Why collector current/base current a constant

Discussion in 'General Electronics Chat' started by uzair, Jan 6, 2008.

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  1. uzair

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    Dec 26, 2007
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    In a transistor circuit,when collector-base junction is reverse biased and the emitter-base junction is forward biased,the ratio of collector current to the base current is a constant called beta.Why is there ratio a constant?:confused:
     
  2. Papabravo

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    Feb 24, 2006
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    Equilibrium. The three currents in a transistor must add up to zero. That's KCL. It is the physics of the junctions and the way the materials are fabricated that producses this behavior.
     
  3. Ron H

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    I'm thinking he wants a physics-based answer.
     
  4. uzair

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    Dec 26, 2007
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    Perfectly right!:D
     
  5. uzair

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    Dec 26, 2007
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    Papabravo please keep in mind the fact that i am a newcomer in the electronics field.It will be a kind act to give answers which are easily understandable for a neophyte like myself.:)
     
  6. Audioguru

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    Dec 20, 2007
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    We have been talking "geek-talk" for many years. I can't remember when I was a noobie (48 years ago?).
    So it is difficult and maybe impossible for us to talk to a neophyte.
     
  7. uzair

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    Einstein said :-
    "Every intelligent fool can make things complex, but only a genius can make complex things easier and understandable.":rolleyes:
     
  8. Papabravo

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    Like...
    In an unbiased transistor there is a potential barrier that prevents electrons from crossing the junction to get to the other side. A small amount of forward bias changes the height of the potential barrier so that electrons can easily surmount the potential barrier and get to the other side. The current required to support this lowering of the potential barrier is on the order of 1% of the collector current which flows and this constant relationship is true over a wide range of supply voltage and temperature variation.
     
  9. Papabravo

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    It was exactly the kind of answer that I thought I was giving. I'm sorry you didn't like it. I have no idea what level of explanation you're prepared to accept. We can talk quantum electrodynamics if you want to.
     
  10. Ron H

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    And also fairly constant over a range of (base-emitter) forward bias voltages, more for some transistors than others. But why?
    I may have known at one time, but not now.
     
  11. Papabravo

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    I think the why is that for any silicon junction the I-V curve is exponential. Small changes in voltage allow for large increases in current. At some forward bias voltage the transistor can have all the current it wants UNLESS the base current is limted externally; by a base resistor for example.

    I think where we want to get to is the Ebers-Moll Equation. I'm a bit rusty on the derivation, but I can dig out my notes if anybody is interested.

    Let's start with a pn junction and observe that ther are two types of carriers called "holes" and electrons. A hole is by definition the absence of an electron in what would otherwise and occupied state in the valence band of an atom. There are two types of motion possible in a semiconductor material and they are called Drift and Diffusion. Diffusion is the result of a concentration gradient. The concentration we are speaking of is either the hole concentration or the electron concentration. Drift on the other hand is the result of an Electric Field. We can calculate the junction potential as follows:
    Code ( (Unknown Language)):
    1.  
    2. Let Na be the concentration of acceptor atoms; Na = 10^15 atoms/cm^3
    3. Let Nd be the concentration of donor atoms; Nd = 10^16 atoms/cm^3
    4. Let Ni be the intrinsic carrier concentration; Ni = 1.5 * 10^10 atoms/cm^3
    5. Let T be room temperature; T= 300 dgrees K
    6. Le q be the charge on an electron; q = 1.602 * 10^-19 coulombs
    7. Let k be Boltzmans Constant; k = 8.62 * 10^-5 eV/degree K
    8.  
    9. Φ0 = (kT/q)*ln(Na*Nd/Ni)≈.63 Volts
    10.  
    As you can plainly see this function describing the junction potential of a pn junction depends linearly on temperature and logarithmically on concentration. Note also the doping with donor atoms is an order of magnitude larger than the doping of acceptor atoms.
     
  12. Ron H

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    Papabravo, I'm not sure we are on the same page. My question was why is the beta of some transistors, such as 2N3904, flat over several decades of collector (and emitter) current. If you answered that, it went over my head.
    From the diode equation, two decades of current change requires about 120mV change in Vbe. That's a LOT. The 2N3904 beta is probably flat below 100uA for a decade or so, also, if we can deduce that from the graph below.
    BTW, this is from the Fairchild 2N3904 datasheet.
     
  13. Papabravo

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    Getting to the Ebers-Moll equation takes more than a little bit of background. That was just the warm up. Are you ready for a long haul?
     
  14. Ron H

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    Go for it, but don't generalize too much, because lots of transistors do NOT have constant beta vs collector current. I suspect geometry and doping are the primary factors (are there others?).
    I gotta admit it probably won't affect my life much, even if I have an epiphany. I'm just curious, mostly.
     
  15. JLuis_GT

    New Member

    Jan 18, 2016
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    Hi
    I read and read and can't figure out how a small current (I_b) can control a big current(I_C) at atoms level, let's say. I know that it is in function of the doping level and geometry of the junction but HOW? How I_B allows a proportionally I_C current?

    The voltage controlled perspective almost make me understand how, except that I can't figure out how changing R_B resistor (and at the same time I_B) we change V_BE, when in the text's this value is fixed at 0.7V.
     
  16. ScottWang

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    Aug 23, 2012
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    Please do not reply to a old thread, specially it is 7 years ago, this thread will be closed.
     
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