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If you look at the circuit diagram for a Colpitts crystal oscillator, it's pretty simple -- a crystal, load resistor, and capacitive voltage divider, with the positive supply feeding the control element (base of a transistor, or control grid of a vacuum tube) through a resistance, and the voltage between the capacitors tied to the negative supply side of the gain device (emitter of an NPN, or cathode/filament of a tube).

Colpitts Crystal Oscillator

Now, the equivalent of a crystal is a series inductance, resistance, and capacitance, in parallel with another capacitance -- a tuned circuit.

Crystal equivalent circuit

It seems to me it ought to be possible to replace the crystal in a crystal oscillator circuit with a variable tuned circuit, to make a simple crystal-controlled radio work like one with a VFO.

Given I don't see a lot of people converting their Pixie or Cricket transceivers to be frequency mobile by doing this, I guess there's something I'm missing. What prevents replacing the crystal with its equivalent circuit (containing variable induction and/or capacitance) to allow tuning an entire band with a radio made for crystal control?

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The Heathkit HW-7 offered the option of crystal or VFO control via front-panel pushbutton switch. Pierce crystal oscillator Q5 was repurposed as a buffer amplifier for use with a VFO by switching out the crystal in the feedback path from collector to base. Given all the modern options for generating stable signals, this seems like a good approach today, too.

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  • $\begingroup$ Reading this, and looking at the circuit diagram in the linked manual, it appears that the operator had the option to either use a crystal for transmit, or bypass the crystal socket and use the VFO -- more or less identical to the concept in my question. Is that a correct understanding? $\endgroup$ – Zeiss Ikon Apr 20 at 22:57
  • $\begingroup$ I believe correct in concept, but different in execution, based on paper's use of the Pierce configuration. If you want to use the Colpitts, I believe C1 and C2 would have to be taken out of the circuit, and the biasing (R1, R2, R3) might need adjustment. So, paper's Pierce approach appears simpler than Colpitts topology in your question. $\endgroup$ – Brian K1LI Apr 21 at 0:43
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I'd frankly not replace the crystal with an oscillating circuit of adjustable resonance frequency, like you're recommending, but the whole oscillator: remove (the unlabeled) C3, and just insert the output of your complete VCO circuit there, AC coupled on its own.

Just going from "the crystal has a component-wise identical equivalent circuit" to "I can replace it with that circuit" is a bit questionable: You're relying on a simplified model of a crystal be functionally identical to the simplified model of a VCO – that might in many cases work, but it might require a lot of hand-tuning, or simply might not work. The phase response of a crystal is pretty sharp, and the lag you'll see in a RLC might simply not do it for the transistor together with C1,C2.

However, VCO circuits can be built that include an active part (e.g. at least one amplifying transistor) at little added complexity, but without the hoping and tuning. So, I'd do that, verify its operation in isolation, and then have a switch that switches between the original colpitts and the VCO.

I know this is not the "market" you're in, but I'd like to also point out how frequency-agile radios do it these days to have both crystal-grade frequency accuracy and VCO-grade adjustability whilst maintaining low harmonics: They use a fixed crystal as the primary source of frequency, then use adjustable frequency dividers (i.e. fast digital counters), fixed frequency multipliers (e.g. square the sine signal, e.g. with a diode, filter out harmonics) and adjustable frequency multipliers in control loops.
The adjustable part is typically realized through having a VCO with a counter that counts the VCO cycles during reference cycles, and adjusts the VCO control voltage accordingly. For example: You have a 10 MHz crystal, you want to get a stable 88.88… MHz; you program your counter to count 9 crystal cycles until it emits one pulse at 1.11… MHz (that's 10 MHz / 9). Then your PLL is programmed to count the reference cycles in e.g. 80 VCO cycles; if that's less than 10, increase VCO voltage, if it's more, decrease.
In reality, these devices can be even more complicated, and allow for non-rational ratios of in- to output frequency through the elegance of a bit of algebra.

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