hole-electron recombination current v.s. collector current

[questron]

in this picture, iC is the collector current, and iB2 is the recombination current.
the question is how are these two currents related? does iB2 change linearly with iC?
any takers?

[T3sl4co1l]

I think so... to first order anyway, in the same way that hFE is constant to first order.  Recombination is proportional to concentration, which is proportional to the current diffusing through the base.

Tim

[questron]

thank you Tim!

looks like bjt's are rather messy devices, albeit it might be the case that we'll never find clean devices in this universe

i was imagining iB2 is the root reason for bjt's non-linearity, but now iB2 is non-linear as well, where does its non-linearity come from? there is some energy loss in diffusing current in the base region? through what mechanism? or something else completely different?

also, as such, every current is proportional to every other current, the ratio ib2/iC will never change, no matter how much we increase or decrease any of the currents and/or voltages involved in a bjt, yeah? (i'm not sure about this at all, and am seeking confirmation on it.)

so we are doomed, the only thing we can do is patching it from the outside, and the better the patching, the dearer the price. is it reasonable to say then such is the story of bjt's? 

...this is all so strangely interesting...

[T3sl4co1l]

I remember there being some exponentials and tanh floating around, but I don't remember if that was related to carrier concentration, or some bulk parameters (like the derivation of the Gummel-Poon model, or something like that).

BJTs are the messier device; FETs are easy, and were known theoretically for something like half a century before manufacturing improved to the level where they could be made practically.

Also don't remember if we covered the reasons for high level injection phenomena, namely that hFE reduces at high current / charge density, and so on.

Mmm, hFE reducing at low current density should be a recombination thing though.  Which suggests a certain constancy rather than proportionality to it.

Dunno, read the textbook and ask your prof.  That's what they're there for...

Tim

[Smokey]

A basic spice sim should be able to show this right?

[T3sl4co1l]

Well, if you set up a "physical model" simulation, perhaps.  But you'd have to know the equations to begin with...

If you mean internal SPICE models, no, those are crude approximations built by curve fitting.  They have nothing at all to do with charge diffusion.  There's no way to separate Ib2 from Ib.

Tim

[free_electron]

without knowing the doping strength you will get nowhere. the base domain is doped much more weakly than the emitter domain

[questron]

thank you all guys for helping, all that is helpful already!

the text book touched upon recombination, but no details at all, which is fine.

i did do a LTspice simulation on a shunt biased bjt amplifier in common emitter configuration, and kept reducing the two resistor values to get larger and larger collector and base current, and the THD kept going down. when collector current was around 65ma to 200ma, say, the THD got very low, to something like 0.000028%. that made me wonder about how iB2 is related to iC.

it makes sense the base region is doped much lighter, maybe that's where hFE come from, and it may also have to do with reduced hFE at low current density, only a wild guess.

i don't really need a quantative rigorous mathematical analysis on this, i won't be able to understand it anyway. just some qualitative idea on what is going on inside a bjt will do.

so all has been helpful, thank you guys!

[free_electron]

i wrote a lenghty explanation on this forum about bjt's , including the doping and how the barriers move and you get the electrons to flow.

[T3sl4co1l]

Distortion in the common emitter amplifier has nothing to do with recombination current.

[questron]

i wrote a lenghty explanation on this forum about bjt's , including the doping and how the barriers move and you get the electrons to flow.

thanks free-electron, i'll look for that.

[questron]

Distortion in the common emitter amplifier has nothing to do with recombination current.

ok, that makes sense, if iB2/iC stays the same.

what are some of the major contributors to distortion then?

[Smokey]

Free_Electron posts mentioned above...

How transistors work:
https://www.eevblog.com/forum/beginners/how-transistors-work/msg109166/#msg109166

How transistors REALLY work:
https://www.eevblog.com/forum/chat/how-transistors-really-work/msg164422/#msg164422

[T3sl4co1l]

The elephant in the room is the inherent exponential transfer function.  It's not that subtle effects give rise to distortion, it's that the transistor is one hundred percent distortion, all the time.  The only reason* linear amplifiers exist is simply negative feedback.

*Technically, not.  But it sure does a hell of a lot of good.

Tim

[David Hess]

T3sl4co1l beat me to it.

The exponential relationship between Ib and Vbe primarily determines non-linearity.  If the signal change is a small fraction of the operating point, then distortion is minimized and feedback creates this very situation.

[GK]

You mean Ic and Vbe. If the transistor is truly current driven (generally impractical) Vbe is an irrelevant quantity. When the base is voltage driven (most of the time) Ib is generally a secondary contributor to distortion due to a non zero driving impedance.
 

[T3sl4co1l]

Now, if you're doing ideal current drive, you need negative feedback more than ever (hFE has a huge tempco, far more than I_s or V_T).  You also encounter much larger nonlinearities in hFE which are due to spooky things like recombination current, or current crowding and stuff.

A current mirror corrects with Vbe at point-of-use, and hence can have modest current gains (usually under 20) with reasonable linearity.  But you can't make a current mirror without an Ebers-Moll or better model, so, arguably in a sense, it's still not a pure current-mode amplifying device (this is in a similar sense as the vacuum tube triode having internal negative feedback, hence an unusually low plate resistance).

Tim