---
title: "Self and line commutation; minimum gate pulse width"
subject: "Power Electronics"
chapter: 1
key: "semester_7/power_electronics:self-line-commutation-gate-pulse"
source: https://www.bctengineer.com/q/semester_7/power_electronics/self-line-commutation-gate-pulse
site: BCT Engineering
---

# Self and line commutation; minimum gate pulse width

Power Electronics · Chapter 1: Characteristics and specification of power electronic devices

- Asked in: 2081 Bhadra, 4+4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/power_electronics/self-line-commutation-gate-pulse
- Whole chapter: https://www.bctengineer.com/md/semester_7/power_electronics/chapter-1

## Question

Explain about self and line commutation with circuit and its waveform. A 10 V source is connected across RL load having R = 10 Ω and L = 10 mH. A thyristor having latching current of 200 mA is used as switch for the circuit. Calculate minimum gate pulse width to Turn ON the thyristor.

## Short answer

Self-commutation uses a resonant LC to create a current zero; line commutation relies on AC supply reversal. For the RL load, current rises as i(t)=1(1-e^{-1000t}) A. Setting i=0.2A gives required gate pulse width t = -ln(0.8)/1000 = 223.1µs.

## Answer

**Commutation** is the process of turning OFF a conducting thyristor by bringing its anode current below the holding current and applying reverse voltage for longer than its turn-off time.

#### Self commutation (load / resonant commutation)

```text
   +Vs                 
    |     L      C
    +---[SCR]--LLLL--||---+
    |                     R (load)
    +---------------------+
```

The SCR is in series with an under-damped $L$-$C$ (and load $R$) circuit. When fired, the current is a damped sinusoid. After half a period the current tries to reverse and falls through zero; the SCR turns OFF by itself, and the charged capacitor applies reverse voltage across it. Used in series inverters and DC choppers.

```text
 i  ^   .-.
    |  /   \
 ---+-'-----'-------> t
       SCR off at i = 0
 vC ^       ______
    |    .-'      (holds reverse
 ---+-.-'          voltage on SCR)
```

#### Line (natural) commutation

```text
  ~ vs ---[SCR]---+
                  R
  ----------------+
```

In a.c. circuits the supply voltage reverses every half cycle. At the end of the positive half cycle the anode current falls to zero naturally and during the negative half cycle the SCR is reverse biased, so it turns OFF without any extra circuit. Used in controlled rectifiers, AC voltage controllers and cycloconverters.

```text
 vs ^  .-.         .-.
    | /   \       /
 ---+-|----\-----/----> t
      a     \___/
 io ^  |\
    |  | \  current falls to 0
 ---+--+--\------------> t
```

#### Numerical: minimum gate pulse width

**Given:** $V = 10$ V, $R = 10\ \Omega$, $L = 10$ mH, $I_L = 200$ mA. For an RL circuit the current after firing is
$$
i(t) = \frac{V}{R}\left(1 - e^{-tR/L}\right), \qquad \frac{V}{R} = 1\ \text{A}, \quad \frac{L}{R} = 1\ \text{ms}
$$
The gate pulse must last until $i$ reaches $I_L$:
$$
\begin{aligned}
0.2 &= 1\left(1 - e^{-t/10^{-3}}\right) \\
e^{-1000t} &= 0.8 \\
t &= -10^{-3}\ln(0.8) = 0.2231\ \text{ms}
\end{aligned}
$$

**Answer:** minimum gate pulse width $= 223.1\ \mu$s.

## Check yourself

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

1. Why does an SCR in an a.c. circuit turn OFF by line (natural) commutation?
   A. A resonant capacitor reverses the current
   B. The supply reverses each half cycle, so current falls to zero and the SCR is reverse biased
   C. The gate is pulsed negative
   D. A auxiliary thyristor is fired
   Answer: B. At the end of the positive half cycle the anode current naturally falls to zero and the negative half cycle reverse biases the SCR. (Key point: Line commutation)

2. How does self (load/resonant) commutation turn the SCR OFF?
   A. The damped L-C current falls through zero and the charged capacitor reverse-biases the SCR
   B. The supply voltage reverses
   C. Gate current is reversed
   D. The load is disconnected mechanically
   Answer: A. In an under-damped L-C-R circuit the current rings through zero; the SCR turns off and the capacitor holds reverse voltage across it. (Key point: Self commutation)

3. For the RL load, the minimum gate pulse width is the time for the anode current to reach:
   A. The holding current
   B. The final value V/R
   C. The latching current IL
   D. Zero
   Answer: C. The gate pulse must last until i(t) reaches the latching current (200 mA) so the SCR stays ON after the pulse ends. (Key point: Gate pulse criterion)

4. With V = 10 V, R = 10 ohm, L = 10 mH and IL = 200 mA, what is the minimum gate pulse width?
   A. 200 us
   B. 100 us
   C. 223.1 us
   D. 1 ms
   Answer: C. i = 1(1 - e^(-t/1ms)) = 0.2 gives e^(-t/1ms) = 0.8, so t = -1 ms x ln(0.8) = 223.1 us. (Key point: Pulse width value)

## Related in Power Electronics

- [Thyristor V-I, latching/holding, gate signal circuit](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Athyristor-vi-latching-gate-circuit) — Power Electronics, chapter 1
- [Thyristor V-I; latching vs holding current](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Athyristor-vi-latching-vs-holding) — Power Electronics, chapter 1
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- [Thyristor V-I, holding/latching; vertical BJT](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Athyristor-vi-vertical-bjt) — Power Electronics, chapter 1
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- [Pulse train generation for thyristor firing](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Apulse-train-gate-firing) — Power Electronics, chapter 1

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