To test the measurement and calculation of total harmonic distortion.
Problem Definition
The limits on voltage harmonics are thus set at 5% for THD and 3% for any single harmonic. It is important to note that the suggestions and values given in this standard are purely voluntary. However, keeping low THD values on a system will further ensure proper operation of equipment and a longer equipment life span
Introduction
One method to characterize the linearity of an amplifier is to measure its total harmonic distortion (THD). The power quality of distribution systems has a drastic effect on power regulation and consumption. Johan Lundquist of the Chalmers University of Technology, Sweden quotes, The phrase ‘power quality’ has been widely used during the last decade and includes all aspects of events in the system that deviates from normal operation.”1 This has been especially true after the second half of the 20th century when new types of electronic power sources caused distortion in waveforms of the power system. Power sources act as non-linear loads, drawing a distorted waveform that contains harmonics. These harmonics can cause problems ranging from telephone transmission interference to degradation of conductors and insulating material in motors and transformers. Therefore it is important to gauge the total effect of these harmonics. The summation of all harmonics in a system is known as total harmonic distortion (THD). This paper will attempt to explain the concept of THD and its effects on electrical equipment. It will also outline the low THD of the Associated Power Technologies (APT) line of programmable sources and how these can be used to more effectively test equipment. What is Total Harmonic Distortion? Total harmonic distortion is a complex and often confusing concept to grasp. However, when broken down into the basic definitions of harmonics and distortion, it becomes much easier to understand. Imagine a power system with an AC source and an electrical load . Harmonic distortion is measured by applying a spectrally pure sine wave to the amplifier in a defined circuit configuration (i.e., bias conditions, output amplitude or output power level, frequency, etc.) and observing the output spectrum. The amount of distortion present at the output of the amplifier depends on several parameters, such as: • Small and large signal nonlinearity of the amplifier being tested • Amplifier’s output amplitude or power level • Frequency response of the amplifier • Load applied to the output of the amplifier • Amplifier’s power supply voltage • Circuit board layout • Grounding • Thermal management, etc. Measurements based on amplitudes (e.g., voltage), must be converted to power to make the addition of harmonic distortion meaningful.
For example, for a voltage signal, the ratio of the square of the RMS voltages is equivalent to the ratio of the power. Harmonic distortion may be measured by applying a spectrally clean sine wave voltage signal to the input of the amplifier under test (may require a band pass or low pass filter if the excitation RF source has high harmonic output content). Next, adjust the input power level to the amplifier for a desired output power level and then looking at the output harmonic spectrums (second, third, and fourth harmonics, etc.) of the amplifier on a spectrum analyzer relative to the amplitude of the output fundamental signal, see 0 example. Another method is to measure the output waveform signal of the amplifier using a high speed/bandwidth oscilloscope (i.e., has BW greater than six to ten times of the fundamental frequency). Detrend the data if needed (i.e., remove offset; normally not required for a CW signal), and then perform a FFT to get the amplifier output’s harmonic content. The power levels of the individual measurement harmonic values (second, third, and fourth, etc.) are usually expressed in decibel format, (dBc is relative to the fundamental carrier power level, or dBm is in absolute power). The simplest measurement unit to use for the harmonic measurement is dBm. This allows the tester to not have to keep track of the amplitude signal level of the fundamental frequency. For example, if measured in dBc, before calculating the THD, one needs to convert the dBc value to dBm value for each of the harmonic values before calculating their individual power level in watts.
Harmonic Content of an Amplifier’s Output
Power System with AC source and electrical load
Now imagine that this load is going to take on one of two basic types: linear or nonlinear. The type of load is going to affect the power quality of the system. This is due to the current draw of each type of load. Linear loads draw current that is sinusoidal in nature so they generally do not distort the waveform. Most household appliances are categorized as linear loads. Non-linear loads, however, can draw current that is not perfectly sinusoidal. Since the current waveform deviates from a sine wave, voltage waveform distortions are created.
Past Studies
Keeping a low THD With the use of non-linear loads on the rise globally, isolation for poor quality distribution systems and mitigation of harmonics will become increasingly important. The limits per IEEE Std 519 are not enforced limits but suggestions on acceptable levels. As a result, THD on certain power systems could be much higher, especially considering the difficulty in attaining harmonic measurements. The APT line of programmable AC power sources isolates electronic equipment from a distorted mains supply while maintaining low THD during testing and measurement. Below are THD specifications for the full APT line of sources. THD is maintained below 2% for full frequency range:
APT power sources are measured for THD up to the 40th harmonic for the various frequency outputs of the source (mains frequency up to 1000Hz). This ensures a low THD value over the entire operating frequency range of the instrument. Utilizing an APT source will provide a clean signal with low THD and isolation from local supply interference.
Objective Function
Harmonics have frequencies that are integer multiples of the waveform’s fundamental frequency. For example, given a 60Hz fundamental waveform, the 2nd, 3rd, 4th and 5th harmonic components will be at 120Hz, 180Hz, 240Hz and 300Hz respectively. Thus, harmonic distortion is the degree to which a waveform deviates from its pure sinusoidal values as a result of the summation of all these harmonic elements. The ideal sine wave has zero harmonic components. In that case, there is nothing to distort this perfect wave. Total harmonic distortion, or THD, is the summation of all harmonic components of the voltage or current waveform compared against the fundamental component of the voltage or current wave:
The formula above shows the calculation for THD on a voltage signal. The end result is a percentage comparing the harmonic components to the fundamental component of a signal. The higher the percentage, the more distortion that is present on the mains signal.
Total Harmonic Distortion (THD) is expressed in Root-Sum-Square (RSS) in percentage. The THD is usually calculated by taking the root sum of the squares of the first five or six harmonics of the fundamental.
Methodology Samples
Let’s assume, there is negligible error when only the second and third harmonics are included, as long as the higher harmonics are three to five times smaller than the largest harmonic. For example, 0.10 is one harmonic value and 0.03 is another higher harmonic value but three times smaller in amplitude:
An example of THD calculation will be provided at end of this application note.
Equations for THD Calculation
If the measurement data is in power
or, if the measurement data is in volt,
Example of THD Calculation is the output waveform from the amplifier under test. The fundamental frequency is at 2.5 GHz and the output amplitude level is at 3.6 Vpp (driven into saturation). We will use this captured signal in our THD calculation example. One method is to use a spectrum analyzer to measure the amplifier’s harmonic output and the other method is to use an high speed/bandwidth oscilloscope/DCA to capture the amplifier’s output signal waveform and then perform FFT to get its harmonic content. (This application note assumes the user knows how to perform FFT.)
Graphical representation of two measurement results.
The comparison result shows there is about 0.8 % difference in the THD calculated results between the two test methods (spectrum analyzer vs. oscilloscope). This difference can be caused by the measurement uncertainty, measurement repeatability, frequency response error, and the oscilloscope’s amplitude sensitive of measuring a small harmonic signal in the presence of a large fundamental signal. Based on the results, both THD test methods will work. Possible simulations from MATLAB will explain the process and show how this interesting study will progress.
Importance of THD
While there is no national standard dictating THD limits on systems, there are recommended values for acceptable harmonic distortion. IEEE Std 519, “RECOMMENDED PRACTICES AND REQUIREMENTS FOR HARMONIC CONTROL IN ELECTRICAL POWER SYSTEMS” provides suggested harmonic values for power systems: “Computers and allied equipment, such as programmable controllers, frequently require ac sources that have no more than 5% harmonic voltage distortion factor [THD], with the largest single harmonic being no more than 3% of the fundamental voltage. Higher levels of harmonics, result in erratic, sometimes subtle, malfunctions of the equipment that can, in some cases, have serious consequences.”
Recent Findings
Harmonic distortion can have detrimental effects on electrical equipment. Unwanted distortion can increase the current in power systems which results in higher temperatures in neutral conductors and distribution transformers. Higher frequency harmonics cause additional core loss in motors which results in excessive heating of the motor core. These higher order harmonics can also interfere with communication transmission lines since they oscillate at the same frequencies as the transmit frequency which if left unchecked, increased temperatures and interference can greatly shorten the life of electronic equipment and cause damage to power systems.