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So then I decided to give myself another 5 minutes to build a crystal oscillator the way I would have done if somebody had said: "Build a simple crystal oscillator." I.e. with an 'HC00. Of course this one works just fine. I didn't bother tuning it, I used the first capacitors that I picked up from the drawer, which turned out to be 22pF. Build time was just under 3 minutes including stripping some wire to make links.
 

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And this is how it looks with a 4MHz xtal.

*BONUS POINTS for anyone who noticed I had the scope's 20MHz bandwidth limiting switched on. The actual output waveform is very ringy because I did a lousy job of decoupling the power supply (stood a ceramic 0.1 across the IC without chopping its leads down). You can change the W/F just by bending this component about. It could be fixed but... time's up!

E2A, I semi-fixed it (relocated the bypass cap and poked the probe direct into the breadboard)
 

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very interesting update.
I managed to split 1/10 of my test PWM original fv. From its 850Hz down to 85Hz
Now Im playing with some capacitors values to bring it down to 1/100.
My target end result will be 1/1000.
And, I did managed to --average-- the 1/100 values. I say average because the fv counter is jumping a couple of Hz up and down. It should be 8.5Hz but is heavily fluctuating with diverse values between 10Hz and 6Hz. So I am theoretically at 8 but because is jumping all around these values, it was hard in the beginning to understand where I stand. But staying and watching these values for a while, a couple of minutes, I concluded it is jumping around these margins. That might be from the High resolution of the splitting, all the circuit(s) combined might present some tolerances, especially the capacitors and resistors and why not the chip(s).
At 1/10, it does not jump at all, it stays put at that fv. So.... I think im good at this point.
I might have to make a second circuit that will split another 1/10 from this one that is 1/100 and in the final output will get 1/1000. And I expect it will be extremely jumpy at that Very High resolution. If it is a way of "average" all these jumping, especially at 1/100 stage I am right now. That will give a good clear chance for the 1/1000 stage. Hmmm. But it is in plan. For now, I have to reach that 1/1000 target and Im GOOD, literally. Haha.
 
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A crude simulation attempt, did not work at 20MHz with 2N2222 but OK with BC548, also used low-Q crystal model so faster to build up (along with 1mV kick at t=0)
View attachment 97652

Time-domain for test point in Tr1 collector:
View attachment 97653
I had another go this morning after thinking about the small signal model of this circuit and why the ratio of Rc to Re matters so much- see first attachment. I tried Rc = 1kR and Re = 4.7kR and even exchanged the BC549s for two new but in my construction it did not oscillate. Not enough feedback methinks so I swapped Rc for 100R and the symmetrischer oszillator found its 20MHz voice. We did it Sir and self starting to boot! 🙂
 

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Not enough feedback methinks so I swapped Rc for 100R and the symmetrischer oszillator found its 20MHz voice. We did it Sir and self starting to boot! 🙂
Excellent!

While the E-E impedance should be roughly -2*Rc quite possibly the higher Rc values along with stray capacitance might cause too much phase shift. I seem to recall that 10-20MHz crystals are below 100R series resistance so indeed 100R values for Rc would be adequate, as you have so well demonstrated!
 
q12x. : My next step is to take the small amplitude 20MHz sine wave and turn it into 20MHz pulse stream of TTL logic 0 and 1s to feed into the divider circuit.
 
Congratulation mister @marconi I am really happy you made it !
But I am not sure I understand completely your values.
So I grabbed all the information you provided so far:
Rc for 100R and the symmetrischer oszillator found its 20MHz voice.
did not work at 20MHz with 2N2222 but OK with BC548
I tried Rc = 1kR and Re = 4.7kR
and I redraw the circuit with the new values:
- Are these the values you used?
-Oscillator Circuit of The First Quartz Wrist Watch(Symmetrischer Oszillator) - Copy.jpg
 
Congratulation mister @marconi I am really happy you made it !
But I am not sure I understand completely your values.
So I grabbed all the information you provided so far:



and I redraw the circuit with the new values:
- Are these the values you used?
View attachment 97682
Yes. VB is 5 Volts not 1.35V. The npn transistors are BC548B types. the letter A, B or C after BC548 indicates the so-called direct current gain of the transistor - the hFE - and relates the emitter-collector current flow to the base-emitter current flow eg: Ice/Ibe. Which BC548s do you have? Cs have higher gain than Bs than As so I used the mid-range gain type.

See top of page 2 of:

BC548B datasheet - https://datasheetspdf.com/pdf-file/1292183/Kingtronics/BC548B/1
 
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Which operational amplifiers do you have please and I will use the same ones to amplify the small amplitude 20MHz sine wave.
 
Mine are BC548 B - coincidence! like yours.
I have uA741(not that used anymore) and LM358(most used)
Updated circuit after your last specifications:
Ive added + and 5V and gnd symbol. Also B after tr name.
-Oscillator Circuit of The First Quartz Wrist Watch(Symmetrischer Oszillator) - Copy copy.jpg
 
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