range converters. Converters with 4-to-1 or even 10-to-1 input ranges do have a place in universally powered systems. These converters are simply a poor choice, however, in the unique case of long-distance operation, in which the source resistance drops a significant amount of voltage.

You can use several guidelines to make your remote dc/dc converter work as you expect. The first such guideline is to use solid design practice, which dictates that you leave key system parameters flexible early in the design phase. Important and fixed parameters may include an estimated load-power requirement and line resistance. Consider the remaining parameters, however, with as much flexibility as possible.

If you are designing your own dc/dc converter or are buying a custom supply, you can use an appropriate method to limit the input-voltage range to less than 2-to-1. This range allows the converter to start unconditionally into any design value of source resistance. The biggest problem of setting the optimum input-voltage range occurs when you use standard supplies, because they may lack the optimum input range your design requires. The input range of most standard supplies usually starts at 2-to-1. Also, most manufacturers of standard supplies don’t tightly control the input range; the range can actually extend significantly below the data sheet’s listed minimum value. You may have to apply some external limits on the input range. For some helpful advice, see, “Limiting a dc/dc converter’s input-voltage range.”

Another design suggestion is to use the highest source voltage possible, assuming matched R_S and R_L, so that the converter delivers maximum power to the load. One possible limit here is the maximum voltage that a safety-regulating agency allows. Also, don’t push the system to extremes; allow for tolerances. You might find that the system can operate only with a 1.8-to-1 input-voltage range to provide enough dynamic headroom to keep the load well-regulated. Consider whether a short circuit can occur at the load, because this situation can cause the input power to increase dramatically, even if only for a short time. This increase can cause system lockup at an undesirable operating point that can persist even when you remove the short circuit.

Be realistic about the achievable efficiency of the converter. Although any efficiency is theoretically possible, pushing the efficiency beyond easy limits escalates the converter’s cost exponentially and lowers the power density. At the 0.5-to-1W level, most converters readily achieve 70 to 75% efficiency. At the 5-to-25W level, typical efficiencies are around 80 to 85%, especially when the system is operating over a less-than-2-to-1 input-voltage range. Many self-contained smart-power ICs can achieve efficiencies of only 75 to 80% because of the relatively high on-resistance of the onboard power switches.