Harmonics and intermodulation distortions
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This document discusses harmonic distortion and intermodulation distortion in electrical systems. It defines harmonics as frequency components that are integer multiples of the fundamental frequency, such as 50Hz in India. Harmonics are caused by non-linear loads. Intermodulation distortion occurs when multiple frequencies interact in a non-linear system, producing new frequencies that are the sum and difference of the original frequencies. Both distortions can be measured by total harmonic distortion, with 7% or less considered acceptable. Harmonic and intermodulation distortions can overload systems and devices, and solutions include filters and active power filters.
![The performance of an ideal amplifier can be represented by the transfer function:
V out
A0
A1V in
An amplifier with some distortion due to nonlinearities can be expressed by a transfer function in the form of a
power series expansion:
V out
A0
A1V in
A 2V in
An input signal with two frequencies
The first order term
A0
A 2V
2
A 2V 12
A 2V 2
A 2V1
2
2
2
DC terms
and
A3V in
2
3
A 4V in
2
4
....
V in
may be shown as:
A1V in gives the fundamental products
The second order term A 2V in
2
in
1
2
V out
V1 cos(
A0
1
t)
V 2 cos(
A1V1 cos(
1
t)
t
2
cos(
t)
A1V 2 cos(
determines the second order products:
2
2
cos( 2
t)
1
A 2V 2
cos( 2
2
2nd harmonic terms
t)
2
A 2V1V 2
2
[cos(
1
2
t)
2nd order IMD terms
1
t
2
t )]
2
t)](https://image.slidesharecdn.com/harmonicsandintermodulationdistortions-140303094015-phpapp02/85/Harmonics-and-intermodulation-distortions-10-320.jpg)
![The third order term A 3V in
A3V
3
in
3 A3
V1V
2
A3V13
2
2
cos( 3
4
V1
3
determines the third order products:
3
cos(
2
1
t)
A3V 23
1
t)
3 A3
2
cos( 3
4
2
3
V2
2
cos V1 V 2
4
2
2
Fundamental frequency terms
t)
3rd harmonic terms
t)
2
3 A3V1 V 2
cos(
2
[cos( 2
1
t
2
t)
cos( 2
1
t
2
t )]
3 A3V1 V 2
4
[cos( 2
2
t
1
t)
cos( 2
2
t
1
t )]
3rd order IMD terms – The troublemakers](https://image.slidesharecdn.com/harmonicsandintermodulationdistortions-140303094015-phpapp02/85/Harmonics-and-intermodulation-distortions-11-320.jpg)
Harmonics and intermodulation distortions
- 1. HARMONIC & INTERMODULATION DISTORTION Anjani Kumar Yadav 11115013
- 2. WHAT IS DISTORTION IN ELECTRICAL SYSTEMS? Alteration of the original shape (or other characteristic) of sound or waveform.
- 3. WHAT IS HARMONICS? “A COMPONENT FREQUENCY OF A HARMONIC MOTION OF AN ELECTRO MAGNETIC WAVE i.e. AN INTEGRAL MULTIPLE OF FUNDAMENTAL FREQUENCY”. FUNDAMENTAL FREQUENCY in India is 50Hz.
- 4. WHAT CAUSES HARMONICS ? NON-LINEAR LOAD ::: CURRENT IS NOT PROPOTIONAL TO VOLTAGE e.g . DIODE , TRANSISTOR , NON-LINEAR AMPLIFIERS ETC. Some devices and loads: Converters, Devices which includes semi-conductor elements, Generators, Motors, Computers, Electronic ballasts, Switching power supplies, Welding machines, Control circuits, HVDC transmission systems, Electrical Communication systems. Transformers
- 5. EFFECT OF HARMONIC ON WAVE FORM
- 6. TOTAL HARMONIC DISTORTION (THD) Total Harmonic Distortion(THD): ------ Measure of amount of harmonics THD of the load should be less than 7% for acceptable performance THD for intermodulation distortion can also be calculated in a similar way.
- 7. INTERMODULATION DISTORTION distortion (IMD) is the amplitude Intermodulation or intermodulation modulation of signals containing two or more different frequencies in a system with nonlinearities Intermodulation occurs when the input to a non-linear system is composed of two or more frequencies. Consider an input signal that contains three frequency components at fa ,fb and fc which may be expressed as :
- 8. Output signal Y(t) = G(x(t)) Y(t) will contain three frequencies fa ,fb and fc of the input signal as well as number of linear combinations of these fundamental frequencies: Kafa+Kbfb +Kcfc Where Ka Kb and Kc are arbitrary integers which can assume positive or negative values. These are the intermodulation products (or IMPs). Intermodulation order: The order O of a given intermodulation product is the sum of the absolute values of the coefficients O= |Ka|+|Kb|+|Kc| In our example 3rd order intermodulation products occur where
- 10. The performance of an ideal amplifier can be represented by the transfer function: V out A0 A1V in An amplifier with some distortion due to nonlinearities can be expressed by a transfer function in the form of a power series expansion: V out A0 A1V in A 2V in An input signal with two frequencies The first order term A0 A 2V 2 A 2V 12 A 2V 2 A 2V1 2 2 2 DC terms and A3V in 2 3 A 4V in 2 4 .... V in may be shown as: A1V in gives the fundamental products The second order term A 2V in 2 in 1 2 V out V1 cos( A0 1 t) V 2 cos( A1V1 cos( 1 t) t 2 cos( t) A1V 2 cos( determines the second order products: 2 2 cos( 2 t) 1 A 2V 2 cos( 2 2 2nd harmonic terms t) 2 A 2V1V 2 2 [cos( 1 2 t) 2nd order IMD terms 1 t 2 t )] 2 t)
- 11. The third order term A 3V in A3V 3 in 3 A3 V1V 2 A3V13 2 2 cos( 3 4 V1 3 determines the third order products: 3 cos( 2 1 t) A3V 23 1 t) 3 A3 2 cos( 3 4 2 3 V2 2 cos V1 V 2 4 2 2 Fundamental frequency terms t) 3rd harmonic terms t) 2 3 A3V1 V 2 cos( 2 [cos( 2 1 t 2 t) cos( 2 1 t 2 t )] 3 A3V1 V 2 4 [cos( 2 2 t 1 t) cos( 2 2 t 1 t )] 3rd order IMD terms – The troublemakers
- 12. THIRD ORDER INTERCEPT POINT The 3rd order products will be the largest (loudest) of the intermodulation products. As a general rule, the 3rd order products will increase (grow) 3-times faster than the fundamental signal (the signal of interest)
- 13. DISADVANTAGE S Increased losses on the distribution system due to increase in the effective rms current Overloads, vibration and premature ageing of the generators, transformers and motors as well as increase in the noise level. Distortion of the supply voltage that can disturb the operation of the sensitive loads Disturbances in the communication networks and telephone lines SOLUTIONS Selective filters for low-order harmonics. Active power filters before non-linear loads. THD based power tarrifs methods.