Lecture note

1. Sinusoidal PWM and Modulation
Index in Voltage Source Inverters
• PWM is a technique used to control output
voltage and harmonics in inverters.
• It compares a reference sine signal with a
high-frequency triangular carrier.
• Applications: motor drives, UPS, renewable
converters.

2. Sinusoidal PWM (SPWM) Principle
• A sinusoidal reference is compared with a
triangular carrier.
• Switch turns ON when reference > carrier.
• Average output voltage follows a sine pattern.
• Key parameters: carrier frequency (f_c),
modulating frequency (f_m), ratio N=f_c/f_m.

3. Definition of Modulation Index
(m_a)
• m_a = V_m / V_c
• V_m: amplitude of sine modulating wave
• V_c: amplitude of triangular carrier wave
• m_a < 1: Linear region
• m_a > 1: Overmodulation region

4. Effect of Modulation Index on
Output Voltage
• Linear region: V_o1 = m_a × (V_dc/2)
• Overmodulation: increased distortion
• Square wave region: maximum V_o1 = V_dc/2

5. Bipolar Sinusoidal PWM
• In output, voltage swings between +V_dc and
-V_dc.
• Both switches of same leg operate
complementarily.
• Advantages: simple control, low common-
mode voltage.
• Disadvantages: high harmonic content and
switching loss.

6. Unipolar Sinusoidal PWM
• Each leg modulated with phase-shifted sine
waves.
• Output switches between +V_dc/2, 0, and -
V_dc/2.
• Advantages: lower harmonics, higher
efficiency.
• Disadvantages: more complex control logic.

7. Comparison Between Bipolar and
Unipolar PWM
• Bipolar: two-level (+Vdc, -Vdc) output, higher
THD, simpler.
• Unipolar: three-level (+Vdc/2, 0, -Vdc/2),
lower THD, efficient but complex.
• Unipolar preferred in high-performance
inverters.

8. Summary
• • Modulation index (m_a) controls output
voltage amplitude.
• • m_a > 1 leads to overmodulation and
distortion.
• • Unipolar SPWM gives superior harmonic
performance and efficiency.