KCC's quizzes AQQ235 about a bipolar common emitter amplifier - a kind proposal from our colleague Martin Walker

Hi, according to me there are not sufficient information to calculate the gain. The equivalent small signal model shows that the gain is dependent by parameters like output resistance hoe and hfe. (low freq. range)

There is not any feedback. Nor signal neither DC feedback. The bias condition is affected by temperature. Adding an emitter resistor will allow to fix the gain to RC/RE and to have feedback to the bias point fixing the bias current. 

Thanks Giovanni for your feedback. You are right in saying that there is apparently no feedback, nor AC, nor DC. Usually one inserts a resistor in the emitter: this would insure a solid DC (negative) feedback in the circuit. But here...

The circuit is bad in the sense its behavior changes a lot with temperature. 

Having that said, the circuit works as amplifier. It does so thanks to the fact that the collector acts as a quite stable good current source; quite independent of supply change

yes, it acts as amplifier but the questions were:

1. Is there enough information to work out the gain of this circuit?NO, the gain is not fixed and depends by BJT parameters that have its own variation part to part and with temperature 
2. If so, what is the voltage gain of the circuit?Difficult to say with only the input data provided
3. Is it a good amplifier?NO, it is amplifier but not good. Temperature derivation can change the bias point so much that the output waveform can be distorced when the output signal is big enough. so surely it is NOT a good amplifier

Thanks

yes, it acts as amplifier but the questions were:

1. Is there enough information to work out the gain of this circuit?NO, the gain is not fixed and depends by BJT parameters that have its own variation part to part and with temperature 
2. If so, what is the voltage gain of the circuit?Difficult to say with only the input data provided
3. Is it a good amplifier?NO, it is amplifier but not good. Temperature derivation can change the bias point so much that the output waveform can be distorced when the output signal is big enough. so surely it is NOT a good amplifier

Thanks

What you say is absolutely correct, in that the gain depends on the BJT parameters which vary greatly with temperature.  However, it's a bit of a tricksy question because the temperature is specified at 25degC.  We've also not explicitly specified the bias, other than it is implicit in Vout being at 1/2 Vcc or 3V under quiescent conditions.

The gain of a grounded common emitter amplifier is just -gmRc and gm=Ic/(kT⁄q).  Rc is just Vcc-Vout/Ic.  Vout-Vcc=3 and the Ic's cancel each other out, so we end up with small-signal gain as 3/kT/q.  kT/q is roughly 25mV at 25degC, so this works out to be a gain of about 120 or 41dB.

Of course, it's a terrible amplifier because the gain is both temperature and input signal dependent.  The input impedance and loading of the input signal also varies as this is affected by the re and beta of the BJT.  This is why most common emitter amplifiers have an emitter resistor to provide negative feedback to reduce and stabilise the gain.

As I say. it's a bit of a tricksy question but I'm glad everyone had some fun with it.  I first came across this brain-teaser in a video by Paul Brokaw on ADITube.  The link is further up the comments and is well worth a look.