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I have come across the following circuit where a BJT works as switch when I apply 23 volts to base using a 100k resistor.

A 3.2 mA constant current source is connected to the collector of the BJT and that current flows when the base current is present. From the practical observations, the BJT seems to be in saturation mode (Vce_SAT=0.1V.)

How can I mathematically prove that the transistor is in saturation modr? How can I relate that VCE<0.7 Volts mathematically?

enter image description here

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    \$\begingroup\$ Homework questions with no attempt at a solution are closed. \$\endgroup\$ – Leon Heller May 6 at 17:09
  • \$\begingroup\$ A little bit of initial hint would really be appreciated.Thank you \$\endgroup\$ – Rohan May 6 at 17:37
  • \$\begingroup\$ Search web, Common emitter to a very common question \$\endgroup\$ – Sunnyskyguy EE75 May 6 at 18:20
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    \$\begingroup\$ What base current is needed to saturate the transistor if Ic = 3.2mA. What base current is flowing in your circuit? Is this current is enough to saturate the transistor? \$\endgroup\$ – G36 May 6 at 18:22
  • \$\begingroup\$ You can't mathematically prove the transistor is in saturation. Even by making assumptions and having specific modeling parameters in hand and specific operational details into which all of this can be deduced. Even with all that, it isn't a mathematical proof. But it might be considered as making a good engineering argument. \$\endgroup\$ – jonk May 6 at 20:03
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23 = 100K * Ib + 0.7

Ib = 223 uA

Ic = Beta * Ib = 200 * 223uA = 44.6mA

Verdict:

A base current is enought to switch even 44.6 mA, not only 3.2mA

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