# Distortion Power Factor in Your Nonlinear Circuits

### Key Takeaways

• Nonlinear circuits cause harmonic generation in an input waveform, leading to distortion in the time domain and additional peaks in the frequency domain.

• Distortion power factor defines how the total harmonic distortion of a nonlinear load decreases the total average power delivered to the load.

• Total harmonic distortion (THD) is the measure of the deviation of voltage or current waveform from ideal sinusoidal shape. Nonlinear components and circuits create distortion, which will reduce average power seen by a load component connected to a nonlinear circuit.

Many different types of circuits may need to deliver stable power to a load component or load circuit. Sometimes, a circuit has some nonlinear behavior that creates power distortion, leading to undesired harmonic generation and loss of power at the load component. To properly quantify the limits of acceptable distortion, we use a metric called the distortion power factor, which is related to total harmonic distortion (THD) in nonlinear circuits.

Let’s take a closer look at the meaning of distortion power factor and how it can be compensated in nonlinear circuits.

## Distortion Power Factor Definition

Distortion power factor is the nonlinear analogue of the conventional power factor, which relates the real and apparent power delivered to a load. The conventional power factor equation is only defined for linear circuits, which may include some reactance. The reactance in a linear circuit can create a phase shift between voltage and current, which creates a difference between the real and apparent power delivered to a circuit.

For nonlinear circuits, the power factor calculation needs to account for harmonic generation by nonlinear components. The definition of power factor relates the current in the primary harmonic to the RMS current contained in all harmonics: Definition of distortion power factor in terms of total RMS current in all harmonics

We can define this in terms of the total harmonic distortion (THD): Definition of distortion power factor in terms of THD

Note that, in both equations above, the current terms in the denominator are absolute values, while the term in the numerator can be a complex number that includes a phase factor. In other words, the above equation needs to be modified to include the phase angle between current and voltage: Definition of distortion power factor in terms of phase angle

This now tells us everything needed to calculate the distortion power factor in a (nonlinear circuit + load) network. In any circuit being designed for power delivery, the goal is to keep THD as close to 0 as possible, which will bring distortion power factor closer to 1. Once you know the distortion power factor in your system, you’ll know how much distortion you need to compensate to bring distortion power factor close to 1.

## Distortion Power Factor Compensation

The exact method for compensating distortion and increasing the distortion power factor back to 1 depends on the exact circuit and how it functions. Unfortunately, there is no single power factor correction method for every circuit. However, there are some steps a systems designer can take in different systems to reduce distortion and bring power factor closer to 1. To see how these work, it’s best to look at some common examples.

### Filter Compensation

The simplest way to compensate for low power factor is with filtration. In particular, a very high order bandpass filter can be used to pass a small amount of power in parallel with the nonlinear circuit and deliver this power to the load. A simple block diagram for this scheme is shown below. Using a parallel bandpass filter to correct distortion power factor

In this circuit, the power output from the nonlinear load could also be filtered to remove some of the harmonics, and it could be phase shifted to bring its phase closer to matching with the bandpass filter output. For ultra-precise phase matching at high frequencies, an analog PLL or DLL could be used with a feedback line to the source, which would also suppress any phase noise on the power source.

### Switching Regulators and PFC Circuits

High current switching power converters that include a switching regulator often use a power factor correction (PFC) circuit. When driven with an AC line voltage, distortion power factor arises due to the switching action in the regulator, which draws spikes of current that do not match the input voltage waveform. In the US and Europe, PFC is required on high power systems to prevent harmonic distortion and low efficiency in the utility grid.

PFC circuits involve a current sense feedback loop and a PWM MOSFET driver. The block diagram below shows an example PFC circuit architecture with a converter section (usually just a rectifier) and a switching regulator section. PFC circuit block diagram

The current sense block in this system senses the current being output from the regulator section, which then triggers the MOSFET driver. A half-bridge or full-bridge MOSFET arrangement in parallel with the converter section is switched and begins sourcing some current. The current delivered to the regulator will more closely follow the voltage waveform. This brings the phase angle between the voltage and current closer to 0, which brings the power factor closer to 1.

### Power Amplifiers

Power amplifiers are normally run near saturation, so they always create some harmonics. When driven with a harmonic signal, there will be some harmonic distortion that limits the useful output power from the amplifier. RF power amplifiers driven with FM signals have an additional problem called intermodulation distortion, where additional terms are added to the RMS current in the denominator of the distortion power factor equation.

We often state that maximum power transfer always occurs when two impedances are conjugate matched, but this is only true for linear circuits. For nonlinear circuits, a power amplifier may have greatest power delivery when there is some slight impedance mismatch between the power amplifier output and the load component. The appropriate impedance mismatch can be determined using load-pull analysis, either through measurements or with proprietary simulation packages.

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