Explanation of AC analysis of oscillator

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miki1221

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Can someone explain how we do a AC analysis of harmonic oscillator on following example.
I've done the the 16 Mhz oscillator, and simulated it, but I'm trying to understand how it is really working.


The equivalent circuit is over here(hope so)



So my question is, when I start to analyse by hand on paper, I find problem almost on every step, actually I'm not sure if I'm doing it right, so can someone help me go trough it.
I'm very interested in undarstanding of these and simmilar oscillators so, for you maybe this is quite simple, but I'm new in this so everything seems very complicated for me.
I'll be very appreciate if someone finds time to check and answer my question.
Here are results of DC analysis:
1. Ključni elementi kruga:

  • Ucc: 5 V
  • Transistor (Q1): S3018 (NPN)
    • R2=100 kΩ
    • R3=100 kΩ
    • R4=1 kΩ
    • R5=1 kΩ
    • R6=100Ω
    • C16=4.7 nF
    • C15=33pF
    • C15=33pF
  • Kristal:
    • XTAL1=16 MHz
2. (S3018):

  • HFE (β): 200


Ub=2,5V
Rb=50kΩ
UE=1,8V
IE=1,8mA=IC
UC=3,2V
UCE=1,4V

​
 

Solution
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Hello all

After several iterations (building transistor AC model, merging transistor amplifier i/o impedances with impedances of other circuit components, etc) I ended up with below oscillator AC model.
I recognise that it is Pierce crystal oscillator.
For analysis of crystal operation I used this technical note.



Most challenging for me is to prove phase shift in feedback loop.
Desired phase shift at second (B2) voltage divider is -105deg,
but when I calculate crystal impedance @16MHz and put it into voltage divider equation,
phase shift I got was about -120deg

I used math solver to check possible values of the crystal impedance (and B2 voltage divider gain and phase shift) between the crystal's serial and...
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Hello All

It looks like we are reinventing a wheel!
Below is picture from this Microchip technical note
Phase shifts at each stage are similar to my calculations: 75deg and 105deg.


Also I made Bode plots for second voltage divider (B2 stage), and found that it is not so sensitive to change in Cp
I used 0.1pF (0pF plot is not readable and invokes divide by zero in my calculations), 1pF, 3pF and 7pF.
And operation frequency change is several hundreds of Hz.
 

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I didn't understand what you wanted to say, can you explain? now I'm even more confused, what kind of analysis should I try?
 

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You are quite right that your analysis is like Microchip’s Analysis. My bias must have come from using log-log curves rather than lin-lin plots. However I still say if the ratio of Cp/Cload is significant that phase noise will also be significant.

Cp=7pF bypasses the parallel resonance with 33 pF load caps equiv to 16.5 pF || Lp and significantly degrades the wide and noise suppression of the Xtal. which cannot be seen in lin-lin plots (Increased phase noise)

But good on you for your similar phase plots.
 

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miki1221 said:
How to find the self-excitation condition for a pierce oscillator?
Click to expand...
Pierce Oscillator or another type of oscillator.
The Start-Up Condition is already known as Barkhausen Conditions. It's been already mentioned in many literature.
When you calculate node to node Trasnfer Function, you'll get a s-domain Transfer Function and Zeros and Poles.
Since that Barkhausen Conditions are satisfied, the oscillator will start to oscillate.
 

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This is driving me crazy!! 33pF is fixed, what values of Ls and Cp do I need to use to pro-oscillate?
 

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miki1221 said:
This is driving me crazy!! 33pF is fixed, what values of Ls and Cp do I need to use to pro-oscillate?
Click to expand...
As a step toward getting a grasp, Tony's post #9 has a link to the animated interactive simulator. Turn on 'Show Current' (under Options) and move Current Speed slider toward right. You should notice how the necessary rhythm becomes obvious, as the transistor is biased at the correct moments to make the LCC tank continue oscillating. An L:C ratio that works generally makes the inductor 1000 or 10,000 or 100,000 times the capacitor value.

Your latest schematic (post #26) is getting more complicated. Success depends on getting everything right or it won't oscillate. Or it will oscillate and fade. For crystals or LCC tanks there is a simple oscillator based on an invert-gate. That's another good topology to get a grasp.
 

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Unfortunatel your LC oscillator design doesn't fulfill the oscillation condition. LC circuit doen't achieve 180° phase shift. Below circuit e.g. does oscillate



Bode plot shows positive gain at phase = 0.

 

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Is problem in multisim? Look what I've got :/
Even your circuit is LC, I have to do an crystal( so I made simplified equivalent model, neglecting Rs and Cs (only Ls and Cp remain connected in parallel)
--- Updated ---

L:C in equivalent of crystal?
 

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miki1221 said:
Even your circuit is LC, I have to do an crystal( so I made simplified equivalent model, neglecting Rs and Cs (only Ls and Cp remain connected in parallel)
Click to expand...
It's no useful crystal model, transfer function is completely different. Cs is essential to model a crystal. I was using your LC circuit in my simulation because you apparently switched from crystal to LC oscillator. Now I hear it's only for simplification, but that doesn't work.

.tran simulation of crystal oscillator is difficult due to high resonator Q. Startup time is in ms range, even with "kick-start" pulse.
 

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The single NPN Pierce Osc must 1st stabilize Iq from the DC bias then how the signal slowly with very little excess gain and the time constant to stabilize max Vac swing depends on the Q of the design. AT cut 16MHz Xtals tend to have a Q=10k = fo/BW. The rise time is related to the BW. Do you know how?
 

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I dont know.
Look what I found...

Unstable Oscillation in Pierce Oscillator

Here is a Pierce Oscillator that I built to oscillate at 16 MHz. I put the parts on a breadboard (I know its a bad idea, but this is what I have with me). And here is the result: As we can see I am
electronics.stackexchange.com
--- Updated ---

V.L.C. ? What does it means?
 

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