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Collpits oscillator is one of the most widely used oscillators.

colpitts oscillator

It's frequency equation is like this:

colpitts equation

According to the equation, we can change its frequency by changing its LC tank parameters L and C. However, making adjustable capacitors and inductors are not much realistic. Also, their capacitance and inductance value can not vary that much to obtain \$f_{0}\$ - 100x\$f_{0}\$ oscillation frequency range.

So here is my question, how can I make this oscillator adjustable in a way that it can oscillate to 100x\$f_{0}\$?

Note: We can add any digital or analog block to the circuit to realize the goal.

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    \$\begingroup\$ None of the common LC oscillator designs really lend themselves to adjustability, and certainly not over that kind of range. Why do you want this? Have you considered DDS instead? \$\endgroup\$ – Jack B Sep 14 '16 at 15:23
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    \$\begingroup\$ If you can add a digital block, then fix the oscillation at the top end and add a PLL at the output. Or just use a crystal like everyone else. \$\endgroup\$ – pjc50 Sep 14 '16 at 15:30
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    \$\begingroup\$ Notice the square root sign in the equation? That means you have to vary L or C, or their product, by 10000:1 to achieve 100:1 tuning range. Practically you can vary C by about 10:1 for 3;1 tuning range. To extend the range further, you'll need to switch in different inductors. (Or use frequency synthesis instead) \$\endgroup\$ – Brian Drummond Sep 14 '16 at 16:00
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    \$\begingroup\$ Crazy idea: what if you use Miller effect for multiplying the capacitors? You would need an amplifier with a bandwidth much higher than the maximum frequency you intend to tune the oscillator to \$\endgroup\$ – Daniel V Sep 14 '16 at 16:16
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Say you want a frequency of 1 MHz to 100 MHz - that's 100:1 in range. To do this you'll need two sinewave oscillators and a mixer (balanced modulator).

Set one oscillator to be (say) 300 MHz and the other to vary betweeen 301 MHz and 400 MHz.

"Mix" the two outputs together and you get sum and difference frequencies. Clearly the sum frequencies will be from 601 MHz to 701 MHz but, importantly, the difference frequency will range from 1 MHz to 100 MHz.

Low pass filter the output to largely get rid of the sum frequencies. This filtering process is made easier the higher you choose the individual oscillator frequency range (say) 1.01 GHz to 1.1 GHz.

Both oscillator can be colpitts type in fact they're the one I'd recommend. If you want decent stability of the 1 MHz output be aware that this is quite difficult to achieve given the the stability needed for the oscillators but good luck; I've used this method.

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