# Difference between Harmonics and Sub-harmonics

Harmonics in electrical system is the signal having frequency which is integral multiple of fundamental frequency. This means, if the frequency of fundamental component is 50 Hz, then the frequency of harmonics will be 2×50 (=100 Hz), 3×50 (=150 Hz) and so on.

If the frequency of harmonics is even multiple of fundamental frequency then it is said to be even harmonics. Hence, signals with frequency 100 Hz, 200 Hz, 300 Hz are the even harmonics of fundamental component with frequency 50 Hz. Similarly, if the harmonic frequency is odd multiple of fundamental frequency, then it is called odd harmonics. Obviously, for fundamental frequency of 50 Hz, the frequency of odd harmonics will be 150 Hz, 250 Hz, 350 Hz and so on.

Thus we see that, the frequency of harmonics is ** nxf** where f is fundamental frequency and n is an integer. Thus, the harmonic frequency is always greater than the fundamental frequency. Harmonics in a system is generated due to non-linearity. For example, major cause of harmonics in transformer excitation current is due to non-linearity of its B-H curve.

If the frequency of a signal is less than the fundamental frequency then it is called sub-harmonics. This means, the frequency of sub-harmonics will be (1/n)^{th} times of the fundamental frequency. Thus, a frequency of 25 Hz, 17 Hz,12 Hz, etc. are sub-harmonics.

Thus, the major difference between harmonics and sub-harmonics is that prior is having frequency of ** nf** while latter have

**,where f is fundamental frequency. Another difference is that, harmonics have frequency more than fundamental frequency whereas sub-harmonics have less than fundamental frequency.**

*(1/n)f*Sub-harmonic currents are often observed in series compensated transmission line. When the line is compensated using series capacitors it produces currents of sub harmonic frequencies, which can be dangerous. One major problem offered by sub-harmonic current is under-reach or over reach of distance relay meant to protect the line.