# Calculating the base emitter voltage increase for an ideal transistor

For a approximately ideal transistor (η = 1) at an emitter current of = 1μA the Base emitter voltage is = 0.60V. How can I work out how much the base emitter voltage increases if the emitter current rises to 100μA?

I am aware of the formulae relating the currents at the base, emitter and collector as well as relating alpha and beta but how can I relate these to the base emitter voltage?

• $V_{BE}$ can be related as $V_{BB} - I_{B}R_{B}$. However, this is assuming you're biasing the base. They'll be different formulas depending on how you bias on the BJT, which you have not revealed. – KingDuken Feb 2 '17 at 21:47
• Thank you for your comment - I tried using the formulae you suggested, eliminated Vbb and substituted Ib for Ie/1+Beta however then I just end up with a relationship involving Rb/1+Beta. I'm assuming with the very little info I have that this is the best form I can leave it in and that I cannot get an exact value? – Tech Feb 3 '17 at 10:23

For answering your question you need the well-known Shockley equation describing the current-voltage relation for a pn junction: Ic=Is*exp[(Vbe/Vt)-1].

(a) If you know one pair of values (Vbe, Ic) you can find the corresponding saturation current Is. From this, it is easy to find any other pair of values (this is the principle which the infos are based on as given in the answer from analogsystemsrf).

(b) Because the saturation current has very large tolerances (this is the reason for the large beta tolerances) it is not possible to find the corresponding Vbe voltage - with sufficient accuracy - for a given collector current Ic (and for a particular BJT type or part).

This uncertainty is the reason for using a stabilizing emitter resistor RE (emitter degeneration, voltage feedback). This stabilization reduces the sensitivity of the collector current against these tolerances as well as temperature influence.

The Veb increases 0.026 volts for every factor of 2.718.. (e) increase in current.

Or 0.018 volts for every factor of 2:1 increase; bandgap references use this fact, often hidden behind 0.036 v for 4:1 or 0.054 volts for 8:1.

Or 0.058 volts for every factor of 10:1.

Or 0.58 volts for 10^10 increase, such as 1 picoAmp to 10milliAmp.