# Using Average or RMS in Efficiency Calculation

Ming Sun / October 21, 2022

6 min read • ––– views

## Background

The most import parameter or performance metric for any switching regulator is efficiency, because that is the main purpose switching regulators are designed for. The question is we should ask is that when calculating or measuring switching regulator's efficiency, should average value or the RMS (root mean square) value be used?

For example, we all know for a buck converter, its input current is pulsating. Now, the question is we should ask is that when testing efficiency, should we use RMS value or the average value for the input power calculation?

Most often, when test engineers or designers measure the efficiency during the bench measurement, the average value is being used. So what is the reason behind the scene?

## Math derivation

The efficiency can be calculated by its definition:

Where, ** E_{out}** is the output energy,

**is the input energy,**

*E*_{in}**is the output power and**

*P*_{out}**is the input power.**

*P*_{out}To calculate the power, three methods can be used:

### When to use average value:

Typicall when measuring the efficiency of the switching regulator, ** V_{in}** is supplied with a DC source, which means

**is a constant.**

*V*_{in}**is typically supplied from a DC current source, which can be considered as a constant as well. Therefore, Eq (3) can be rewritten as:**

*I*_{out}Where, ** V_{out,avg}** is the average value of switching regulator's output voltage and

**is the average value of the inptu current.**

*I*_{in, avg}Conclusion:During the bench test or simulation, if we bias

with a DC voltage source andV_{in}with a DC current source, when measuring efficiency, we should use average value ofI_{out}andI_{in}.V_{out}

### When to use RMS value:

Now, we do not always use a DC current source at the switching regulator's output. Sometimes, we use a resistive load as well. In such case, Eq. (3) can be rewritten as:

Where, the RMS value of ** V_{out}** is defined as:

## Conclusion

From the above discussion and math equations, it is clear that when one of the parameter is set to be constant when using V*I to calculate the efficiency, we should use average value for the other term.

If we use

orV^{2}/R, we should use RMS value for the other term.I^{2}*R