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schematic

simulate this circuit – Schematic created using CircuitLab

As I understand this circuit has some initial gain at startup, then as the oscillation builds up gain goes to unity at some moment. How to modify such circuit to change crystal power dissipation from lets say 1mw to 100uw, but still keep initial gain same for reliable startup? I mean, how to control transition point where it goes to unity gain? Also, what could be possible consequencies of adding series resistor to a crystal to lower drive level? Say 5 to 10 Ohms?

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  • \$\begingroup\$ Instead of posting a circuit that you aren't using, why don't you post the circuit that you are? There's a schematic editor, so you can edit your question. The answer I want to give is "change the bias", but your JFET circuit is almost certainly biased differently than the given BJT circuit. \$\endgroup\$
    – TimWescott
    Jul 11, 2019 at 14:38
  • \$\begingroup\$ I wanted my original question to be a generic design question about Colpitts circuit. I want to better understand initial gain and transition to unity gain. I think crystal drive level will be directly related to that transition point. \$\endgroup\$
    – Vincent
    Jul 11, 2019 at 15:40

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The initial gain of the circuit is essentially what drops out of the small signal model -- some perturbation of the voltage or current at some point of the circuit will result in some perturbation of that same thing. In order for oscillation to occur, the output needs to be greater than, and equal in phase to, the input.

The operating point at which the circuit reaches effective unity gain is all about the nonlinear behavior of the circuit. Something will hit a limit, and what hits a limit has a strong effect on how well the oscillator will work. The received wisdom that I operate on comes from Wes Hayward's Introduction to RF Design (ISBN 978-0134940212), and Randal Rhea's Oscillator Design and Computer Simulation (ISBN 978-1884932304). It is, basically, to design the amplifying element of your oscillator so that it runs out of current before it hits any voltage limits.

In other words, you want to design your amplifying element so that as the oscillations grow stronger, the amplifying element delivers narrower and narrower current pulses, but never hits a voltage where a previously reverse-biased diode suddenly gets forward biased (e.g. the C-B junction in a BJT, or the gate junction in a FET, or if you're going retro, the grid-cathode or grid-anode "diode" in a tube).

The way that you change the operating point at which unity gain is achieved is mostly by varying the bias in that amplifying element, but also by changing the impedance level at which the circuit operates -- i.e., C1, C2 and C3 in your schematic. In general, for the same drive voltage, increasing the transistor current and decreasing the values of C1 and C2 will do this. Changing the ratio of C1 and C2 can also do this (in general, decreasing the value of C1 increases gain and thus final drive, but there's an optimal value that you can exceed).

I usually find this out by modeling the circuit in Spice (LTSpice seems to deal well with oscillators) and giving the simulation enough time to settle (for a crystal oscillator this will take a lot of processing time). You want to see current spikes on the emitter/source/cathode, with no dramatic spikes (indicating forward bias) on the base/gate/grid.

Adding a series resistor to the crystal will reduce drive, but it'll also reduce the circuit Q, which will make for a more poorly performing oscillator. It's necessary when you're using a CMOS inverter as an amplifying element because you can't control the bias -- but with a single transistor (BJT, JFET, MOSFET or Glass-FET) you have much more control.

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  • \$\begingroup\$ I tried simulation on NI Multisim, which was very slow on my laptop and I just quit it. Question about bias. If I will change bias to introduce more limiting, will it not introduce harmonic distortion? If it is supposed to be sine output, it is also supposed to operate in linear region of amplifying element, right? \$\endgroup\$
    – Vincent
    Jul 11, 2019 at 17:42
  • \$\begingroup\$ Try LTSpice. It's optimized for switching power supplies, and somehow that seems to make it happy with oscillators, too. You could also try changing the simulation parameters in Multisim, if it'll let you -- switch the solver to "gear", and try opening up the tolerances. \$\endgroup\$
    – TimWescott
    Jul 11, 2019 at 18:04
  • \$\begingroup\$ It absolutely positively won't limit if it's operating in the linear region, nor will it be efficient. In general you want the oscillator to hold frequency nicely, and if you want less harmonics, you deal with that in subsequent stages. If you absolutely must have sinusoidal output from the oscillator itself you can play games with where you pick off the signal -- but filtering after the oscillator is better, IMHO. \$\endgroup\$
    – TimWescott
    Jul 11, 2019 at 18:05
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It depends on gm*Re of FET and ESR of Xtal to achieve reliable oscillation and startup.

  • adding Rs =X is a good way to measure this gain margin and but to limit current to some extent, add an R between Re fromthe output to 1st cap.
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