--- title: "Step-down chopper with RL load" subject: "Advanced Electronics" chapter: 7 key: "semester_4/advanced_electronics:step-down-chopper-rl" source: https://www.bctengineer.com/q/semester_4/advanced_electronics/step-down-chopper-rl site: BCT Engineering --- # Step-down chopper with RL load Advanced Electronics · Chapter 7: Introduction to Power Electronics - Asked in: 2071 Shrawan, 6 marks - Video: [Step down chopper with R L load](https://www.youtube.com/watch?v=FTO3yxfOIRI) — EngineeringBoom - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/step-down-chopper-rl - Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-7 ## Question Explain the working of a step-down chopper with RL load with necessary derivations and diagram. ## Answer A **step-down chopper** gives an average output voltage lower than the input: Vo = k·Vs, where k = Ton/T. With an RL (or RLE) load, a freewheeling diode carries the load current when the switch is OFF. ```text CH +Vs --/ --+--------+ | R FD L (↑) E (back emf, may be 0) | | − ------+--------+ ``` #### Working **Mode 1 (CH ON, 0 < t < Ton):** Load connected to Vs, FD reverse biased. Load current rises exponentially from I1 to I2. ```text Vs = R·i + L di/dt + E i(t) = (Vs − E)/R · (1 − e^(−t/τ)) + I1·e^(−t/τ), τ = L/R At t = Ton: i = I2 ``` **Mode 2 (CH OFF, 0 < t' < Toff):** Inductor current continues through FD; load voltage = 0. Current decays from I2 to I1. ```text 0 = R·i + L di/dt + E i(t') = I2·e^(−t'/τ) − (E/R)(1 − e^(−t'/τ)) At t' = Toff: i = I1 ``` #### Waveforms ```text vo Vs |‾‾‾‾|____|‾‾‾‾|____ 0 Ton T io I2 | /\ /\ | / \ / \ I1 | / \_/ \_ (continuous current) iCH | /| /| (rising part) iFD | \_ \_ (falling part) ``` #### Expressions (steady state) Solving the two modes with i(T) = i(0) = I1: ```text I2 = (Vs/R)(1 − e^(−kT/τ))/(1 − e^(−T/τ)) − E/R I1 = (Vs/R)(e^(kT/τ) − 1)/(e^(T/τ) − 1) − E/R ``` Average output voltage and current: ```text Vo = (1/T)∫₀^(Ton) Vs dt = k·Vs Io = (Vo − E)/R = (k·Vs − E)/R ``` Peak-to-peak ripple current: ```text ΔI = I2 − I1 = (Vs/R)·(1 − e^(−kT/τ))·(1 − e^(−(1−k)T/τ)) / (1 − e^(−T/τ)) ``` ΔI is maximum at k = 0.5: ```text ΔImax = (Vs/R)·tanh(R/(4fL)) ≈ Vs/(4fL) when 4fL >> R ``` So a larger inductance or higher chopping frequency reduces the ripple. Used in DC motor speed control (with E as motor back emf) and battery-operated vehicles. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the average output voltage of a step-down chopper? A. Vo = k·Vs with k = Ton/T B. Vo = Vs/(1 − k) C. Vo = Vs/k D. Vo = (1 − k)Vs Answer: A. Vo is Vs for Ton and zero otherwise, averaged over T. (Key point: Output voltage) 2. What does the freewheeling diode do when the switch is OFF? A. Blocks the load current B. Carries inductor current, so load current decays from I2 to I1 with load voltage zero C. Reverses the load voltage to −Vs D. Charges the supply to Vs Answer: B. Without FD the inductor current would have no path. (Key point: Role of FD) 3. During CH ON the current rises according to? A. Linearly with Vs/L only B. Falls exponentially C. Exponential: i = (Vs−E)/R(1 − e^(−t/τ)) + I1·e^(−t/τ), τ = L/R D. Remains constant Answer: C. Vs = Ri + L di/dt + E. (Key point: ON mode) 4. How can the ripple current be reduced? A. Decrease L B. Decrease frequency C. Set k = 0.5 D. Increase L or chopping frequency Answer: D. ΔImax ≈ Vs/(4fL), and is maximum at k = 0.5. (Key point: Ripple) ## Related in Advanced Electronics - [Chopper classification; step-down chopper RL load](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aclassify-chopper-step-down-rl) — Advanced Electronics, chapter 7 - [Freewheeling diode; step-up chopper principle](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Afreewheeling-diode-step-up-chopper) — Advanced Electronics, chapter 7 - [Chopper classification; step-up converter](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Achopper-classification-step-up) — Advanced Electronics, chapter 7 ## Related in other subjects - [Step-down chopper RLE load, 5 kHz](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Astep-down-chopper-rle-5khz) — Power Electronics, chapter 4 - [Step-down chopper RLE load continuity](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Astep-down-chopper-rle-200v) — Power Electronics, chapter 4 - [Step-down chopper: fundamental of load current](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Astep-down-chopper-fundamental-load-current) — Power Electronics, chapter 4 - [Step-down chopper with DC motor load](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Astep-down-chopper-dc-motor) — Power Electronics, chapter 4