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I want to calculate the input impedance when I am using a Darlington pair and I'm getting a little confused on the appropriate equation to use.

In Electronic Devices by Floyd he gives and example of a Darlington emitter-follower circuit and when he calculates the input impedance he has B^2*(re+Re) where Re is RE||RL and re is the ac emitter resistance.

I was watching a video by David Williams who is explaining the input impedance and goes through the derivation of a emitter follower Darlington pair (which made sense as he went through it) and goes up with the input impedance of B^2(2re+Re).

So my question is when trying to calculate the input impedance, am I supposed to be using 2re or re in the equation? Or if they are both valid is there a rule of thumb when to choose which. Image from the two sources are below

Floyd Darlington Pair

David Williams Darlington Pair

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  • \$\begingroup\$ Can you provide a link to his video. I’d like to look at it. \$\endgroup\$
    – Leoman12
    Commented Apr 21, 2020 at 1:04
  • \$\begingroup\$ @Leoman12 youtu.be/esSCw8fz6ko \$\endgroup\$
    – pnd1987
    Commented Apr 21, 2020 at 1:15

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It seems then that the equation in the video and in Floyd’s book differ by what assumptions they take. The input impedance presented in Floyd uses the special case where beta of both transistors are the same. Also in the book they ignore re1.

Two other books I have shown an equation of Zin=beta1*beta2*Re where Re=RE||RL. There they make the assumption that re1 and re2 terms are small compared to RE.

Shown below is a capture of one such equations derived from one of these books

Source: electronic devices and circuit theory boylestad

enter image description here

So the equation you use really depends on what assumptions you want to take and how close you want to to be to represent each piece of the model. If that makes sense.

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  • \$\begingroup\$ Thank you, I figured that might be the case with how close you want to approximate. I think with the video he had the betare1 + beta^2*re2+... and a relationship that he previously showed that re1 = beta *re2. So with subsitution he had beta(betare2) + beta^2*re2 + ... and factoring out the beta^2 he got beta^2(2re2+...). \$\endgroup\$
    – pnd1987
    Commented Apr 21, 2020 at 2:06
  • \$\begingroup\$ You’re right, my mistake. I didn’t notice that. But he does consider only the case where beta1=Beta2=beta. \$\endgroup\$
    – Leoman12
    Commented Apr 21, 2020 at 2:29
  • \$\begingroup\$ I believe that the zi1 shown in picture in my answer is the most accurate. The cases in video and Floyd can be derive from this actually . \$\endgroup\$
    – Leoman12
    Commented Apr 21, 2020 at 2:41
  • \$\begingroup\$ Funny thing is that after doing some math and reviewing all possibility's, Floyd is most inaccurate. And the formula in video is the same as the one shown in my post when beta1=beta2=beta. \$\endgroup\$
    – Leoman12
    Commented Apr 21, 2020 at 2:53

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