# When does I_C be approximately equal to I_E

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 $$I_E = I_C$$

• It is \$for beta on start and end just like$\$ – DKNguyen Feb 13 at 14:34
• You can also use &beta; – 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.