# Thyristor/SCR $i^2t$ and $i^2\sqrt{t}$ Rating

I have commonly seen the $i^2t$ rating for fusing in a SCR datasheet. This is a helpful rating for assessing if pulses which exceed the surge current rating (Itsm) of the SCR will damage it.

However, I have also come across the $i^2\sqrt{t}$ rating. These are commonly found in Vishay datasheets. The $i^2\sqrt{t}$ rating in the datasheets is constant for pulse widths ranging from 0.1ms to 10ms. I am guessing that the $\sqrt{t}$ is the thermal response of the SCR junction.

Has anyone come across this rating before and is there any literature that explains this rating? Google is giving me a hard time.

My application is a pulse width of 100-200us at an interval of 1.0s. I am trying to justify if I can use a SCR where I exceed the Itsm rating.

Sample Vishay Datasheet = http://www.vishay.com/docs/94679/vs-25tts16spbf.pdf

• How about a link to a DS that specifies root(t) – Andy aka Apr 16 '18 at 10:40
• Updated with datasheet link. – Oneneo Apr 16 '18 at 21:19

The $i^2 t$ is associated with the devices energy capability.

The maximum non-repetitive on-state surge current is generally quoted for one 10 millisecond sinusoidal. Such non-recurrent ratings are usually specified to allow fuse and circuit breaker short-circuit protection. The I2t rating for a 10ms period is another parameter used for fuse protection, where I is non-repetitive rms current.

However... This is only part of the story. When employed in a crowbar circuit, especially with a local DClink capacitor that will equally be rapidly discharged via the SCR, the energy capability of the SCR is closer to $i^2 \sqrt t$

The mathematical derivation of $i^2 \sqrt t$ can be seen in this SCR application notes.

https://edisciplinas.usp.br/pluginfile.php/2587503/mod_resource/content/2/Onsemi_Thyristor_Theory_and_Design_Considerations_Handbook_HBD855-D.pdf

Above the rated DC current the pulse duration is limited by the dissipation capability of the device. $$\int{i(t)^2\mathrm{d}t}<\mathrm{[I^2t]}$$ For small pulse durations the thermal response of the junction limits the pulse current rating:

It has been shown that the dissipation capability of a device varies as to the $$\\sqrt{t}\$$ for the first tens of milliseconds of the thermal response and, in effect, the measure of a device’s energy capability would be closer to $$\i^2\sqrt{t}\$$.
ON Semiconductor, 2006: Thyristor Theory and Design Considerations

Here the math for arbitrary current pulse waveforms is not quite straightforward. $$i(t)\sqrt{\smallint{i(t)^2\mathrm{d}t}}<\mathrm{[I^2\sqrt{t}]}$$ I tried to summarize the pulse current rating for the VS-25TTS16SPbF thyristor with the values from its datasheet: For your application with repeating pulses you need to additionally ensure that your RMS current is within the specifications.