# Using Power Factor Calculations for PCBA Reliability

July 30, 2020

### Key Takeaways

• What is the power factor (pf)?

• How to perform power factor calculations for circuit boards.

• How to use power factor calculations to improve PCBA reliability. Measuring the power factor

I suppose you could say that I was lucky in that I got a chance to study electrical engineering not only theoretically, but also by working in laboratories that contained state-of-the-art equipment, as well as classic tools. For example, there was no shortage of digital meters; however, there were also various magnetic ones that measured everything from volts and current to teslas. The most useful, aside from the oscilloscope, are the meters that provide information about a circuit’s ability to utilize or supply power.

Arguably, the most important aspect of a circuit, board or system’s power is the power factor (pf). The pf provides the ratio of usable electric power, known as real power and denoted by watts (W), to the total or apparent power denoted by volt-amperes (VA). The apparent power is determined by vectorially adding the real power and reactive power - denoted by volt-amperes reactive (VARs) - which is the power absorbed or emitted from a reactive circuit element. This relationship does present a challenge for directly measuring the pf. Let’s take a look at how power factor calculations can be made and utilized to optimize your design for reliability ## How is the Power Factor Calculated for Electrical Circuits?

Prior to defining the power factor, it is informative to define the various types of power in electrical circuits and their relationship to each other. This is done graphically in the power triangle figure below. Power triangle with leading and lagging power factor

As shown in the figure, there are three electrical power quantities: P - the real power; Q - the reactive power and S - the apparent power. Real power is the power that actually does work and it is either supplied from or absorbed by resistive elements.  The reactive power is supplied or absorbed by elements with reactances. The apparent power represents the total power supplied to the circuit or available for transfer and is the sum of the real and reactive powers, vectorially.

### Maximum Power Transfer

Still referring to the figure, the reactive power vectors, QL and Qc, are orthogonal to the real power vector, P. For a circuit or system, the reactive power is calculated by algebraically summing +QL and -Qc and denoted as follows:

If QL> Qc, then the circuit inductive.

If QL< Qc, then the circuit capacitive.

An interesting situation occurs when  QL=Qc or if Q=0.  For this case,  S= P, and all of the power is real or usable for work. This is known as maximum power transfer and is the ideal condition for signal transfer between circuits.

### Actual Power Transfer

Although the ideal case is typically the objective, most often Q ≠  0 and neither is the angular displacement between S = P. Instead, the power angle Ø vectorially, illustrates the magnitude of the reactive power vector and the displacement between the real and apparent power vectors. This angle is important as it defines the power factor, as shown below

. From the figure above it is obvious that the power factor and power angle are inversely proportional, as shown below. This relationship provides a means of designing electrical circuits for the optimization of the pf and maximizing actual power transfer. Now, let’s see if there is a benefit to considering the power factor and how these and other power factor calculations can be used to improve board design.

## Are Power Factor Calculations Important for PCBAs?

The short answer to this question is YES! In order to be utilized in electronic devices, products, systems, appliances or aboard vehicles, PCBAs must interconnect to other boards or devices. Additionally, today’s circuit boards typically contain one or more high-speed electrical signals that make signal integrity, which includes optimizing power transfer and minimizing losses, a primary design consideration.

Whether transferring from component to component on an individual PCBA, between connectors on different boards or to a load device, the level of power, and therefore, the power factor, is an important PCB layout design factor. And power factor calculations can be incorporated into the design process, as discussed below.

## How to Use Power Factor Calculations for More Reliable Board Designs

As stated earlier, the power factor is calculable as the cosine of the power angle. Again, referring to the power triangle illustration, it is apparent that for the actual case (Q0), it is a right triangle. This allows us to make use of the following trigonometric functions.

## How to Use Power Factor Calculations for More Reliable Board Designs All of these equations can be easily derived from the equation for the Pythagorean Theorem, as shown below related to the Power triangle. (2)

Noting that the apparent power is the product of the voltage and current, yields the following equations: Any of the equations above; including derivations, can be used to determine the power factor(s) on your board.

Optimizing power transfer and minimizing power factors should be done prior to having your boards built as making design changes afterward will result in increased time and costs for PCBA development. To avoid these, you should perform simulations and analysis during design. However, this does require that you have the tools; such as PSpice shown below, that can provide you with the necessary data for power flow calculations. Using PSpice simulation to optimize circuit power factor

As shown in the figure, PSpice can provide a graphical representation of the power factor; including whether it is leading or lagging. This capability is integrated into Cadence’s PCB Design package and provides all the mixed-signal simulation and analysis capability you need to design your boards to reliably perform as desired once in the field.

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