Introduction:
In single pulse modulation of PWM (Pulse Width Modulation) inverter, the objective is to generate a sinusoidal output voltage by varying the width of the pulses. The modulation technique involves adjusting the pulse width according to the reference sinusoidal waveform. However, this modulation technique introduces harmonics in the output waveform, including the 3rd harmonic.

Eliminating the 3rd Harmonic:
To eliminate the 3rd harmonic in single pulse modulation of PWM inverter, the pulse width needs to be adjusted to a specific value.

Pulse Width:
The pulse width of the PWM waveform is usually represented as a percentage of the total time period. For example, if the pulse width is 50%, it means the pulse is active for half of the time period.

Equation:
The equation for the nth harmonic is given by:
\[ V_n = \frac{4V_m}{n\pi} \times \sin(n\omega t + \phi) \]
where:
- Vn is the magnitude of the nth harmonic
- Vm is the magnitude of the fundamental component
- n is the harmonic number
- ω is the angular frequency
- t is the time
- ϕ is the phase angle

Finding the 3rd Harmonic:
In the case of the 3rd harmonic, n = 3. To eliminate the 3rd harmonic, the equation can be modified as:
\[ V_3 = \frac{4V_m}{3\pi} \times \sin(3\omega t + \phi) \]

Condition for Elimination:
To eliminate the 3rd harmonic, the pulse width needs to be adjusted such that the phase angle ϕ of the 3rd harmonic becomes 120 degrees. This can be achieved by adjusting the pulse width to a specific value.

Explanation:
When the pulse width is adjusted to a value where the phase angle ϕ of the 3rd harmonic becomes 120 degrees, the sinusoidal waveform generated by the PWM inverter will have a null or zero amplitude for the 3rd harmonic. This effectively eliminates the 3rd harmonic from the output waveform.

Conclusion:
In single pulse modulation of PWM inverter, the 3rd harmonic can be eliminated by adjusting the pulse width to a value where the phase angle ϕ of the 3rd harmonic becomes 120 degrees. This adjustment ensures that the 3rd harmonic has zero amplitude in the output waveform, resulting in a cleaner and more sinusoidal output voltage.