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. All electrical power consists of true power (dissipated in resistive elements) and reactive power (stored and released in reactive elements). Together, these two portions of total power form a complex number, which we call “apparent power.” Because apparent power contains resistive and reactive parts, we need to treat it vectorially, just like we would with impedance. We can visualize each of its parts graphically (as shown in the power triangle figure below).
Power triangle with leading and lagging power factor
As shown in the figure, we define three electrical power quantities: P = true power; Q = reactive power; S = apparent power. True power is the power that actually does work, and it is either supplied from or absorbed by resistive elements. In the latter case, this means that true power is dissipated as heat. The reactive power is supplied or absorbed by elements with reactance and is only applicable in AC circuits. The apparent power represents the total power supplied to the circuit or available for transfer and is the sum of the true and reactive powers, vectorially.
A circuit’s power factor is defined as P/|S|, or the ratio of the true power to the magnitude of the total power. If you remember Euler’s formula from your linear algebra class, then you may remember that the apparent power S can be defined in terms of a phase angle. Simply put, this phase angle is the angle shown in the above power triangle. Using Euler’s formula, we can define the power factor as follows:
When designing electrical circuits that are intended for power delivery, the design goal is to maximize PF as measured at a resistive load by minimizing inductive and capacitive contributions to the power factor. This can be done in multiple ways, which we’ll explore a bit later.
Most often, systems will operate with Q ≠ 0 and S ≠ P, meaning some power is stored and released as reactive power. For components in some systems, e.g., a transformer in a power conversion system, we would prefer this to be the case, as we would like the circuit to not lose any true power through heat dissipation. The power angle, vectorially, illustrates the magnitude of the reactive power vector and the displacement between the true and apparent power vectors.
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.
This formula implies that, if a power system has a low power factor, the real power transfer to the load could be increased by adding some reactance (either capacitance, inductance, or both). This is one way that power conversion and delivery is compensated and controlled in resonant switching converters. Specific circuits that are designed to provide this function are called power factor correction (PFC) circuits, and these may be required on some systems depending on locality.
Trigonometric Functions for Power Factor Calculations
As stated earlier, the power factor is normally calculated using the cosine of the power angle. However, we could use other quantities that make up the definition of apparent, true, or reactive power to calculate the phase angle θ, and thus the power factor cos(θ). Using the definitions of the basic trigonometric functions and their inverses in the power triangle above, we can make use of the following relations.
All of these equations can be easily derived from the equation for the Pythagorean Theorem, as shown below related to the Power triangle.
S2=P2+Q2 --> S=P2+Q2 (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.
Example Power Factor Calculation
Consider a power system with 60 Hz voltage output of V = 5.12 V @ +16° phase angle and current output of I = 1.3 A @ -32° phase angle. What is the power factor for this system? You can follow these steps:
- Calculate the phase angle between voltage and current: +16° - (-32°) = 48°
- Calculate the true power: P = (5.12 V)(1.3 A)cos(48°) = 4.454 W
- Calculate the apparent power: S = (5.12 V)(1.3 A) = 6.656 VA
- Divide #2 by #3 to get PF = 0.6691, or about 67%.
The savvy reader should notice that the power factor is just equal to the cosine of the phase difference between voltage and current. Note that this only applies when the voltage and current have the same sinusoidal behavior and frequency. More generally, this is not the case with arbitrary waveforms (e.g., real switching converters). However, for harmonic AC power systems, the phase angle gives another way to calculate the power factor: simply look at the phase difference between the output voltage and current for a given load component and then take the cosine.
For other systems where you know the power delivered to the load and the apparent power, you can use the example power factor calculator shown below to determine the power factor.
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, often with the purpose of delivering power. 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
The goal in maximizing PF for a power system is to ensure power is delivered to a resistive load component, not dissipated as heat in the components. In this way, the design will be made much more efficient. In fact, power factor is a measure of power conversion efficiency. A power factor of less than 95% is sometimes cited as being unacceptable for a power system.
Optimizing power transfer and maximizing the power factor measured at the load component 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.
Power factor is determined from simulation results by comparing the voltage and current measured at the output ports of a power system. Consider the results below. Here, the current and voltage are not lined up in-phase, so some of the power will be dissipated as reactive power. This is your first clue that the design has a low power factor and that there is some reactive or inductive contribution to the power output that needs to be compensated.
Using PSpice simulation to optimize circuit power factor
As shown in the figure, PSpice can provide graphical and numerical results that can be used in power factor calculations. 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.
If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.
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