I have seen in certain problems, they say that $$I_E = I_C$$ by saying that β is very large. I don't understand what can be considered as large β. So, I want to know the range of the values for β for which I can say $$ I_E = I_C $$

  • 1
    \$\begingroup\$ It is \$ for beta on start and end just like $$ \$\endgroup\$ – DKNguyen Feb 13 at 14:34
  • \$\begingroup\$ You can also use β \$\endgroup\$ – Huisman Feb 13 at 14:38

You probably already know that the emitter current \$I_E\$ is actually the sum of the collector current \$I_C\$ and base current \$I_B\$

\$I_E = I_C + I_B\$

Now if we know the current amplification \$\beta\$ we can know that:

\$I_B = I_C / \beta\$

Then the expression for \$I_E\$ becomes:

\$I_E = I_C + I_C/\beta = (1 +1/\beta) * I_C\$

In this expression you can see that influence of the base current \$I_B\$ becomes smaller as \$\beta\$ increases. So when \$\beta\$ is large we can accept some error and just ignore the base current \$I_B\$. Then we just assumne \$I_B = 0\$ so we can use:

\$I_E = I_C\$

For example:

if \$\beta\$ = 10, \$I_B\$ has a value of \$\frac {1}{10}I_C\$ so using \$I_E = I_C\$ would mean we make an error of about 10%

if \$\beta\$ = 100, \$I_B\$ has a value of \$\frac {1}{100}I_C\$ so using \$I_E = I_C\$ would mean we make an error of about 1%

if \$\beta\$ = 1000, \$I_B\$ has a value of \$\frac {1}{1000}I_C\$ so using \$I_E = I_C\$ would mean we make an error of about 0.1%

So it depends on how accurate you need your result to be, if you can accept a 1% error then using \$I_E = I_C\$ is fine as long as \$\beta\$ > 100.

In many practical circuits you would use resistors that have an accuracy of (much) less than 1% so there is no need to take the base current into account if \$\beta\$ > 100 as the error introduced by resistors is usually much larger.


It's a fuzzy line when something becomes small enough to be insignificant (in this case it is actually Ib relative to Ic, via large beta). It is up to your judgement, not a well-defined threshold. Sometimes it is 1:10 (should probably never be less than this), sometimes you can get away with 1:20 or 1:50, sometimes you need 1:100, sometimes 1:1000. Sometimes it doesn't exist (like in accounting where they keep track of fractions of a penny even in multi-million dollar transactions. At what ratio of Ib:Ic do you feel you can treat Ib as zero whenever it needs to be added to Ic?

1:10 was always way too low for my liking. But if your calculations aren't very precise to begin with, using 1:10 doesn't really change how inaccurate your result is and lets you use the approximation more often to save work.


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