BJT differential stage; finding I_c1 and I_c2

Discussion in 'Homework Help' started by u-will-neva-no, Apr 16, 2012.

Mar 22, 2011
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Hey everyone, Im struggling and require your assistance!

From my lecture notes, I have two equations:
$ic1 = \frac{\alpha.I_E_E}{1 + exp{\frac{-v_d}{V_t}}}$
and
$ic1 = \frac{\alpha.I_E_E}{1 + exp{\frac{v_d}{V_t}}}$

I also have a common base current gain equation:
$\alpha.IE_E = i_c_1 + i_c_2$

First i would like to know what the words "...and the transistor Q1 has 4 times the emitter junction area of Q2". From the attached question. Am I correct to say that 4Ic1 =Ic2 or the otherway around? If so, should I just substitute this into the common base current gain? Im not sure what the value of vd is for the other equations which is why I dont want to use them..even though a value of alpha has been given.

thanks for reading my post of confusion!

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2. t_n_k AAC Fanatic!

Mar 6, 2009
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The relationship of particular interest would presumably be that of VBE and the junction saturation current, Is. Since the junction saturation current is notionally proportional to emitter area then that would be the defining requirement which would lead one to a static difference in the VBE values which would ensure collector current equality. So for equal VBE values the transistor with the greater emitter area would take the higher current.

So I think the required difference in static VBE values to balance the collector currents would simply be $\small{V_{{T}}\large{ \ln(4)}$ volts.

Last edited: Apr 17, 2012
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3. Ron H AAC Fanatic!

Apr 14, 2005
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I have been fascinated with this subject ever since Barrie Gilbert published "A New Wideband Amplifier Technique" in 1968. The answers to your questions are in this remarkable paper, if you can dig them out.

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4. t_n_k AAC Fanatic!

Mar 6, 2009
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Thankyou Ron. Much appreciated for the link to the paper.

I think equation (4) is probably relevant to the OP's question.

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