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I have a BT137-600E and I want to know how long it takes to activate, the datasheet does not say anything about time rising or time falling

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    \$\begingroup\$ It's right there in the datasheet. "Gate controlled turn on time". When reading datasheets don't search for specific keywords because often it is not phrased in the way you want it to be phrased. Read what the text actually says. \$\endgroup\$
    – DKNguyen
    Commented Apr 21, 2021 at 19:09

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It's not listed in the datasheet. It's typically in the 100ns range once it triggers (2us typical) and regenerative action occurs, so it is negligible in a typical mains-switching application. Typically turn-off occurs at the current zero crossing.

You must make sure that the rate-of-rise of current does not exceed the datasheet "limiting value" \$dI_T/dt\$ during the switching or the triac may be damaged. This is a function of the circuit you have it connected in.

Many triacs list a critical rate of change of commutating current for turn-off characteristics, but I don't see that here.

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The rise time is specified in Amps per microsecond. The fall time doesn't really apply since the current must go to zero for the Triac to turn-off.

Typical delay before any current flows in T1/T2: enter image description here

Max rise time: enter image description here

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