### Abstract

Due to the nature of multiphase buck converters, perceived efficiency varies for a static operating condition depending on the load and output voltage measurement connections, as well as the symmetry of the PCB layout. An engineer evaluating multiphase buck converters should understand the nuance of efficiency measurement that this article explores, as well as PCB layout. How to fairly compare efficiency of multiphase buck converters on different evaluation boards needs to be addressed. This application note explores the underlying reasons and offers a method for measuring the most accurate efficiency in a multiphase buck converter.

### Introduction

Measuring the efficiency of a multiphase DC-DC converter can be tricky. Layout imbalances lead to voltage differences between each of the phases. Engineers must carefully consider how they are measuring input and output voltages and currents when evaluating these converters to arrive at the correct number. This application note explores the nuances of multiphase buck (step-down) converters and offers a method for properly measuring efficiency

### Background

Due to the nature of multiphase buck converters, perceived efficiency varies for a static operating condition depending on the load and output voltage measurement connections, as well as the symmetry of the PCB layout. An engineer evaluating multiphase buck converters should understand the nuance of efficiency measurement that this article explores, as well as PCB layout. How to fairly compare efficiency of multiphase buck converters on different evaluation boards needs to be addressed. This application note explores the underlying reasons and offers a method for measuring the most accurate efficiency in a multiphase buck converter.

Calculate the efficiency of any DC-DC converter with the following equation:

Define P_{IN} as the power delivered to the input of the integrated circuit (IC) from the power source (instead of the power generated by the source). Estimate P_{IN} by measuring the voltage across the input capacitor (or as close to the pin as possible), measuring the input current with an ammeter between the power source and the power input of the IC, and multiplying the two (P = V × I). Define P_{OUT} as the power delivered at the output of the buck converter to the load (instead of the power consumed by the load). In a single-phase buck converter, estimate P_{OUT} by measuring the voltage across the output capacitor (or as close to the pin as possible), measuring the output current with an ammeter between the power output of the IC and the load, and multiplying the two. Efficiency (η) is then the ratio of the output power to the input power.

In a single-phase buck converter, there is only one power stage and one output; hence, one point to measure at. In a multiphase buck converter, there are multiple outputs that are connected electrically. Take a four-phase buck for example: a four-phase buck needs four inductors (one for each phase), at least four output capacitors (one or more for each phase), and connects the outputs of the four individual phases together. Which output voltage should be measured to calculate P_{OUT}? It is logical to assume that the output voltages of all four phases are identical, but not entirely true. They are only identical when measured when they meet at a single point on the board. PCB impedances cause voltage drops along the output trace of each phase as it routes from the switching node pins of the IC to the load. A good, symmetric layout will minimize this impact. Layout asymmetries, however, can lead to imbalances in the outputs of the buck. For example, if the copper trace from the first phase to the load is shorter than the trace from the fourth phase to the load, the voltage generated at the pin of the first phase will be lower than the voltage generated at the pin of the fourth output (they must be equal at the point of load, and the fourth phase will incur more voltage drops). This is significant for the calculation of efficiency as mentioned earlier. In this scenario, measuring only the first output voltage and assuming the other phases are the same will give a number that is lower than the real efficiency! The buck is generating a higher output voltage at the fourth phase, and assuming load current is equal between the four phases, means the fourth phase is generating more power than accounted for. Note that this process can also happen in reverse; a higher-than-real efficiency can be measured too. Thus, the perceived efficiency in a multiphase buck converter is dependent on the method of measurement. Take an exaggerated example to illustrate this point.

Figure 1 depicts an exaggerated case of imbalanced routing of a four-phase buck. Note that the inductor (L) and output cap (C) of each phase are not pictured in Figure 1 but do exist. OUTx are the nodes of the output caps on the IC, and V_{X} are the voltages generated directly at those capacitors (where x is one of the four phases). V_{OUT} is to the point-of-load voltage, and I_{OUT} is to the total output current drawn by the load. Imagine a PCB where the length of the OUT4 trace to the load is four times longer than the length of the OUT1 trace. Assume that the extra length contributes four times the resistance as the first phase (4R vs 1R). Using this example, see how the imbalanced layout and loading can potentially cause errors in calculating efficiency:

Assume:

V_{OUT} = 1V

I_{OUT} = 4A

I1 = I2 = I3 = I4 = 1A

R = 0.025Ω

Calculate:

V1 = (I1 × 1R) + V_{OUT} = (1A × 0.025O) + 1V = 25mV + 1V = 1.025V

V2 = (I2 × 2R) + V_{OUT} = (1A × 0.050O) + 1V = 50mV + 1V = 1.050V

V3 = (I3 × 3R) + V_{OUT} = (1A × 0.075O) + 1V = 75mV + 1V = 1.075V

V4 = (I4 × 4R) + V_{OUT} = (1A × 0.100O) + 1V = 100mV + 1V = 1.10V

Observe that the voltages generated by the buck converter directly at the output caps must be higher than V_{OUT} to compensate for the drops along the PCB paths. Phase one only has a (1 × R) drop, but phase four has a (4 × R) drop.

In a real lab, the engineer tasked with calculating efficiency for this multiphase buck needs to measure four quantities: V_{IN}, V_{OUT}, I_{IN}, and I_{OUT}. Input voltage and current are simple enough; there is only one input source to the converter, therefore one place to attach a voltmeter and one place to insert an ammeter. Output current is simple; one ammeter between the load and the output of the buck. Output voltage, however, might be a bit trickier. If the engineer attaches the voltmeter at the point of load and reads V_{OUT} = 1.0V, they automatically include the PCB losses from the local output caps to the point of load and calculate an incorrect efficiency. Typically, Maxim Integrated EV Kits come with kelvin sense test points to help engineers avoid that difficulty.

Assuming that the output current is shared evenly between the four phases at 1A per phase (assume the buck converter has a good current sharing loop), calculate the output power of each phase, and then the total output power if the other phases are assumed to be generating the same voltage:

**Measuring V _{OUT} at OUT1:**

P1 = 1.025V × 1A = 1.025W

Assuming the other three phases are also at 1.025V gives 1.025W × 4 = **4.1W P _{OUT}**

**Measuring V _{OUT} at OUT2:**

P2 = 1.05V × 1A = 1.05W

Assuming the other three phases are also at 1.05V gives 1.05W × 4 = **4.2W P _{OUT}**

**Measuring V _{OUT} at OUT3:**

P3 = 1.075V × 1A = 1.075W

Assuming the other three phases are also at 1.075V gives 1.075W × 4 = **4.3W P _{OUT}**

**Measuring V _{OUT} at OUT4:**
P4 = 1.1V × 1A = 1.1W

Assuming the other three phases are also at 1.1V gives 1.1W × 4 = **4.4W P _{OUT}**

Find the actual output power by measuring each phase individually:

P_{OUT} = P1 + P2 + P3 + P4 = 1.025W + 1.05W + 1.075W + 1.1W = **4.25W P _{OUT}**

There is a fixed input power required by the buck for this condition. Assume that input power is **5W** (just a contrived number). Use the actual output power to calculate the efficiency of the device:

Efficiency = P_{OUT} / P_{IN} = 4.25W/5W = **85%**

If the engineer had only measured OUT1, they would calculate an efficiency of **4.1W/5W = 82%**. And if they had only measured OUT4, they would calculate an efficiency of **4.4W/6W = 88%**. Depending on where they connect their output voltage measurement, the calculated efficiency could be as much as +/- 3% wrong! That could be the difference between selecting one IC over another.

This example is contrived to illustrate the point, but the theory stands. See the following experiment with the MAX77711 quad-phase buck converter to test this theory in a real-world IC.

### Hypothesis

Consider this hypothesis: in a multiphase buck converter, the most accurate efficiency can be obtained by individually measuring the power delivered by each phase and summing them to exclude all PCB losses, and get the correct output power to be used in the efficiency calculation.

The theory states that perceived efficiency can be lower or higher than the true efficiency depending on both the layout quality and the method of measurement. Measuring the output voltage of only one phase and assuming the same voltage for the others leads to a perceived converter efficiency that is incorrect (with the magnitude of error dependent on the quality of the layout). The hypothesis implies that measuring all output phases individually eliminates the error in the calculation.

### Experiment

In a configurable four-phase buck regulator like MAX77711, the EV Kit must allow for evaluation of all possible phase configurations. In doing so, the layout sacrifices some symmetry for configurability. This makes it a good candidate for testing the hypothesis. Consider an experiment with three main objectives:

- Determine the worst-case scenario when measuring four phase efficiency: how low or high can the efficiency numbers get?
- Determine the real efficiency of the converter.
- Offer a recommendation for measuring efficiency.

Refer to Figure 2, which shows the MAX77711 EV kit in a four-phase configuration (one output). To highlight the point made with Figure 1, note the varying lengths of traces that the current must flow through if the load is taken from the OUT4 terminal. Phase one (blue) takes the longest path, phases two and three (purple and green, respectively), take the second longest paths, and phase four (yellow) takes the shortest path. This means that OUT4 should see the least amount of PCB loss, and OUT1 should see the most.

There are 16 unique combinations of loading and measuring but focus on just a few to simplify the experiment. One set of combinations should be sufficient to prove or disprove the hypothesis. Attach a load at the OUT4 terminal and measure the output voltage at each of the four phases. Define the experiment as follows:

Measure V_{IN} – Connect a voltmeter across the input capacitor (kelvin sense test points INxS and GNDxS).

Measure I_{IN} – Connect an ammeter between the power source and the input to the buck (SYS test point).

Measure V_{OUT} – Connect a voltmeter across the output capacitor of phase x for output voltage (across kelvin sense test points OUTxS and PGNDxS, where x = 1, 2, 3, or 4).

Measure I_{OUT} – Connect an ammeter between the output pin of phase 4 and an electronic load for output current (loaded at OUT4).

Sweep the load with some step value and record a single input voltage, input current, output voltage, and output current.

Use these numbers to calculate efficiency. Repeat the efficiency measurements for each value of x to test all combinations.

Finally, perform one last efficiency sweep, but with a voltmeter for each phase output voltage (four in total) and an ammeter for each phase output current (four in total). Input voltage and current meters stay the same. This sweep should provide the truest regulator efficiency.

### Results

Refer to Figure 3 for a graph of the plotted efficiency data for each case. Since the load was taken from OUT4, it makes sense that the red curve (when V_{OUT} is measured from OUT4 which generates the lowest voltage) has the lowest efficiency. Measuring V_{OUT} from OUT4 does not consider the extra output power generated by the other phases to compensate for their PCB losses. Conversely, the purple curve (when V_{OUT} is measured from OUT1 which generates the highest voltage) is the highest efficiency since it assumes that the other phases are generating more output power than they are. It is a little difficult to see, but the green and yellow curves (OUT2 and OUT3 V_{OUT} measurements, respectively) are right on top of each other.

The blue curve shows that the real efficiency of the MAX77711 is somewhere between the red and purple boundaries. But measuring carelessly could produce an efficiency error of up to 3%!

### Conclusion

The data shown in Figure 3 proves that the hypothesis is correct. Measuring efficiency of multiphase DC-DC converters requires careful placement of the measurement equipment. Asymmetric PCB layouts potentially lead to losses that might be accounted for during evaluation. The method for measuring the most accurate efficiency is to measure the output power of each phase individually and sum them to get the total output power.

It is not always feasible for an engineer to get eight meters to measure the efficiency of every multiphase buck converter they come across. The engineer should keep in mind the results of this article, and assess the quality and symmetry of the PCB, load, and measurement setup when evaluating efficiency. A good rule-of-thumb is to take the load from a middle point and measure the output voltage from a middle point, or as close to a middle point as possible.