Philips Electromagnetic Lamp ft = 4U/π sinω t + 1/3sin3ω t + 1/5sin5ω t +, Harmonic distortion

5

3.9 Harmonic distortion

1

U

3
5
7
9
π	2π

0

Fig. 123. Lamp voltage wave form constructed by the odd harmonics from one to nine, according to the formula:

f(t) = 4U/π (sinω t + 1/3sin3ω t + 1/5sin5ω t + ....).

The second reason for the presence of harmonics in the lamp current is the hysteresis of the ballast coil.With the aid of the relationship between ballast voltage and ballast current (B-H curve of the ballast coil, see Fig. 124), the resulting current can be found for any ballast voltage. Even with a pure sine-wave ballast voltage there will be some harmonics in the ballast current, but this effect is small, compared with the harmonics caused by the lamp.

The impedance of the coil becomes higher for higher frequencies, so in practice only odd harmonics up to the seventh are of any importance for the lamp current.

Practical values in percentage of the fundamental for most inductively stabilised discharge lamps are:

fundamental:	100 %
third harmonic:	10 %
fifth harmonic:	3 %
seventh harmonic:	2 %
ninth and higher harmonics:	1 % or lower

When the supply voltage contains harmonics, these values can change somewhat, but the ballast coil prevents dramatic increases.

B,Φ,V
	B,Φ,V
	H,i
H,i	t

Fig. 124. Hysteresis cur ve of a typical copper-iron ballast.

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