Operating regions of a transistor switch

So it is operated in either saturation or cut off region but in between these two there is linear region (the intermediate region between the LOW and HIGH states of the transistor and the transistor will obviously pass through that going from cut off to saturation and vice versa.How does that work?

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How do you imagine - B lies between A and C, going from A to C passes through B. What else is there to say?

Well actually there is quite a lot to say about Miller effect, stored charge in saturation, these are covered in many texts on BJT's.

I guess the most likely issue you will encounter is the delay before turn-off and slow turn-off due to stored charge in the base region during saturation - for fast logic using BJTs (ie the old TTL families) it was common to add schottky clamp diodes between base and collector to prevent full saturation and thus prevent stored charge build up.

Stored charge in the base takes a while to clear once the base lead current stops, a common technique to speed up switch-off is to reverse-drive the base to speed switch off (but not too much, as its very easy to completely destroy a BJT with more than a couple of volts reverse bias on the base-emitter junction)

Stored charge effects are most noticable in darlingtons, turn off delays of many µs or tens of µs are common. Its the reason silicon phototransistors are much slower than silicon photodiodes too (as used in many optocouplers), and why darlington motor drivers like L298 cannot handle high PWM frequencies...

Not sure what you are getting at. Assuming an npn, in common emitter : When the transistor is cut off , it in a “ high impedance” state with “no”. In this situation there is no base current . As you increase base current the transistor goes through its active region , where the collector current is the gain of the transistor multiplied by the base current ( this is used in amplification) . As the base current increases, the transistor saturates and the collector curent maximises. If using a transistor as a switch , you design with enough base current to saturate it , or no base current . In switching, you pass thro the active region very quickly , delayed only by any capacitance in the device.