# Bias stabilization of a transistor

The instability of Collector current(Ic) of a transistor depends on three factors viz. Icbo, Vbe & Beta. Can you explain why Vbe decreases(by 2.5 mV/°C) with increase in temperature?

• I talk a bit about this here and here. Some more in other places I'd have to go find. – jonk May 9 '20 at 7:11

"Can you explain why Vbe decreases(by 2.5 mV/°C) with increase in temperature?"

To me, this is not the correct wording and can lead to misunderstandings.

No - Vbe does not decrease. The other way round: When the temperature goes up, the collector current increases. However, if you want to keep the collector current constant you must (externally) decrease the Vbe voltage by 2.5mV/K.

This tempco is attributet to the temperature sensitivity of Icbo only.

This link leads you to a note written by one of the best-known electronic engineers (Robert A. Pease): https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=9&ved=2ahUKEwiyz5qugKfpAhVmShUIHdoDBM0QFjAIegQIAxAB&url=ftp%3A%2F%2Ftelescript.denayer.wenk.be%2Fpub%2FCD-Microcontrollers%2FIIW%2FABA%2FCD_analoog_e%2Fbijlagen%2Ftransistoren%2FVbe_stuff.pdf&usg=AOvVaw2Z5cjXa6fAcZPkYwGkO7F3

• "However, if you want to keep the collector current constant you must (externally) decrease the Vbe voltage". Well, but if the collector current is kept constant, like it happens in a PTAT thermometer, Vbe will decrease without external intervention. On page 3, Pease shows how to control Vbe by means of Ic: "Another useful way to look at it, is that any time you change the current by a factor of 10 at room temp (about +27 degrees C), the VBE will shift by 60 mV, up or down, as appropriate." Just saying :-) – Sredni Vashtar May 9 '20 at 16:44
• @Sredni Vashtar...In all his considerations Pease presupposes that Ic is determined by the voltage Vbe. It is therefore clear - when he speaks of a Vbe change - that he means the "necessary" change. Anything else would be a misinterpretation of the exponential relation Ic=f(Vbe). How should a change in Ic automatically (internally in the transistor) affect the voltage Vbe? And this is, of course, also not the case with the PTAT sensor - after all, the base receives the necessary voltage externally via the connection to the collector (voltage divider principle). – LvW May 10 '20 at 9:04
• Ic is imposed by a constant current source. You can imagine a solar cell under a constant flux of photons.You change the flux of photons, you change Ic, and Vbe changes accordingly. You do not even need to know what is the value of Vbe, in fact you have to measure it in order to tell the temp in a PTAT thermometer (well, you read two Vbes). You need to jump through hoops to justify Ic=f(Vbe) as a causal relationship. The relationship is there, but causality is not implied. – Sredni Vashtar May 10 '20 at 18:07
• Your "example" (flux of photons) results from a mistake in thinking (because photons cause an imbalance of charged carriers within the base region); and the sentence "...VBE changes accordingly" is a very vague statement. Does it change automatically ? Are the terminals floating? No - of course not. Are you really satisfied with these "examples"? I really do not know what you are trying to proove? – LvW May 11 '20 at 7:30
• Sredni Vashtar...I am afraid, your misunderstandings result from the fact that you still believe that the BJTs collector current would not be determined and controlled by the base-emitter voltage. I remember a corresponding discussion between us some month (or years ?) ago. – LvW May 11 '20 at 7:53

The diode current has the formula

Idiode = Is * e ^ [Q * Vdiode / (K * T)]

WIth the T being temperature, and a common voltage at 1milliAmp being about 0.6 volts, we can simply divide that 0.6 volts by room temperature of 290 degree K, and we have about 2.1 milliVolts change per degree. This however requires the WRONG POLARITY of voltage change.

Digging further, wikipedia says I am wrong, and that the change of Is will be the far greater (and opposite polarity) effect. Check out Wikipedia "diode equation".

examining "reverse saturation current" on Wikipedia, we see the useful statement "a rule of thumb is that the current doubles for every 10 ° C". We can use that, along with 18 milliVolts being adequate to cause Idiode to double, and see this predicts 18/10 == 1.8 milliVolts decrease.