--- title: "Centre-tapped cycloconverter, one-third frequency" subject: "Power Electronics" chapter: 6 key: "semester_7/power_electronics:cyclo-center-tap-one-third" source: https://www.bctengineer.com/q/semester_7/power_electronics/cyclo-center-tap-one-third site: BCT Engineering --- # Centre-tapped cycloconverter, one-third frequency Power Electronics · Chapter 6: AC voltage controller - Asked in: 2070 Chaitra, 8 marks - Video: [step down cycloconverter | rl load | midpoint type | in power electronics | cycloconverter in hindi](https://www.youtube.com/watch?v=lPulPKk36aA) — Mind of Engineer - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/power_electronics/cyclo-center-tap-one-third - Whole chapter: https://www.bctengineer.com/md/semester_7/power_electronics/chapter-6 ## Question Draw the circuit of a single phase cycloconverter using a center tapped transformer; Prepare a table showing the conduction pattern of thyristors and current paths for an output frequency of one-third the input frequency. ## Short answer A centre-tapped cycloconverter uses four thyristors P1, P2, N1, N2. For fo = fi/3, each output half-cycle uses three input half-cycles: P1, P2, P1 for positive output, then N1, N2, N1 for negative output, repeating every six input half-cycles. ## Answer A single-phase cycloconverter with a centre-tapped transformer uses four thyristors: P1, P2 (positive group) and N1, N2 (negative group). For one-third frequency ($f_o = f_i/3$, e.g. 50 Hz to 16.67 Hz), each output half cycle is built from **three input half cycles**. #### Circuit ```text a o----+---P1->|---+ | +---|<-N1---+ ~ vs Tr| | O o----[ R ]-----+ K | | b o----+---P2->|---+ +---|<-N2---+ vo = v_KO; positive when current flows K -> O ``` - $v_{aO}$ positive = positive supply half cycle (then $b$ is negative w.r.t. O). - P1 conducts when $a$ is positive; P2 when $b$ is positive. - N1 conducts when $a$ is negative; N2 when $b$ is negative. #### Conduction pattern and current paths ($f_o = f_i/3$, R load) | Input half cycle | Supply | SCR ON | Current path | $v_o$ | |---|---|---|---|---| | 1 | + ($a$ +) | P1 | a → P1 → K → R → O | + | | 2 | − ($b$ +) | P2 | b → P2 → K → R → O | + | | 3 | + ($a$ +) | P1 | a → P1 → K → R → O | + | | 4 | − ($a$ −) | N1 | O → R → K → N1 → a | − | | 5 | + ($b$ −) | N2 | O → R → K → N2 → b | − | | 6 | − ($a$ −) | N1 | O → R → K → N1 → a | − | The pattern repeats every 6 input half cycles (3 input cycles = 1 output cycle). #### Waveforms ```text vs /\ /\ /\ / \ / \ / \ --/----\/----\/----\/----\/----\/-- 1 2 3 4 5 6 (halves) vo /\ /\ /\ / \/ \/ \ --/------------\------------/-- \ /\ /\ / \/ \/ \/ P1 P2 P1 N1 N2 N1 |<----- To = 3 Ti ----->| ``` #### Remarks - Each SCR turns off naturally at the supply zero because the load is resistive. - The output frequency is $f_i/3$ and, with firing angle $\alpha$, the rms output is $V_o = V_s\sqrt{\frac{1}{\pi}\left(\pi - \alpha + \frac{\sin 2\alpha}{2}\right)}$, where $V_s$ is the rms voltage of each half winding. - For an inductive load, longer gate pulses and a dead time at changeover between P and N groups are required. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How many thyristors does the centre-tapped single-phase cycloconverter use, and how are they grouped? A. 2: one per half winding B. 4: P1, P2 positive group and N1, N2 negative group C. 6: three per group D. 8: a bridge in each group Answer: B. The mid-point type uses P1, P2 (positive group) and N1, N2 (negative group). (Key point: Thyristors used) 2. What is the order of conducting thyristors over the six input half cycles for fo = fi/3? A. P1, P2, P1, N1, N2, N1 B. P1, P2, N1, N2, P1, P2 C. P1, N1, P2, N2, P1, N1 D. P1, P1, P1, N1, N1, N1 Answer: A. P1, P2, P1 produce the positive output half cycle and N1, N2, N1 the negative; the pattern repeats every 6 halves. (Key point: Conduction sequence for fo = fi/3) 3. What is the current direction through the load when the negative group conducts? A. a to P1 to K to R to O B. O to R to K to N1 (or N2) back to the supply C. The same as the positive group D. Zero, because N is off Answer: B. The negative group makes the load current flow in the reverse direction, O to R to K, giving negative vo. (Key point: Current path in the negative group) 4. Why does natural commutation suffice for this fo = fi/3 circuit with R load? A. The thyristors have extra circuits B. Load current falls to zero at each supply zero crossing, turning the SCR off C. The load is capacitive D. The output frequency is higher than input Answer: B. With resistive load the SCR current reaches zero as the supply passes through zero, so line commutation turns it off. (Key point: Commutation) ## Related in Power Electronics - [Bridge cycloconverter numerical (one-third frequency)](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Abridge-cyclo-numerical) — Power Electronics, chapter 6 - [Bridge single-phase cycloconverter conduction sequence](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Abridge-cyclo-conduction-sequence) — Power Electronics, chapter 6, asked 3× - [Step-down cycloconverter at one-fourth frequency](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Astep-down-cyclo-quarter-frequency) — Power Electronics, chapter 6 - [Single-phase step-down cycloconverter](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Asingle-phase-step-down-cyclo) — Power Electronics, chapter 6, asked 2× - [Single-phase cycloconverter operation](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Asingle-phase-cycloconverter) — Power Electronics, chapter 6 - [Step-up and step-down single-phase cycloconverter](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Astep-up-step-down-cyclo) — Power Electronics, chapter 6 ## Related in other subjects - [Center tapped full wave rectifier](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Afull-wave-center-tapped) — Basic Electronics Engineering, chapter 2 - [Output (kVA) equation of single phase transformer](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Aoutput-equation-single-phase-transformer) — Electric Machine Design, chapter 3, asked 3× - [Input current, pf and torque of single phase IM](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Asingle-phase-im-input-torque) — Electric Machines II, chapter 3 - [Peak demand of load center from load pattern](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Apeak-demand-load-center-load-pattern) — Transmission and Distribution System Design, chapter 6, asked 2×