---
title: "Step-down chopper variable frequency, 3 ms ON time"
subject: "Power Electronics"
chapter: 4
key: "semester_7/power_electronics:step-down-chopper-variable-frequency-3ms"
source: https://www.bctengineer.com/q/semester_7/power_electronics/step-down-chopper-variable-frequency-3ms
site: BCT Engineering
---

# Step-down chopper variable frequency, 3 ms ON time

Power Electronics · Chapter 4: DC chopper

- Asked in: 2073 Chaitra, 8 marks
- Video: [Chopper Control Techniques | Power Electronics | Lecture 66](https://www.youtube.com/watch?v=gZfUpLEk2rY) — Electronics Maddy
- 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-variable-frequency-3ms
- Whole chapter: https://www.bctengineer.com/md/semester_7/power_electronics/chapter-4

## Question

Figure below shows a step down dc chopper. If it is operated in variable frequency mode with ON time constant at 3msec. Calculate the OFF time for a duty cycle at 30% and average value of output voltage. [Figure: Vdc = 200 V source, a series switch, and a resistive load R with output Vo]

## Short answer

With constant Ton = 3 ms and k = 0.3, period T = Ton/k = 10 ms, so Toff = T − Ton = 7 ms. Average output voltage Vo = k · Vdc = 0.3 × 200 V = 60 V.

## Answer

In **variable-frequency (frequency modulation) control**, $T_{on}$ is kept constant and the duty cycle is changed by varying the chopping period $T$ (hence $T_{off}$).

**Given:** $V_{dc} = 200$ V, $T_{on} = 3$ ms (constant), $k = 0.3$, resistive load.

#### OFF time
$$
\begin{aligned}
k &= \frac{T_{on}}{T} \;\Rightarrow\; T = \frac{T_{on}}{k} = \frac{3}{0.3} = 10\ \text{ms} \\
T_{off} &= T - T_{on} = 10 - 3 = 7\ \text{ms}
\end{aligned}
$$

Chopping frequency $f = 1/T = 100$ Hz.

#### Average output voltage
$$
V_o = kV_{dc} = \frac{T_{on}}{T_{on}+T_{off}}V_{dc} = 0.3\times200 = 60\ \text{V}
$$

```text
 vo  200|___         ___
        |   |       |   |
      0 |___|_______|___|_______ t
         3ms  7ms
        |<--- T = 10 ms --->|
```

**Answer:** $T_{off} = 7$ ms; average output voltage $V_o = 60$ V.

Note: variable-frequency control is simple, but a wide frequency range makes filter design hard and may cause interference; for low $k$ the OFF time becomes very long, so the load current may become discontinuous.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. In variable-frequency control, what is held constant and what varied?
   A. Ton constant; period T (so Toff) varied
   B. T constant; Ton varied
   C. Vs varied; Ton constant
   D. Toff constant; Vs varied
   Answer: A. Duty cycle changes by changing the chopping period. (Key point: Variable frequency control)

2. For Ton = 3 ms and k = 0.3, Toff is:
   A. 3 ms
   B. 7 ms
   C. 10 ms
   D. 0.9 ms
   Answer: B. T = 3/0.3 = 10 ms; Toff = 10 - 3 = 7 ms. (Key point: OFF time)

3. The average output voltage for Vdc = 200 V is:
   A. 200 V
   B. 140 V
   C. 60 V
   D. 30 V
   Answer: C. Vo = 0.3 x 200 = 60 V. (Key point: Average output)

4. A drawback of variable-frequency control is:
   A. It cannot vary the output voltage
   B. It needs a transformer
   C. It raises the average voltage above Vs
   D. The wide frequency range makes filter design hard and gives discontinuous current at low k
   Answer: D. Frequency varies widely and Toff gets very long at low k. (Key point: Drawback)

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## Related in other subjects

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