# Common Emitter Amp - modelled vs actual outputs

#### LvW

Joined Jun 13, 2013
1,586
I think we are looking at the same thing on two different levels, with yours being the more technically correct. My level is what I will call first-order voltage gain of a common emitter stage where "Ae ~ -(0.9Rl/hib), the term hib may be considered as a small resistor in series with the emitter load". As a technician, I never needed to go much deeper than that and most circuits I worked on used an op-amp for gain and transistors for switches, current sources and current buffers and hfe was about all you worried about.
Please, can you explain the expression Ae ~ -(0.9Rl/hib ?
What is the background of the factor 0.9 ?

#### Parkera

Joined May 3, 2016
96
Ae is voltage amplification, in this context, for a common emitter amplifier stage. Rl is of course the collector load resistor and the next stage loading is implied to be a part of it. The 0.9 is a "fudge-factor" lumping in all other causes within the transistor for reducing the gain. If the collector current is about 1mA, hib is approximately 26 ohms and a contact resistance of about 4 ohms can be added to that (or so I was taught 50 years ago).

It's been my experience that this is not a particularly great estimate of gain in a small-signal stage when you don't have an emitter resistor or when the emitter resistor is well bypassed. Maybe it is OK for germanium transistors, but I haven't seen one of them for 60 years.

If you have a significantly larger emitter resistor, stage gain can be estimated pretty well from just the ratio of the collector load and the un-bypassed emitter resistor with a reasonable accuracy (assuming the Beta is 100 or better). For the circuit we have been talking about, the simple gain estimate would be Ae = 470/100 = 4.7. SPICE finds the gain to be 4.76.

#### LvW

Joined Jun 13, 2013
1,586
Thank you.
* To me, the "fudge factor" is somewhat mystic and has (as far as I can see) no real justification.
* From your explanation I learn that the quantity you call "hib" is nothing else than the inverse transconductance 1/gm=Vt/Ic.
* Of course, I agree to the last sentence - this is the classical negative-feedback approximation.

Finally, I like to repeat and underline one of your statements (see post'12):
"...it can be stated for practical purposes hfe does NOT determine the voltage gain."
(My comment: Not only for practical purposes: For the same DC operational point , the voltage does depend on the transconductance only and NOT on the hfe value).

Last edited:

#### Parkera

Joined May 3, 2016
96
* Agreed, the "fudge factor" does not have a real justification, only an empirical adjustment that apparently worked at one time.
* hib is one of the H-Parameters. Admittedly, I never did get a good grasp of H-Parameters. Someday I will revisit them.

Thanks for the memory jogs.

#### LvW

Joined Jun 13, 2013
1,586
* hib is one of the H-Parameters. Admittedly, I never did get a good grasp of H-Parameters. Someday I will revisit them.
Thanks for the memory jogs.
The quantity you call "hib" is a combination of two h-parameters: re=1/gm=(hib)=h11/h21=hie/hfe.
Fot the special case of Ic=1mA the inverse transconductance is 1/gm=Vt/Ic=26mV/1mA=26 ohms.

#### Parkera

Joined May 3, 2016
96
Thanks for that summary, I'll add that to my transistor books.