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.