A single-phase full-bridge VSI is fed from a 48 V battery and delivers power to a resistive load of 10 Ω. Using square wave switching, verify
1. RMS value of fundamental output voltage is 43.2 V.
2. Power delivered by the fundamental component is 186.6 W.
3. Total power delivered to the load is 230.4 W.
Which of the statements are correct?
Answer & step-by-step solution
In 180° conduction, three devices conduct at a time and the fundamental output is higher; the floating star neutral can shift relative to the DC midpoint. Full-bridge square-wave total RMS voltage is 48 V, so total load power=48²/10=230.4 W. Fundamental RMS=4Vdc/(π√2)≈43.2 V and fundamental power≈43.2²/10=186.6 W.
Exam focus: Track pole voltage and load-neutral voltage separately. Common trap: Balanced load does not force the floating neutral to the DC midpoint at every switching state.
Statement-wise Verification
- Statement 1 - Correct.
RMS value of fundamental output voltage is 43.2 V.
Fundamental RMS=4Vdc/(π√2)≈43.2 V and fundamental power≈43.2²/10=186.6 W. - Statement 2 - Correct.
Power delivered by the fundamental component is 186.6 W.
Fundamental RMS=4Vdc/(π√2)≈43.2 V and fundamental power≈43.2²/10=186.6 W. - Statement 3 - Correct.
Total power delivered to the load is 230.4 W.
Full-bridge square-wave total RMS voltage is 48 V, so total load power=48²/10=230.4 W.
Core Concept
Three-phase voltage-source inverters can be operated with 120° or 180° conduction sequences. In 120° conduction, each switch is on for 120° and only two devices conduct at a time, leaving one phase disconnected for intervals. In 180° conduction, three devices conduct at a time and the fundamental output is higher; the floating star neutral can shift relative to the DC midpoint.
Formula / Key Relationship
Conduction duration: 120°→two switches at a time; 180°→three switches at a time.
Step-by-Step Check
Full-bridge square-wave total RMS voltage is 48 V, so total load power=48²/10=230.4 W. Fundamental RMS=4Vdc/(π√2)≈43.2 V and fundamental power≈43.2²/10=186.6 W.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 3. Option B is incorrect because it omits correct statement(s) 1. Option C is incorrect because it omits correct statement(s) 2.
Exam Shortcut / Approach
Track pole voltage and load-neutral voltage separately.
Common Mistake
Balanced load does not force the floating neutral to the DC midpoint at every switching state.
Quick Revision
Square-Wave Fundamental and Load Power is linked with Single-Phase Full-Bridge VSI, Inverters and Power Electronics. Track pole voltage and load-neutral voltage separately.
एक सिंगल-फेज़ फुल-ब्रिज VSI 48 V बैटरी से पोषित है और 10 Ω प्रतिरोधी लोड को शक्ति देता है। स्क्वेयर वेव स्विचिंग का उपयोग करते हुए सत्यापित कीजिए
1. मूल आउटपुट वोल्टेज का RMS मान 43.2 V है।
2. मूल घटक द्वारा दी गई शक्ति 186.6 W है।
3. लोड को दी गई कुल शक्ति 230.4 W है।
कौन-से कथन सही हैं?
उत्तर और चरणबद्ध हल
D — 1, 2 और 3। स्क्वेयर-वेव का कुल RMS = 48 V, कुल शक्ति = 48²/10 = 230.4 W। मूल RMS = 4Vdc/(π√2) ≈ 43.2 V और मूल शक्ति ≈ 43.2²/10 = 186.6 W।
विस्तृत हल (मूल भाषा में)
Statement-wise Verification
- Statement 1 - Correct.
RMS value of fundamental output voltage is 43.2 V.
Fundamental RMS=4Vdc/(π√2)≈43.2 V and fundamental power≈43.2²/10=186.6 W. - Statement 2 - Correct.
Power delivered by the fundamental component is 186.6 W.
Fundamental RMS=4Vdc/(π√2)≈43.2 V and fundamental power≈43.2²/10=186.6 W. - Statement 3 - Correct.
Total power delivered to the load is 230.4 W.
Full-bridge square-wave total RMS voltage is 48 V, so total load power=48²/10=230.4 W.
Core Concept
Three-phase voltage-source inverters can be operated with 120° or 180° conduction sequences. In 120° conduction, each switch is on for 120° and only two devices conduct at a time, leaving one phase disconnected for intervals. In 180° conduction, three devices conduct at a time and the fundamental output is higher; the floating star neutral can shift relative to the DC midpoint.
Formula / Key Relationship
Conduction duration: 120°→two switches at a time; 180°→three switches at a time.
Step-by-Step Check
Full-bridge square-wave total RMS voltage is 48 V, so total load power=48²/10=230.4 W. Fundamental RMS=4Vdc/(π√2)≈43.2 V and fundamental power≈43.2²/10=186.6 W.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 3. Option B is incorrect because it omits correct statement(s) 1. Option C is incorrect because it omits correct statement(s) 2.
Exam Shortcut / Approach
Track pole voltage and load-neutral voltage separately.
Common Mistake
Balanced load does not force the floating neutral to the DC midpoint at every switching state.
Quick Revision
Square-Wave Fundamental and Load Power is linked with Single-Phase Full-Bridge VSI, Inverters and Power Electronics. Track pole voltage and load-neutral voltage separately.
એક સિંગલ-ફેઝ ફુલ-બ્રિજ VSI 48 V બેટરીથી પોષિત છે અને 10 Ω અવરોધક લોડને પાવર આપે છે. સ્ક્વેર વેવ સ્વિચિંગનો ઉપયોગ કરીને ચકાસો
1. મૂળભૂત આઉટપુટ વોલ્ટેજનું RMS મૂલ્ય 43.2 V છે.
2. મૂળભૂત ઘટક દ્વારા અપાતો પાવર 186.6 W છે.
3. લોડને અપાતો કુલ પાવર 230.4 W છે.
કયાં વિધાનો સાચાં છે?
જવાબ અને પગલાવાર ઉકેલ
D — 1, 2 અને 3. સ્ક્વેર-વેવનું કુલ RMS = 48 V, કુલ પાવર = 48²/10 = 230.4 W. મૂળભૂત RMS = 4Vdc/(π√2) ≈ 43.2 V અને મૂળભૂત પાવર ≈ 43.2²/10 = 186.6 W.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Statement-wise Verification
- Statement 1 - Correct.
RMS value of fundamental output voltage is 43.2 V.
Fundamental RMS=4Vdc/(π√2)≈43.2 V and fundamental power≈43.2²/10=186.6 W. - Statement 2 - Correct.
Power delivered by the fundamental component is 186.6 W.
Fundamental RMS=4Vdc/(π√2)≈43.2 V and fundamental power≈43.2²/10=186.6 W. - Statement 3 - Correct.
Total power delivered to the load is 230.4 W.
Full-bridge square-wave total RMS voltage is 48 V, so total load power=48²/10=230.4 W.
Core Concept
Three-phase voltage-source inverters can be operated with 120° or 180° conduction sequences. In 120° conduction, each switch is on for 120° and only two devices conduct at a time, leaving one phase disconnected for intervals. In 180° conduction, three devices conduct at a time and the fundamental output is higher; the floating star neutral can shift relative to the DC midpoint.
Formula / Key Relationship
Conduction duration: 120°→two switches at a time; 180°→three switches at a time.
Step-by-Step Check
Full-bridge square-wave total RMS voltage is 48 V, so total load power=48²/10=230.4 W. Fundamental RMS=4Vdc/(π√2)≈43.2 V and fundamental power≈43.2²/10=186.6 W.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 3. Option B is incorrect because it omits correct statement(s) 1. Option C is incorrect because it omits correct statement(s) 2.
Exam Shortcut / Approach
Track pole voltage and load-neutral voltage separately.
Common Mistake
Balanced load does not force the floating neutral to the DC midpoint at every switching state.
Quick Revision
Square-Wave Fundamental and Load Power is linked with Single-Phase Full-Bridge VSI, Inverters and Power Electronics. Track pole voltage and load-neutral voltage separately.
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