In single-pulse width modulation control, there is only one pulse per half-cycle and the width of the pulse is varied to control the inverter output voltage. The generation of gating signals and output voltage f single-phase full bridge inverters is shown in Fig.1. As shown in Fig.1, the gating signals are generated by comparing a rectangular reference signal of amplitude, $E_{R},$ with a triangular carrier wave of amplitude $E_{c}$. The fundamental frequency of output voltage is determined by the frequency of the reference signal. The pulse-width, $P,$ can be varied from $0^{\circ}$ to $180^{\circ}$ by varying $E_{R}$ from 0 to $E_{c}$ . The ratio of $E_{R}$ to $E_{c}$ is the control variable and is defined as the amplitude modulation index. The amplitude modulation index, or simply modulation index is

$$M=\frac{E_{R}}{E_{c}}-----(1)$$

The following Fourier-series describes the waveform of $E_{L}$ as

$$E_{L}=\sum_{n=1,3,5, \ldots}^{\infty} \mathrm{A}_{\mathrm{n}} \sin n \omega t+\sum_{n=1,3,5, \ldots}^{\infty} B_{n} \sin n \omega t-----(1)$$

where

$$\quad A_{n}=\frac{2}{\pi} \int_{0}^{\pi} E_{\mathrm{dc}} \sin n \omega t \cdot \mathrm{d}(\omega t)=\frac{2}{\pi} \int_{(\pi / 2-p)}^{(\pi / 2+p)} \sin n \omega t \cdot \mathrm{d}(\omega t)$$

$$=\frac{4 E_{\mathrm{dc}}}{5 \pi} \sin \frac{n p}{2}$$

and $$\qquad B_{n}=\frac{2 E_{\mathrm{dc}}}{\pi} \int_{(\pi / 2-p)}^{(\pi / 2+p)} \cos n \omega t \cdot \mathrm{d}(\omega t)=0-----(2)$$

Thus, $$\quad E_{L}=\sum_{n=1,3,5, \ldots}^{\infty} \frac{4 E_{\mathrm{dc}}}{n \pi} \sin \frac{n p}{2} \sin n \omega t-----(3)$$

When pulse-width $P$ is equal to its maximum value of $\pi$ radians, then the fundamental component of output voltage $E_{L},$ from Eq. $(3),$ has the peak value of $$E_{L 1 m}=\frac{4 E_{\mathrm{dc}}}{\pi}-----(4)$$

The RMS output voltage can be found from,

$$E_{L m \mathrm{s}}=\left[\frac{2}{\pi} \int_{(\pi-p) / 2}^{(\pi+p) / 2} E_{\mathrm{dc}}^{2} \mathrm{d}(\omega t)\right]^{1 / 2}=E_{\mathrm{dc}} \cdot \sqrt{\frac{P}{\pi}}-----(5)$$

The peak value of the $n$ th harmonic component from Eq. $(3)$ is given by, $$E_{L n m}=\frac{4 E_{\mathrm{dc}}}{n \pi} \sin \frac{n p}{2}-----(6)$$

From Eqs $(4)$ and $(6), \frac{E_{L n m}}{E_{L1 m}}=\frac{\sin \frac{n p}{2}}{n}-----(7)$

The ratio as given by Eq. $(7)$ is plotted in Fig.2 for $n=1, n=3, n=5,$ 7 for different pulse widths. From these curves it may be observed that when the fundamental component is reduced to nearly $0.33,$ the amplitude of the third harmonic is also $0.33 .$ When fundamental component is reduced to about 0.143 , all the three harmonics $(3,5,7)$ become almost equal to the fundamental. This shows that in this type of voltage control scheme, as great deal of harmonic content is introduced in the output voltage, particularly at low output voltage levels.