--- title: "Variable inverter output; SCR full-wave average" subject: "Advanced Electronics" chapter: 7 key: "semester_4/advanced_electronics:inverter-variable-output-scr-fwr" source: https://www.bctengineer.com/q/semester_4/advanced_electronics/inverter-variable-output-scr-fwr site: BCT Engineering --- # Variable inverter output; SCR full-wave average Advanced Electronics · Chapter 7: Introduction to Power Electronics - Asked in: 2072 Chaitra, 2+5 marks - Video: [Single Phase Full Wave Controlled Rectifier with R Load | Power Electronics | Lecture 43](https://www.youtube.com/watch?v=3CAdY-fnPxA) — Electronics Maddy - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/inverter-variable-output-scr-fwr - Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-7 ## Question Is it possible to get variable output voltage in inverter? How? Derive expression for average output voltage of SCR full wave rectifier. ## Answer #### Variable output voltage in inverter Yes. The output voltage of an inverter can be varied by: 1. **Varying the DC input voltage** using a controlled rectifier or chopper before the inverter. 2. **Pulse width modulation (PWM) inside the inverter** (most common): single-pulse, multiple-pulse or sinusoidal PWM. Changing the pulse width (modulation index) changes the RMS output while the frequency stays fixed. 3. **Controlling the AC output** with an AC voltage controller or a tapped transformer. 4. **Series/phase-shift connection** of two inverters, where varying the phase shift between them changes the resultant voltage. #### Average output voltage of SCR full-wave rectifier Consider a centre-tapped full-wave controlled rectifier with resistive load (a bridge gives the same result). ```text T1 +---|>|---+ ) | ) vs +---[ R ]---+ )==CT-----------------+ ) vs | ) | +---|>|---+ T2 ``` - Positive half cycle: T1 is forward biased and fired at ωt = α; it conducts until π. - Negative half cycle: T2 is fired at π + α and conducts until 2π. - Load voltage repeats every π. ```text vo | /‾\ /‾\ | / \ / \ |/ | \/ | \ --+---+--+----+---+--> ωt 0 α π π+α 2π ``` **Derivation:** ```text Vdc = (1/π)∫α^π Vm sin ωt d(ωt) = (Vm/π)[−cos ωt]α^π = (Vm/π)[−cos π + cos α] Vdc = (Vm/π)(1 + cos α) ``` - At α = 0, Vdc = 2Vm/π (same as uncontrolled full-wave rectifier). - At α = π, Vdc = 0. - Average load current Idc = Vm(1 + cos α)/(πR). RMS value for reference: ```text Vrms = (Vm/√2)·√[ (π − α)/π + sin2α/(2π) ] ``` ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which is the most common way to vary inverter output voltage? A. PWM inside the inverter B. Changing the load resistance C. Changing the DC supply polarity D. Using a larger capacitor Answer: A. Changing pulse width changes RMS output while frequency stays fixed. (Key point: Variable inverter output) 2. Which is also a valid method? A. Reducing the output frequency to zero B. Varying the DC input using a controlled rectifier or chopper C. Removing the feedback diodes D. Using only one switch Answer: B. A variable DC link gives variable output amplitude. (Key point: Variable output options) 3. What is the average output voltage of the SCR full-wave rectifier? A. Vdc = (Vm/2π)(1 + cos α) B. Vdc = (Vm/π)(1 − cos α) C. Vdc = (Vm/π)(1 + cos α) D. Vdc = (2Vm/π) cos α Answer: C. Load voltage repeats every π, so average uses 1/π over α to π. (Key point: Full-wave average) 4. What is Vdc for α = 0 and α = π? A. Vm/π and Vm B. Vm and 0 C. 0 and 2Vm/π D. 2Vm/π and 0 Answer: D. At α = 0, (Vm/π)(2) = 2Vm/π; at α = π, 1 + cos π = 0. 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