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This may be a weird question but for a BJT, we have

enter image description here

\$I_S\$ is the reverse saturation current and \$I_C\$ is the collector current which flows through all three parts of the BJT.

Now my question is, \$I_S\$ should also flow through all three parts of the BJT, so can't we just add/subtract \$I_S\$ from \$I_C\$ via KCL? Is that where the -1 comes from?.

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    \$\begingroup\$ -1 is there to make the Ic zero when Vbe is zero. \$\endgroup\$ – atmnt Jan 16 at 22:56
  • \$\begingroup\$ \$I_S\$ is a property of the transistor, not a physical current that actually flows through it. The \$I_S\$ in that equation is close to the reverse saturation current of the base-emitter junction, but the equation is off by a factor of \$\beta\$. \$\endgroup\$ – TimWescott Jan 16 at 23:26
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    \$\begingroup\$ I discuss it here and here. \$\endgroup\$ – jonk Jan 17 at 3:06

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