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What is Total Harmonic Distortion (THD)?

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Total harmonic distortion (THD) is a function versus frequency that helps quantify how well the output of a system replicates the input. The lower the THD values, the less the noise or distortion in the system output.

 

THD measurements are used in many applications by different industries.  This article concentrates on the use of THD in closed loop vibration control systems.

 

In a closed loop vibration control system, there are many components: amplifier, shaker, test fixture, test object, and a control accelerometer (Figure 1). A low THD of each component, and of the combined system, is desirable.  

 

Closed_Loop_Control.pngFigure 1: Sine vibration control system components

A system with a low THD is easier to control.  In a sine test, the THD will be different at each frequency, making some frequencies easier to control than others.

  

THD Background

 

The THD of a system is determined by inputting a single frequency into a system, and measuring the output.  The output may contain additional harmonic frequencies of the input frequency, as shown in Figure 2. For example, if a 100 Hertz sine was input into the system, the output may contain 100 Hz and multiples like 200, 300, and 400 Hz.

 

2.jpgFigure 2: Harmonic distortion is when the output of a system creates additional harmonics that did not exist in the input

The THD is the ratio of the energy in the output signal that is not related to the input sine tone (Equation 1):

 

3.jpgEquation 1: Total Harmonic Distortion (THD)

THD is usually calculated over a range of frequencies (for example, 20 to 2000 Hz).  The input sine frequency is swept over the desired range and a THD value at each frequency is recorded.

 

In a digital spectral measurement, the energy referred to in Equation 1 is measured by calculating the RMS value over a frequency range or around the main harmonic.

 

The results for a THD test are plotted in Figure 3.

 

4.jpgFigure 3: Total Harmonic Distortion plotted as function of frequency for a system

THD has a value between zero and one for each frequency tested:

 

  • ZERO - A value close to zero means that the output has low harmonic distortion. The sine wave of the output has similar frequency content as the input.
  • ONE - A value close to 1 means that there is a lot of harmonic distortion present in the signal. Almost all the frequency content in the signal is not at the same frequency as the input signal.

THD can also expressed in percentage, from 0 to 100%, where 100% corresponds to 1. 

 

In many applications, a low THD is desired.  A low THD means that the system output is similar to the system input, with minimal distortion.

 

In practice, there are differences in how THD may be calculated for a given spectrum.  For some methods, only the energy at harmonics are considered.  Sometimes the calculation is limited to first five or ten harmonics of the output signal.

 

Other methods consider the total RMS of the output signal. These methods are sometimes designated as THD+N, because the noise between harmonics is included in the calculation. The N is short for noise.

 

THD in Vibration Control shaker systems

 

A THD function can be measured on components (amplifier, shaker, test structure) or on combinations of components for a shaker system.

 

For example, the quality of amplifiers is often specified using THD. An amplifier THD of 0.01 or lower is normal (less than 1%).

 

Mechanical systems, on the other hand, tend to have higher THD values than electronic amplifiers.

 

For example, measuring the THD of an amplifier and shaker (without a test structure) usually has THD values below 2%, with some spikes of about 10% (blue curve, Figure 4). 

 

5.jpgFigure 4: THD of a shaker with structure (gold) is higher than the THD of the shaker only (blue)

The THD of a complete shaker system (gold curve, Figure 4) is measured over:

 

  • Input - SCADAS output DAC (Volts) is the input to the shaker system
  • Output – The output of the shaker system is vibration (g’s) measured by a control accelerometer
  • System - The shaker system consists of the amplifier, shaker, test fixture, and test object (g/V)

Adding a test article and fixture to the shaker and amplifier system, can increase the THD significantly.  It can be above 50% at certain frequencies.  Frequencies with a high THD may be difficult to control during a test.

 

Causes of Harmonic Distortion in Vibration Control shaker systems


(view in My Videos)

 

Where do these harmonics come from, when ostensibly, only one controlled sine frequency is being input into the shaker system?

 

As shown in the video, and in Figure 5, despite a single frequency input, several sinusoidal harmonics of the control are also generated.

 

6.jpgFigure 5: Vibration spectrum during sine control test with harmonic distortion

An ideal sine wave has a single frequency in its spectrum, without harmonics.  Harmonics are present when the sinusoidal vibration of the output does not replicate the pure sine wave of the input.

 

 Examples of a pure sine wave versus a sinewave with harmonics is shown in Figure 6.

 

7.jpgFigure 6: Top – Perfect sine wave with no harmonic distortion, Bottom – Sine wave with harmonic distortion

A shaker system may distort a perfect sine wave input in the following ways:

 

  • Friction or rubbing in the shaker armature or bearings.
  • Armature resonance creates motion out of the plane of the input. For example, a bending resonance of an armature creates lateral motion when applying a vertical excitation.
  • The shaker armature is not straight, but instead is slightly bowed or bent. This creates moments perpendicular of the excitation direction, instead of straight linear motion.
  • Localized test object or test fixture resonances at higher frequencies create more energy on one side of test structure than the other side.
  • Force moments caused by the test article center of gravity not directly over the center of shaker (see Figure 7).
  • And more…

Of the two setups in Figure 7, the setup on the right, with an off-center test object, would have higher Total Harmonic Distortion (THD) values than the test setup on the left.

8.jpgFigure 7: Two vibration control setups: system on left expected to have lower harmonic distortion, system on right expected to have higher harmonic distortion

The off-center test object would create forces not aligned with the direction of main excitation.

 

THD and System FRF

 

In a closed loop vibration control system, vibration is reproduced on the test object.  There is a target value for the vibration levels on the test object, and the SCADAS output is adjusted to achieve this level. 

 

To adjust the level properly, a Frequency Response Function (FRF) of the shaker control system is used to predict the input and output levels. It is useful to consider both the THD and the FRF when evaluating a dynamic system.

 

The FRF or transfer function (with units of g/V for a shaker system) also quantifies the relationship between the input and output of a system. In control theory the FRF is called the system gain. The FRF of a shaker control system is overlaid with the THD function in Figure 8.

 

9.jpgFigure 8: Total Harmonic Distortion (Blue, Left Y-axis) versus FRF (Green, Right Y-axis in g/V) of shaker control system

In Figure 8, the following can be observed about THD and the system FRF:

 

  • Looking at Figure 8, where the system gain (i.e., FRF) is high, the THD is low. The harmonics are “washed out” by the high amplitude of the output vibration.
  • Vice versa is also true: where the THD is high, the system gain is low. The effects of the vibration harmonics are more significant when the system vibration response is low.

Trying to control a system with a high THD can be difficult.  Typically a single frequency is being input into the system with a controlled amplitude.  High amounts of harmonic distortion create vibration at other frequencies, which are not controlled.  This increases the vibration amplitude levels on the test object in an uncontrolled, and therefore, unpredictable manner.  There are seveal sine test control parameters that can be adjusted to try and overcome these test difficulties.

 

THD and the system FRF can be measured during a sine control test while using Simcenter Testlab.

 

Measuring THD and FRF in Simcenter Vibration Control

 

A THD and FRF function can be calculated both online and offline in Simcenter Testlab (formerly called LMS Test.Lab):

 

Online Measurement

 

In Simcenter Testlab Sine Control, the ‘THD’ and ‘FRF’ measurements can be turned on in the lower right corner of the ‘Sine Setup’ worksheet as shown in Figure 9. 

 

10.jpgFigure 9: THD and FRF is selectable in the Measurements section of the Sine Setup worksheet

The THD and FRF functions will automatically be stored in the Simcenter Testlab project file during the test, as well as after the test is completed.

 

Offline Processing

 

If a sine sweep test has already been performed, and the time data is available, the application “Offline Sine Data Reduction” can be used to calculate the THD.  “Offline Sine Data Reduction” can be started from the “Simcenter Testlab Environmental” folder.

 

Conclusions

 

Understanding and measuring the Total Harmonic Distortion of a shaker system is helpful:

  • When encountering a difficult to control system, the THD values can be plotted to understand if high amounts of harmonic distortion are present at particular frequencies. Lowering the THD of the shaker test system by eliminating a test fixture resonance, or addressing other harmonic distortion causing issues as previously listed in this article, can make completing a test possible. 
  •  THD is also useful to evaluate if the amplifier and shaker are functioning properly. This is done by measuring the THD periodically.

Questions? Post a reply, or email albert.prosuk@siemens.com.

 

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