SaM - Quartz in a 3 Point Oscillator

Remeber:

We can create a simple oscillator using only capacitances, inductances and an O.A., like so:

• Moreover, we can create two different oscillators with this structure, the Colpits oscillator and the Hartley oscillator.
  • Colpits oscillator: $Z_1=Z_3=C$ and $Z_2=L$.
  • Hartely oscillator: $Z_1=Z_3=L$ and $Z_2=C$.

• For AT-Cut quartz we have seen specifically the Colpits oscillator, where the inductance $Z_2$ is replaced with the quartz, doing so garatnees that ==this circuit will oscillate only at frequency in which the quartz acts as an inductance, so for $f_0$ in the interval $[{\omega }_s,{\omega }_p]$==:
  

We can add a capacitance in series or in parallel to our quartz, doing so we will shrink the freqency range where the circuit oscillates (fine tuning), but we will also decrease the the $Q$-factor value (not good), defined as:$Q=\frac{1}{{\omega }_s{R}_{eq}{C}_{eq}}$ Here is the base reference, with no added capacitances, so base range: $[f_s,f_p]$:
If we add a capacitance in series or in parallel:

• In series: we increase $f_s$.
• In paralle: we reduce $f_p$.
• In both cases we reduce the range $[f_s,f_p]$

Here is a real life example of tuning with $C_L$:IMPORTANTE

• Specifically we see how the bode plot changes with a capacitance $C_L$ in series to the quartz.

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• In principle $Z_i=X_i$ are reactances (capacitances or inductances)
• In the Colpits Oscillator example, this circuit will oscillate if two $Z$s are capacitances and the other is an inductances.
• If we take the Colpits Oscillator if we replace the $L$ (inductance) with the AT-Cut Quartz*, then this circuit will oscillate only at frequency in which the quartz acts as an inductance, so for $f_0$ in the interval $[{\omega }_s,{\omega }_p]$.

So, here’s an example of a simple Colpits Oscillator:

• First graph: ideal situation
• Second graph: If we find a capacitance in series to our quartz.
  ⇒ There is a shift of $f_s$.
• Third graph: If we find a capacitance in parallel to our quartz.
  ⇒ There is a shift of $f_p$.
• NOTE: In both the second and third graph, so if we add a capacitance, we shrink the range.
  We can tune the frequency in this way.
  But this will also change the $Q$-factor value, rember it is defined as:$Q=\frac{1}{{\omega }_s{R}_{eq}{C}_{eq}}$So there is a limit in tuning.

Real life example of tuning with $C_L$:

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