# “Linear” Amplifier

For example, the "small-signal" gain we find for a Common Emitter amplifier is -gmRc, (assuming no emitter degeneration) Rc being the resistance attached between the collector node and supply. Now, if our input signals are "large"/ any arbitrary value, can we use the gm at an Ic (bias+ac) for a particular input level (gm=Ic/Vt)and calculate gain using -gmRc? This however means that the input waveform is scaled by different amounts at different locations, hence kind of distorting the input. So does it mean that the amplifier does not remain linear over arbitrary input levels and linearity holds only for small input excursions? Or do we calculate gain for arbitrary input levels in a different way? How do we go about defining linearity of an amplifier in terms of input signal "limits"?

• (Answer key: No. Yes. May beg the question. Various figures of merit.) I thought Tim Wescott's answer to your question on small signals was pretty good. Perhaps return there and think more closely about it. And in some detail? It might help. I enjoyed reading it, anyway. – jonk Aug 17 '19 at 6:59
• @jonk I m sorry if its too much nagging.. Bt.. Do we designate "small-signals" to the inputs parameters of the amplifier only? If the output swings are large compared to their bias points (which results in amplitude distortion), how are we still using the small signal approximation in thus situation? – Nullbyte Aug 17 '19 at 8:09
• @Nullbyte again, you define what "small" and "large" is, by defining what your models are, and what the acceptable errors of these models are. Accordingly, all parameters of your model apply to that respective model – "in or output" is not a relevant category to that. – Marcus Müller Aug 17 '19 at 8:47
• Perhaps you missed the point that Tim wrote, regarding feedback (negative is implied if not expressly stated) and vacuum tubes vs transistors. Distortion within individual stages is greatly repaired by global NFB. It is almost a miracle to behold! It also can hold your DC quiescent point despite temperature changes, too. I guess I'm suggesting that you think beyond the single stage itself. Or, consider sources of local NFB if only one stage is allowed. – jonk Aug 17 '19 at 8:49

Yes, you are right the Common Emitter amplifier voltage gain is a highly non-linear because with collector current the gain varies with the collector current ($$\g_m = \frac{I_C}{26mV}\$$).

How to derive the precise gain of an NPN common emitter amplifier without emitter degeneration?

And this is why single stage BJT amplifier produces a lot of distortion.

We get about 1% of THD per 1mV at the base (10% THD for Vin = 10mV).

https://www.researchgate.net/publication/242307545_METHODS_FOR_COMPUTING_HARMONIC_DISTORTION_IN_LOW_FREQUENCY_POWER_AMPLIFIER

http://www.kevinaylward.co.uk/ee/bipolardesign2/bipolardesign2.xht

You can improve the distortion by adding the external emitter degeneration resistor (without CE capacitor).

But to get "low THD" we need to pick $$\R_E >> \frac{1}{g_m}\$$.

Therefore it's impossible to get high voltage gain and low THD in such a simple circuit.