Harmonic Analysis of The Load Voltage And Load Current Waveforms
Harmonic Analysis of the load voltage and load current waveforms:
Fig: Square wave load voltage output by half-bridge inverter
- The load voltage waveform shown in Fig. can be mathematically described in terms of its Fourier’s components as:
where ‘n’ is the harmonic order and ω/2πis the frequency (‘f’) of the square wave.
- ‘f’ also happens to be the switching frequency of the inverter switches. As can be seen from the expression of the Fourier’s components. The square wave load voltage consists of all the odd harmonics and their magnitudes are inversely proportional to their harmonic order.
- Accordingly, the fundamental frequency component has a peak magnitude of and the nth harmonic voltage (n being odd integer) has a peak magnitude of . The magnitudes of very high order harmonic voltages become negligibly small. In most applications, only the fundamental component in load voltage is of practical use and the other higher order harmonics are undesirable distortions.
- Many of the practical loads are inductive with inherent low pass filter type characteristics. The current waveforms in such loads have less higher order harmonic distortion than the corresponding distortion in the square-wave voltage waveform.
- A simple time domain analysis of the load current for a series connected R-L load has been presented below to corroborate this fact. Later, for comparison, frequency domain analysis of the same load current has also been done.
Basically the analysis can be classified as:
- Time Domain Analysis
- Frequency Domain Analysis