--- title: "What is sinusoidal pulse-width modulation" subject: "Power Electronics" chapter: 5 key: "semester_7/power_electronics:what-is-spwm" source: https://www.bctengineer.com/q/semester_7/power_electronics/what-is-spwm site: BCT Engineering --- # What is sinusoidal pulse-width modulation Power Electronics · Chapter 5: Inverter - Asked in: 2071 Shrawan, 8 marks - Video: [56. Sinusoidal Pulse Width Modulation](https://www.youtube.com/watch?v=EalV4D9Vp-Y) — Electronic Waves - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/power_electronics/what-is-spwm - Whole chapter: https://www.bctengineer.com/md/semester_7/power_electronics/chapter-5 ## Question What is sinusoidal pulse-width modulation? How is it obtained? Explain with the help of neat diagram. ## Short answer SPWM compares a sinusoidal reference at output frequency with a high-frequency triangular carrier to produce pulses whose widths vary sinusoidally. The modulation index controls fundamental voltage, while the carrier ratio places harmonics in high-frequency groups around multiples of m_f. Low-order harmonics are greatly reduced. ## Answer **Sinusoidal pulse-width modulation (SPWM)** is a method of controlling an inverter in which, instead of equal-width pulses, the output in each half cycle consists of several pulses whose widths vary sinusoidally — narrow near the zero crossings and wide near the peak. The fundamental output is then sinusoidal and low-order harmonics are greatly reduced. #### How it is obtained 1. A **sinusoidal reference** $v_r = A_r\sin\omega_r t$ at the desired output frequency $f_r$ is generated. 2. A **triangular carrier** $v_c$ of amplitude $A_c$ and higher frequency $f_c$ is generated. 3. The two are compared in a **comparator**. The pulse widths are the intervals where $v_r > v_c$ (positive half) or $v_r < v_c$ for the complementary switch. 4. **Bipolar SPWM** (half bridge or full bridge): $v_r > v_c \Rightarrow v_0 = +V_s$, otherwise $v_0 = -V_s$. **Unipolar SPWM** (full bridge): two legs compared with $+v_r$ and $-v_r$, giving $v_0 = +V_s, 0, -V_s$. 5. The gate pulses (with dead time) drive the inverter switches. ```text Ar sin wt --->|+\ | >--> gate S1 (S4 = NOT) triangle ---->|-/ comparator vc /\/\/\/\/\/\/\/\/\/\/\/\/\/\/\ vr .-''-. -----'------'------.------.----- '-..-' v0 +Vs _ __ ___ __ _ 0 _| || || || |_ _ __ _ | || || -Vs |_||_||_| narrow-wide-narrow pulses ``` #### Key definitions - **Amplitude modulation index** $m_a = \dfrac{A_r}{A_c}$. For $m_a \le 1$ the fundamental varies linearly: $\hat V_{1} = m_a V_s$ (full bridge, bipolar) or $m_a V_s/2$ (half bridge). - **Frequency modulation ratio** $m_f = \dfrac{f_c}{f_r}$; number of pulses per half cycle $p = m_f/2$ (unipolar counts differ). In three-phase inverters $m_f$ is chosen odd and a multiple of 3. - Output **frequency** is changed by $f_r$; output **voltage** by $m_a$. #### Harmonic spectrum - Low-order harmonics (3rd, 5th, 7th) are nearly eliminated. - Harmonics appear in groups around $m_f$, $2m_f$, … (e.g. $m_f$, $m_f \pm 2$), which are high and easily filtered by the load inductance or a small LC filter. - With $m_a > 1$ (overmodulation) the output increases non-linearly and low-order harmonics reappear. #### Advantages and uses - Voltage and frequency control in one stage; near-sinusoidal current; small filters. - More switching loss than square-wave operation. - Used in UPS, induction motor drives (V/f control), solar and grid-tie inverters. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In sinusoidal PWM, how do the output pulse widths vary within a half cycle? A. All pulses are of equal width B. Widths vary sinusoidally: narrow near zero crossings and wide near the peak C. Widths are wide at zero crossings and narrow at the peak D. Only the pulse height varies Answer: B. Pulse widths follow the sinusoidal reference, giving a sinusoidal fundamental. (Key point: Definition of SPWM) 2. How are SPWM gate signals produced? A. By comparing a sinusoidal reference at the output frequency with a higher-frequency triangular carrier B. By comparing two sine waves C. By integrating a square wave D. By comparing a dc level with a sine wave Answer: A. A comparator compares vr (output frequency) with the triangular carrier vc; pulses occur where vr > vc. (Key point: How SPWM is generated) 3. What does the amplitude modulation index ma = Ar/Ac control, and what controls output frequency? A. ma controls frequency; fc controls voltage B. ma controls voltage (fundamental = ma Vs for ma <= 1); the reference frequency fr controls output frequency C. ma controls the number of pulses; fr controls voltage D. Both are controlled by Vs only Answer: B. The fundamental varies linearly with ma up to 1, while the reference frequency sets the output frequency. (Key point: Modulation index) 4. Where do the dominant harmonics of SPWM appear? A. At 3rd, 5th and 7th B. Around the carrier multiples mf, 2mf, ..., high and easily filtered C. Only at dc D. At the fundamental only Answer: B. Low-order harmonics are nearly eliminated; harmonic groups sit around mf, 2mf. (Key point: Harmonic spectrum) 5. What happens when ma > 1? A. The output stays linear B. The output falls to zero C. Output rises non-linearly and low-order harmonics reappear D. The carrier frequency doubles Answer: C. Overmodulation loses the linear relation and brings back low-order harmonics. (Key point: Overmodulation) ## Related in Power Electronics - [Single-pulse PWM: modulation index and Fourier series](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Asingle-pulse-pwm-fourier) — Power Electronics, chapter 5 - [Self and line commutation; minimum gate pulse width](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Aself-line-commutation-gate-pulse) — Power Electronics, chapter 1 - [Three-phase sinusoidal PWM inverter](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Athree-phase-spwm-inverter) — Power Electronics, chapter 5, asked 5× ## Related in other subjects - [Analog communication block diagram; modulation and its reasons](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aanalog-comm-modulation-reasons) — Communication Systems, chapter 1, asked 3× - [Modulation; analog communication system block diagram](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Amodulation-analog-block-diagram) — Communication Systems, chapter 1, asked 3× - [Reasons for modulation; digital communication block diagram](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Amodulation-reasons-digital-adv-duplex) — Communication Systems, chapter 1 - [Communication system block diagram; need for modulation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Acomm-block-diagram-needs-modulation) — Communication Systems, chapter 1