--- title: "Step-down chopper with DC motor load" subject: "Power Electronics" chapter: 4 key: "semester_7/power_electronics:step-down-chopper-dc-motor" source: https://www.bctengineer.com/q/semester_7/power_electronics/step-down-chopper-dc-motor site: BCT Engineering --- # Step-down chopper with DC motor load Power Electronics · Chapter 4: DC chopper - Asked in: 2073 Shrawan, 8 marks - Video: [Step Down Chopper with R-L-E Load : Continues Current Conduction Mode](https://www.youtube.com/watch?v=tCHWBwHRYuY) — Learning Electronics - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/power_electronics/step-down-chopper-dc-motor - Whole chapter: https://www.bctengineer.com/md/semester_7/power_electronics/chapter-4 ## Question Explain the operation of a step down chopper with dc motor as load. ## Short answer A step-down chopper controls a DC motor's speed by varying the duty cycle k to change average armature voltage V0 = kVs. In ON state, source supplies armature; in OFF state, current freewheels through diode. Steady-state speed ω = (kVs − IaRa)/(Kφ). ## Answer A step-down (Type-A) chopper controls the speed of a separately excited dc motor by varying the average armature voltage $V_0 = kV_s$. The motor armature is an RLE load: resistance $R_a$, inductance $L_a$ and back EMF $E_b$. #### Circuit ```text +----CH----+-------------+ | | | | | Ra Vs FD ^ La | | (Eb) motor | | | +----------+-------------+ ``` #### Modes of operation **Mode 1: CH ON ($0 < t < T_{on}$).** Source connects to the armature, $v_0 = V_s$: $$ V_s = R_a i_a + L_a\frac{di_a}{dt} + E_b $$ The current rises exponentially from $I_{min}$ to $I_{max}$; energy is stored in $L_a$. **Mode 2: CH OFF ($T_{on} < t < T$).** The armature current freewheels through FD, $v_0 = 0$: $$ 0 = R_a i_a + L_a\frac{di_a}{dt} + E_b $$ The current decays from $I_{max}$ to $I_{min}$. If $L_a$ is small or $k$ is low, it can reach zero before the next ON period (**discontinuous conduction**); then $v_0 = E_b$ for the remaining time. ```text v0 Vs |____ ____ | | | | 0 |____|____|____|____ t ia Imax| /\ /\ | / \ / \ Imin| / \____/ \__ t Ton Toff ``` #### Steady-state relations (continuous conduction) $$ \begin{aligned} V_0 &= kV_s = E_b + I_a R_a \\ E_b &= K\phi\,\omega \\ \omega &= \frac{kV_s - I_a R_a}{K\phi} \end{aligned} $$ So speed is controlled by the duty ratio $k$: increasing $k$ increases $V_0$ and the speed. Torque $T = K\phi I_a$ depends on the load current. Current limits: $$ I_{max} = \frac{V_s}{R_a}\cdot\frac{1-e^{-kT/T_a}}{1-e^{-T/T_a}} - \frac{E_b}{R_a}, \quad I_{min} = \frac{V_s}{R_a}\cdot\frac{e^{kT/T_a}-1}{e^{T/T_a}-1} - \frac{E_b}{R_a} $$ with $T_a = L_a/R_a$. Conduction is continuous if $I_{min} > 0$. #### Features - Operates in the first quadrant only (motoring, forward); braking needs a Class B or C chopper. - High chopping frequency or an added series inductor reduces current ripple and torque pulsation. - Smooth, efficient (no rheostat loss) control; widely used in battery vehicles, forklifts and traction. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How does a step-down chopper control motor speed? A. By varying duty ratio k, thus the average armature voltage kVs B. By varying the field resistance only C. By changing supply frequency to 50 Hz D. By reversing the armature polarity Answer: A. V0 = kVs = Eb + Ia Ra, and speed = (kVs - Ia Ra)/(K phi). (Key point: Speed control) 2. What happens to the armature current when CH is OFF? A. It drops to zero instantly B. It freewheels through FD and decays from Imax to Imin, with v0 = 0 C. It flows back into the source D. It continues to rise Answer: B. The inductance maintains current through the freewheeling diode. (Key point: Mode 2) 3. When can the armature current become discontinuous? A. When k is close to 1 B. When Eb is zero C. If La is small or k is low, current reaches zero before the next ON period, and v0 = Eb for the remainder D. When FD is removed Answer: C. Then the armature voltage equals the back emf for the zero-current interval. (Key point: Discontinuous conduction) 4. In which quadrant does a Type-A chopper-fed motor operate? A. Four quadrants B. First and second quadrants C. Second quadrant only D. First quadrant (forward motoring) only Answer: D. Braking requires a Class B or C chopper. 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