Electronic – Vbe vs Ic characteristics of NPN transistor at different Vce in active region

inputnpn

Below is an NPN transistor characteristics for Vbe versus Ic at different Vcb or Vce:

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It seems like in the active region, Vbe vs Ic curves gets steeper with an increasing Vce.

The following equations relates Vbe to Ic in detail:

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But from the above equations how can we conclude that the above curves become more steeper with increasing Vce?

The first part of the equation(Is) has many dimensional terms. Does any of them changes when the Vce increases? I want to relate the effect of Vce to the above curves through the above equations..

Best Answer

The Early effect causes the effective base width to reduce as the voltage on the collector increases.

This in turn causes the collector current to increase for a given Vbe.