*A New Method to Evaluate DC/DC converter Efficiency*

*This article offers an alternative to efficiency measurements as an evaluation tool of power supplies. The proposed method works well with little dependency on the output voltage and temperature.*

*By Alan Elbanhawy, Fairchild Semiconductor, San Jose CA, USA*

Power supplies have always been evaluated and compared based on the how efficient the conversion process is. Equations 1 and 2 are two of the most used formulae to calculate the power conversion efficiency η. The use of efficiency as a yardstick to evaluate DC-DC converters represents a very simple and in most cases effective way of comparison. Efficiency figure combined with the details of the converter parameters also allows the thermal engineer to calculate the thermal load of the converter and whether heatsink and/or cooling airflow is required. The efficiency tool works very well when we have established standard input and output voltages that are more or less fixed in value.

We will show that the efficiency alone is not the right tool to compare converters operating at different output conditions even with a fixed input voltage and switching frequency. We will explain why that is and propose an alternative methods that measures the performance “almost” independent of the output voltage that gives a much more accurate and unambiguous idea about the converter’s performance so we introduce the concept of the Effective Loss Resistance, Rol.

### Efficiency Calculations

The power conversion efficiency (ζ) may be calculated using the equation:

This equation can also be written as follows:

Figure 1 depicts a simplified block diagram of a synchronous buck converter used in the evaluation of this paper. It is worthwhile mentioning that this work may be adapted to almost all DC-DC converters.

Figure 2 shows the efficiency of a given converter at different output voltages. Although the power loss is mainly dependant on the load current at a fixed switching frequency and input voltage and is very lightly dependant on the output voltage within the range from 2V to 1V i.e. we have “almost” constant power loss in all of the out voltage conditions while the efficiency varies dramatically. So even though the power loss is “almost” a constant, the very fact that we have a smaller output voltage will result in non realistic smaller efficiency figure.

### Synchronous Buck Converter Losses

Loss mechanisms in DC-DC converters can be divided into two major groups as follows: Conduction or Ohmic losses. This is the loss due to I_{load2} x R_{DS(ON)} x Δ where R_{DS(ON)} is the on-resistance of the MOSFET, Iload is the load current and Δ is the duty cycle. Please note that this loss mechanism is mainly dependant on I_{load2} because of the quadratic relationship and to a lesser degree on the output voltage since Δ is a function of the output voltage that is topology dependant.

Dynamic or switching losses = I_{load }x Vin x ½ x fs x (tr+tf) where Vin is the input voltage and tr & tf are the rise and fall times and fs is the converter’s switching frequency. Again you can see that the dynamic losses are not dependant on the output voltage.

This means that the losses are dependant on the output voltage in a secondary way. This leads immediately to the conclusion that we have more or less fixed losses regardless of the output voltage.

Why is this important? Because as can be seen in the efficiency equation (2) above, the smaller the output voltage the smaller the output power for the same output current. This results a lower efficiency for smaller output voltage as can clearly be seen in Figure 2. One can see that there is a limiting condition as the output voltage goes to zero while maintaining the same output current at which point the efficiency is theoretically zero:

That is to say that the efficiency of a given converter is proportional to the output voltage for the same load current. This fact makes the comparison very difficult under different conditions of output voltage. Figure 2 depicts this very case where you can see that the efficiency at an output voltage of 2 volts is about 8% larger than that at 1V output at the same load current though the power dissipation is “almost” the same and the thermal load is also “almost” the same.

It can be shown that the efficiency is different for different heat sinking techniques for the same circuit and the same input and output voltages. In this case, there is less power dissipation where we have a heatsink and air flow compared to the same design in still air and no heatsink.

This leads to the following dilemma, as different DC-DC converter manufacturers show their efficiency results that optimally reflects their products. Starting with two converters, A and B, from two different vendors having the same efficiency figure, the engineer is left to compare them by guessing whether converter A tested at 30 Amps and a heatsink (of unknown performance generally) is better than converter B tested at 25Amp with no heatsink and 400LFM airflow?

The question that can be asked now is, “Is there a different way to evaluate converters independent of the output voltage and heat sinking techniques?”

### The Proposed New Approach

In the above discussion, we have demonstrated the need for a different approach that can has a universal appeal both to vendors and buyers of converters and more importantly, to the circuit and thermal design engineer so that quick decisions regarding design issues can be crystal clear across different disciplines.

One can clearly see that the power loss is a better way to demonstrate the performance of power supplies within a limited span of output voltages, say 1V – 2V where the power loss may be considered constant. Needless to say if we widen the span of voltage say from 1V to 5V all the secondary effects will start becoming prominent and will not yield the same consistent results. Figure 3 shows the losses as a function of the load current for different schemes of heat sinking.

To understand Figure 3 let us see what is happening here. It can be seen that the difference in losses is rather slight up to 60 Amps with less than two watts differential at this point. We can deliver currents up to 120 Amps when we have both heatsink and airflow from the same board because we can remove heat very efficiently from the board due to the use of the air and heatsink. The reader is unlikely to easily figure out that all four curves are taken for the very same VRM with heat sinking as the only difference though this is the case. In Figure 3 the testing was stopped when the board temperature reached 105°C – 110 °C.

It is worthwhile mentioning that the difference in power dissipation between the fully heat sinked case and the still air case is mostly due to temperature differential since the fully heat sinked case is running at a much lower temperature and since the MOSFET on-resistance may be expressed as follows:

Where RDS(ON)_{T} and RDS(ON)_{a} are the MOSFET on-resistance at a temperature T and ambient temperature and ΔT is the temperature rise above ambient. The above equation indicates that at higher temperatures, the on-resistance is higher resulting in higher losses that can be observed in Figure 3.

### Effective Loss Voltage

One way to explore the converter performance is to introduce the term: “Effective Loss Voltage,” which is equal to:

This represents a DC voltage in series with the converter output which dissipates power when I_{load} passes through it as can be seen in Figure 4. On the y axes we have the “Effective Loss Voltage” and the x axes we have the load current.

Here are the benefits of this representation: We have direct evaluation of the losses as a function of heat sinking. This graph translates the abstract efficiency curve into a actual performance as a function of the load current and power losses.

### Effective Loss Resistance

The second way is to propose the measuring of the “Effective Loss Resistance” Rol.

Figure 6 shows Rol for similar set of tests measured in Figure 2 with different output voltages and heat sinking scheme. It clearly shows that for a given current, the effective loss resistance, Rol is “almost” the same and “almost” independent of the heat sinking technique. Clearly Rol will differ slightly from one heat sinking technique to the other and the concept of “Rol Band” could be utilized to describe the difference in maximum and minimum Rol as will be shown later.

Figure 5 shows the effective loss resistance Rol in all four cases of heat sinking and clearly showing that the converter performance is “almost” independent of the cooling and output voltage leading to the conclusion that the effective loss resistance Rol, is a reliable means to evaluate the converter performance.

As mentioned above, there are some differences in the losses between a 1V and 2V output. A “Rol Band” could apply here too to fully describe the circuit performance. This may be presented as Rol = Ro ± Δ*R*. Where this equation applies to say ½ load to full load losses. Now we have a very simple parameter with spread that describes the performance of a given converter say a VRM operating between 1V and 2V. One may derive an equation for Rol that may help in converter comparison using an analytical approach such as a spreadsheet or a mathematical software analysis tool.

An unbiased comparison of different power supplies may now be done either using a set of curves as in Figure 5 or a set of equations in Rol and I_{load} mentioned above.

For completion, Figure 6 shows Rol for different heat sinking conditions. As can be seen, Rol has a mean value and band at each current that represents the spread of the data range. In this particular case the data spread is due mainly to the temperature effects on the converter as explained above.

By knowing Rol and the ± spread one can immediately evaluate the effect of heat sinking on the total performance and would allow for correct decision making regarding whether the converter requires heat sinking.

**Conclusion**

Some conditions must apply for power efficiency measurements to be used as a comparison tool between different converters. These conditions are the same input and output voltages, same switching frequency, same heat sinking and the same range of load current. A tool is needed that is independent of the above mentioned conditions. The Effective Loss Resistance, Rol, of a synchronous buck converter is “almost” independent of the output voltage and the heat sinking approach.

Effective Loss Resistance may be published in the data sheet of DCDC converters allowing the design engineer to hold a very simple and accurate comparison between any number of converters.

The mean value of Rol measured at the current range of interest may be used to determine the best converter for the application.

**References:**

1) A. Elbanhawy, "Effect of Parasitic Inductance on switching performance," in Proc. PCIM Europe 2003, pp.251-255.

2) A. Elbanhawy, "Effect of Parasitic inductance on switching performance of Synchronous Buck Converter," in Proc. Intel Technology Symposium 2003.

3) A. Elbanhawy, “Mathematical Treatment for HS MOSFET Turn off," in Proc. PEDS 2003.

4) A. Elbanhawy, "A quantum Leap in Semiconductor packaging," in Proc. PCIM China, pp. 60-64.