2
\$\begingroup\$

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 $$ I_E = I_C $$

\$\endgroup\$
  • 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
6
\$\begingroup\$

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.

\$\endgroup\$
5
\$\begingroup\$

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.

\$\endgroup\$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.