Colpitts Oscillator Circuit Analysis (7 - Oscillators) 

look at 5:23 the guy said this using impedances X1 and X2

Students sometimes find the abstract models too difficult at the beginning, so I'm trying to avoid them and instead concentrate on the oscillation condition.

Finally I have figured it out. Yes, V2 is in fact dependent on Z2 through the fact that the current in the branch depends on it, but it does not matter, since we have to multiply with both the numerator and denumerator with this current and so it cancels out. This also applies in the V2/V1 case, but the current is the generator current, and it also cancels out. I wrote this answer to my own question in case someone else needs it in the future. :)

When considered X1+X2+X3=0 was to guarantee phase zero? Another condition from Barkhausen?

@@MrCleitonls correct

In this oscillator, it is required that there be a non-zero Rout (or that there be some kind of resistor there). If the amplifier were perfect and Rout=0, then Z2 would have no effect on the voltage at node V2 because Z2 would be in parallel with a perfect voltage source. There would then be insufficient phase shift around the loop to achieve oscillation; the equations would thus fail to give a single frequency of oscillation without the added constraint as you rightly pointed out.

@@adanner Thank you. I did do a calculation along the lines of V2/V1=Z2/(Z2+Z3), V1/V2=Z1/(Z1+Z3) …. Multiply these together, set them to one and you get the required Z1+Z2+Z3=1 relationship. I think this mimics the situation if Rout=0. It is all academic I suppose since we do live in the real world without perfect amplification. I was thinking of the impedance element as a filter so I approached it as such. I very much appreciate your presentation. So often I see a superficial approach like calling the impedance in this oscillator a tank circuit when it really isn’t. Yes the equation is the same for the frequency but no one but you showed mathematically the inverting nature or the feedback decency on Z1 and Z2. Once again, thank you. Charlie

@@stevekim6923 Yes, it is equivalent to what is written since (X1 + X3) = -X2.

@@adanner Thank you very much! Before you answered this, I deleted the question because I understood it later on. I guess i wasn't fast enough.

You could look at his two port network examples to see why you don't want a voltage source driving a capacitor. infinite current required?

There is a resistor in serie to CE to control amplifier gain. This resistance is reflected to the base multiply to HFE. This way if the resistor value is 500 Ohms and HFE 100. The resistance seen from the base will be 50K Ohms plus rpi which depending Ib current.

Thus Rin will be in fact much bigger than Z1 and the equivalent resistence will change just a little bit.

RE is used for BJT DC polarization (and designed to get a gain of 1 at DC or low frequencies), but for AC this resistor may be too high and CE allows to lower emitter resistor (and increase BJT gain at high frequencies to make sure the oscillator keeps working) by connecting RG in parallel to RE.

RE has function to keep polarization stable avoiding HFE variations cause by temperature changes or transistor substitution with different HFE's. CE desacopplishs RE avoiding change DC polarization and increase considerably the gain of amplifier because the AC signal won't see RE and it will can use the DDP RE to increase his excursion over VCE. The amplifier gain without CE will be RC/RE, but whit CE the gain increase a lot and to don't distort the AC signal he put a serie resitor that work like RE just to control the excursion of the AC signal without distortion.