CE BJT Amplifier - Collector Resistance

[hisotaso]

We are studying single transistor amplifiers, and in the text where the collector resistance of the CE amplifier, Ric, is derived, the final equation is

Ric = ro[1+gm(Re||r∏)] (approximation)

This equation is highlighted and emphasized as something we should remember, then shown again in a large blue box on the next page as a "Design Note" (large emphasis in this text).

However in the table at the end of the section that summarizes the CE/CS amplifier design summary, and the big table at the end of the chapter that lists the design summary for all of the BJT amplifiers, the equation is given as

Ric = ro(1+gm*Re)

I have been looking for hours and there is nowhere that I can find where this transition takes place. The text is Microelectronic Circuit Design, 4th edition by Jaeger and Blalock. I am at a loss.

 

[Jony130]

Well they simply assume the Re<<r∏ so Re||r∏ ≈ Re

And sometime we use this version

Rci ≈ ro * (re + Re)/re

Where

re = 1/gm = 26mV/Ic

But Ric cannot be greater than Rci_max = β*ro for Common-base amplifier.

 

[hisotaso]

Thank you Jony130 for your reply. I apologizr for not being clearer, this is a common emitter amplifier (CE), I don't know if this makes a difference.

Also you have pointed out something that has been driving me crazy with this text, that is approximations are often made without explicitly stating so. This is frustrating when learning a new subject and not completely confident with the subject matter.

 

[Jony130]

Simply you should always remember that if you use this equation
Ric = ro[1+gm(Re||r∏)]
If result is greater than β*ro your approximation equations tricks you. Because Ric can never exceed β*ro.

 

[alphy]

I understand your confusion and frustration with the discrepancy in the equations for the collector resistance of a CE BJT amplifier. It is important to note that in engineering and scientific texts, there can often be slight variations or approximations of equations depending on the context or application.

In this case, the equation Ric = ro[1+gm(Re||r∏)] is an approximation that takes into account the parallel combination of the emitter resistance (Re) and the Early voltage (ro). This approximation may be more suitable for certain design scenarios where the Early voltage plays a significant role in the overall amplifier performance.

On the other hand, the equation Ric = ro(1+gm*Re) is a simplified version that neglects the Early voltage and only considers the effect of the emitter resistance. This may be more suitable for simpler amplifier designs or when the Early voltage can be ignored.

It is also possible that the textbook may have made a mistake in presenting the two equations, or that the second equation is simply a typo. I would recommend double-checking with the author or consulting other reliable sources for clarification.

In any case, as a scientist, it is important to understand the underlying principles and assumptions behind equations rather than just memorizing them. So, I would suggest focusing on understanding the concept and derivation of the collector resistance equation rather than getting caught up in the differences between the two equations presented in the text.