PWM Techniques

Sinusoidal Pulse Width Modulation generates AC voltage by comparing a high frequency triangular carrier with a sinusoidal reference signal. It is extensively used in renewable energy inverters to reduce output harmonics.

Core Concept

The modulation index controls the fundamental output voltage amplitude. Keeping the amplitude modulation index below 1.0 ensures linear operation. Overmodulation occurs when the index exceeds 1.0, generating low order harmonics.

The frequency modulation ratio determines the switching frequency. A high frequency ratio like 40 moves harmonics to a much higher frequency band. This significantly reduces the size of the output LC filter.

Bipolar PWM switches the voltage between positive and negative DC levels. Unipolar PWM switches between positive, zero, and negative levels. Unipolar switching effectively doubles the ripple frequency seen by the filter.

Key Formulas

Amplitude modulation index ma = Vref / Vcarrier. Frequency ratio mf = fcarrier / fref. Fundamental peak voltage V1max = ma * Vdc for half bridge.

Given: Vdc = 400 V, ma = 0.8, full bridge configuration.
Formula: V1max = ma * Vdc. V1rms = V1max / sqrt(2).
Steps:
1. V1max = 0.8 * 400 = 320 V.
2. V1rms = 320 / 1.414 = 226.3 V.
Final Answer: V1rms = 226.3 V.

Exam Tip: In bipolar PWM, the dominant harmonics appear at mf. In unipolar PWM, the dominant harmonics appear at 2 times mf. This is a highly tested concept.

Performance Parameters

• Fundamental voltage varies linearly with modulation index up to 1.0.
• Output filter size drops significantly with high switching frequency.
• Switching losses increase linearly with carrier frequency.
• Unipolar modulation has superior harmonic performance.
• Dead time compensation is required to prevent waveform distortion.

Quick Revision

• Compares a reference sine wave with a triangular carrier.
• Controls both frequency and magnitude of output voltage.
• Overmodulation increases fundamental voltage but adds harmonics.
• Bipolar and unipolar are the two main switching schemes.
• High frequency ratio pushes harmonics far from the fundamental.
• Exam trap: Assuming the fundamental voltage keeps increasing linearly during overmodulation.