# Examples of Harmonic Producing Loads

Harmonics are primarily caused by loads that draw current repetitively but in a nonsinusoidal manner. Harmonic loads include: ballast/fluorescent lighting and computer power supplies; uninterruptable power supplies (UPS); variable speed drives; charging circuits incorporating rectifiers; arc welders and three-phase machines. Examples of load current waveforms with harmonics are illustrated in Figure 2.6.

# Harmonics in DC/DC Converter of Isolation Transformer

## A. Isolation Transformer and Excitations

In switching mode power supplies, the isolation transformers are often used in DC-DC converter topologies like zero voltage or zero current switching resonant converters and push-pull current source converters. The HBFEM numerical modeling and computation results can provide more detailed information on harmonic distribution and power

Figure 2.6 Examples of load current waveforms with harmonics losses in transformer, and magnetic flux and eddy current distributions in core and windings respectively [8]. To understand harmonic distribution in the transformer the excitation voltage and magnetic flux waveforms and associated current waveforms should be investigated.

*Sinusoidal Excitation:*

Since vi (instantaneous value of the applied voltage) is sinusoidally varying, the flux must also be sinusoidal in nature varying with frequency *f.* Let:

where *ф*_{mp} is the peak value of mutual flux. From Faraday’s law, the voltage induced in the N-turn coil is:

The r.m.s. value of the induced voltage, *E*_{1}*,* is obtained by dividing the peak value in equation (2-13) by /2:

*Square Wave Excitation:*

With a square waveform excitation voltage, from Faraday’s law, the voltage induced in the N-turn coil is:

Time-dependent magnetic flux (triangular waveform) in the magnetic steady-state case can be expressed as:

Substituting *f* = 1/Г, the magnetic flux is obtained as:

Figure 2.7 (a) Waveforms of flux; (b) voltage for sinusoidal magnetizing current in nonlinear

magnetics

and the induced voltage, *E,* can be obtained as:

*Excitation Characteristics:*

Figure 2.7 shows waveforms of flux and voltage for sinusoidal magnetizing current in nonlinear magnetics, where the distorted waveforms of flux and voltage contain component-only harmonics, as expressed in equations (2-19) and (2-20).

and

Waveforms of flux and voltage for square voltage wave excitation in nonlinear magnetics, time-dependent magnetic flux (triangular waveform) in the magnetic steady state case will be illustrated as:

In the majority applications of switching mode power supplies, it is desirable to incorporate a transformer into the switching mode DC/DC converter, to obtain DC isolation between the converter input and output. In off-line power supply applications, isolation is usually required by regulatory agencies. This isolation could be obtained by simply connecting a 50 Hz or 60 Hz transformer at the power supply AC input terminals. However, since transformer size and weight vary inversely with frequency, incorporation of the transformer into the converter can make significant improvements; the transformer then operates at the converter switching frequency of tens or hundreds of kilohertz.

The size of modern ferrite power transformers is minimized at operating frequencies ranging from several hundred kilohertz to roughly one megahertz. These high frequencies lead to dramatic reductions in transformer size [9]. When a large step-up or step- down conversion ratio is required, the use of a transformer can allow better converter optimization. By proper choice of the transformer turns ratio, the voltage or current stresses imposed on the transistors and diodes can be minimized, leading to improved power efficiency and lower cost.

There are several ways of incorporating transformer isolation into any DC-DC converter, such as the full bridge, half-bridge, forward and, push-pull converters. Zero- voltage or current-switched resonant and LLC resonant converters are commonly used isolated versions of DC/DC converters. The flyback converter is an isolated version of the buck-boost converter. Isolated variants of the Cuk converter are also known. The full-bridge, forward, flyback and LLC converters, with isolated transformer, are briefly described in the following section.