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Beta? Hfe? Gain? 2N3904s! I think its transistor theory…

So a bunch of the folks were talking about engineering and electronics and the like in our irc room and I got to talking about how engineers love smashing a whole bunch of letters and numbers together to make chip names sound ridiculous.  So I asked folks what their favorite transistor was for audio applications and instead of getting 10 different kinds, a few of them agreed on the 2N3904 (spoilsports :p).

Anyway so somehow they got to explaining how to find the DC current gain of a transistor based on its datasheet and such:

Explanation 1:

Per @mgburr and Lancelot: A 2N3904 transistor’s beta max value is 150 and min value is 100.  When figuring out DC current gain, the beta value is part of the formula.  In the sheet above, it is also known as as hFE.  (hFE = beta = gain for easier understanding)

So if you need to build an amplifier with a gain of 300, you set up 3 transistor stages.  A good rule of thumb is to build it using the minimum beta value instead of the max:

[100] + [100] + [100] = 300…So even if it’s at its minimum, it still has enough gain
[150] + [150] + [150] = 450…If all of the transistors were at their max, gain = 450

If you based the gain off of the maximum beta value instead of minimum:

[150] + [150] = 300….  This is possible if it works at its maximum gain BUT
[100] + [100] = 200….  This wouldn’t give you enough gain!

Now hFE and beta cannot be greater in value than allowed by the gain.  Otherwise you get noise caused by saturation and clipping of the signal

If we look further into this, beta/hfe/gain = the ratio of the current going through the collector/the current through the base.

Explanation 2: 

Per @brainwagon: Transistor Man looks at the current going from the base to the emitter.  He then adjusts the collector/emitter current to be hFe * Ib. 

  • hFE is found on the datasheet (also known as beta/gain) as highlighted in the above datasheet.
  • Ib is the current at the base.

These are 2 ways to prove that hFE=Gain

Our players are:

  • Current at the base = Ib
  • Current at the collector = Ic (or hFe*Ib)
  • Gain = Gain

First explanation from @mgburr and Lance: Beta/hFE/Gain = the ratio of the current going through the collector/the current through the base

  • Gain = Ic/Ib
  • Gain = (hFe*Ib)/Ib
  • Gain = hFe

Second explanation from @brainwagon: Collector/Emitter current = hFe * Ib

  • Ic = hFe*Ib
  • hFe = Ic/Ib
  • hFe = (hFe*Ib)/Ib
  • hFe = hFe = Gain

Whew!

@atdiy/@tymkrs

Filed under beta hfe gain 2n3904 tymkrs amplification transistor man transistors

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