Isn't the derivative of an exponential also an exponential, then how is your r = 26mV/IC, can you please show all the math on how you came up with the r equation. Also isn't IC dependent on VCE by Early Effect, what happened to that in the equation and subsequent derivation, because a small change in VBE can actually cause big change in VCE.
All true! It would be difficult for me to try to show the derivation in a comment, but no problem! You will find it in glorious detail (with appropriate graph) in section 7.2 of my Semiconductor Devices text which you can download for free. See the links in the video description, above.
@@ElectronicswithProfessorFiore Thanks for the textbook, it's very helpful, however I didn't find in it the derivation for r which showed what happened to Early Effect?
@@whatever3041 For basic amplifier designs, the Early Effect is a very, very minor concern when it comes to determining the voltage gain or input impedance. EE hardly changes the value of r'e over the normal range of operation, and we usually minimize the effect of r'e anyway through the use of negative feedback (aka swamping), thus EE is maybe a third order effect.
@@ElectronicswithProfessorFiore thank you, however, I would have preferred that textbooks then showed it as a third order effect with proper math, because even though output resistance of the BJT is quite large textbooks show its calculation. We are trying to develop a small-signal model and in my opinion most time should be spent on how it came about what happened to dvCE/dvBE should all be discussed with proper math, because after the model is developed it’s all just circuit analysis.
@@whatever3041 The proof starts with the basic equation developed by Shockley that describes the current-voltage characteristic of a PN junction. There is no need to tease out individually all of the elements that go into that equation.
That comes from the basic junction equation. The derivation can be found in the text (free download if you haven't yet grabbed it). For silicon BJTs, you can think of it as a constant, rather like the the 0.7 V forward junction drop.
@@Chris-hi2hn All of the links are down in the description of the video. There are five text books and seven lab manuals in the series. All are free to download or view on the web, and if you like print versions, those are available on Amazon at very low cost.
Isn't the derivative of an exponential also an exponential, then how is your r = 26mV/IC, can you please show all the math on how you came up with the r equation. Also isn't IC dependent on VCE by Early Effect, what happened to that in the equation and subsequent derivation, because a small change in VBE can actually cause big change in VCE.
All true! It would be difficult for me to try to show the derivation in a comment, but no problem! You will find it in glorious detail (with appropriate graph) in section 7.2 of my Semiconductor Devices text which you can download for free. See the links in the video description, above.
@@ElectronicswithProfessorFiore Thanks for the textbook, it's very helpful, however I didn't find in it the derivation for r which showed what happened to Early Effect?
@@whatever3041 For basic amplifier designs, the Early Effect is a very, very minor concern when it comes to determining the voltage gain or input impedance. EE hardly changes the value of r'e over the normal range of operation, and we usually minimize the effect of r'e anyway through the use of negative feedback (aka swamping), thus EE is maybe a third order effect.
@@ElectronicswithProfessorFiore thank you, however, I would have preferred that textbooks then showed it as a third order effect with proper math, because even though output resistance of the BJT is quite large textbooks show its calculation. We are trying to develop a small-signal model and in my opinion most time should be spent on how it came about what happened to dvCE/dvBE should all be discussed with proper math, because after the model is developed it’s all just circuit analysis.
@@whatever3041 The proof starts with the basic equation developed by Shockley that describes the current-voltage characteristic of a PN junction. There is no need to tease out individually all of the elements that go into that equation.
Hi how did you derive 26mV in calculating r?
That comes from the basic junction equation. The derivation can be found in the text (free download if you haven't yet grabbed it). For silicon BJTs, you can think of it as a constant, rather like the the 0.7 V forward junction drop.
Free text? Thanks I wasn't aware, I'm sure you mentioned it but where can I find it 😀
@@Chris-hi2hn All of the links are down in the description of the video. There are five text books and seven lab manuals in the series. All are free to download or view on the web, and if you like print versions, those are available on Amazon at very low cost.
@@ElectronicswithProfessorFiore ...and they are most excellent!