# Analysis of high Frequency Hybrid-pi model of a BJT

Can someone explain the reason behind this modelling of rx?

I had read in the book: "Microelectronics by Sedra & Smith" that rx is added to model the resistance of the silicon material of the base region between the base terminal and a fictitious internal (or, intrinsic) base terminal which is under the emitter region

Now, what is this fictitious internal base terminal in a BJT?

• Since it says "base terminal which is under the emitter", they might be referring to the actual physical layout of a BJT. Perhaps you can add a diagram showing the actual layout/doping of a BJT. In such a diagram, i think you will be able to locate regions in the base doped region where the BJT action doesn't take place and contributes only to resistance and nothing to amplification.
– AJN
Commented Jun 2, 2021 at 12:16
• So, it's all about the physical structure and synthesis portion of the device. Nothing to do with circuit and "actual" analog stuff, right? Commented Jun 2, 2021 at 12:57

Hybrid pi model Wikipedia

The full model introduces the virtual terminal, B', so that the base spreading resistance, rbb, (the bulk resistance between the base contact and the active region of the base under the emitter) and rb'e (representing the base current required to make up for recombination of minority carriers in the base region) can be represented separately.

1. The base is lightly doped compared to the emitter and collector. So resistance felt by the charge carriers while traveling through the base is higher compared to the other two regions.
2. The BJT works because the base is assumed thin and carriers injected from emitter can pass through the lightly doped and thin base to the collector suffering only a small amount of recombination inside the base.
3. In actual BJT construction, the base is thin only in some regions. So the BJT action doesn't take place in the thicker regions.
4. Due to the construction, the carriers need to travel through the thicker regions of the base before reaching the thin active region. The resistance encountered in this journey may not be negligible.
5. So in the equivalent circuit, the (average? equivalent ?) resistance encountered by the carriers before reaching the part of the base where BJT action takes place can be modeled as a resistor.

Image is a modified form of the image taken from Wikipedia

The base is distributed over a region. The carriers can cross the EB junction at several locations. The resistance encountered by each individual carrier just before crossing the junction depends on the exact location where it cross the junction. A carrier crossing at location shown by D1 and another crossing the junction at Dn suffer different resistance on their way to the junction. On average we can find a virtual point in the base where all the charges are assumed to cross the junction so that the net effect is the same as the case where the base is distributed over an area.

• Thank you for the explanation! However, I have got another doubt. Why do we consider this resistance rx only in high frequency model? In low frequency model, we never studied rx. What heppens to B' when low frequency is applied as input? Commented Jun 9, 2021 at 0:36
• I'm not sure. But I suspect that it is because, the capacitance marked by Ce and Cc in the linked Wikipedia pi model page have low reactance at high frequencies. So rbb may be becoming significant when compared to the parallel combination of rbe and Ce and similar for rbc and Cc
– AJN
Commented Jun 9, 2021 at 0:44
• You can consider asking a new question including the relevant details from the textbook / references.
– AJN
Commented Jun 9, 2021 at 0:45
• In Sedra & Smith, it is written that as the value of rx is very much less than r(pi), it's effect will be negligible in low frequency. It's presence is felt only in high frequency, we can't neglect during high frequencies for (may be) the reason you told above (the reason is not clearly given in the book). But rx is certainly of very low value. Commented Jun 10, 2021 at 4:21