GHz frequency tuning using audio vibrations (pet, piezoelectric speaker,etc)?
You can tune VCO frequency by a piezo element. If the resonator is a dielectric one, the piezo tuning element should be located close to it on-axis, and used in place of a tuning screw. The metal coating on the piezo element is important.
Similarly you can tune a stripline or coaxial resonator by the piezo element replacing a capacitor.
Piezo ceramic Alone is not suitable to be a part of a microwave resonator as its permittivity is lossy at microwave frequency.
I have patented a similar principle for a microwave oscillator or resonator sensor using a parasitic element, in 1977. I tested also a piezo tuning element with a DRO, best at 35 GHz.
As the piezo element moves by several micrometers, capacitance change is small and dependent on the gap size. Tuning a dielectric resonator at >10 GHz is easier, you can achieve several MHz change.
Electric tuning by a varicap is easier and preferred in modern oscillators..
you can have a thin metal cover in close proximity to a dro puck, and as vibrations make the cover move, the DRO frequency will pull +/- perhaps 5 kHz.
There is a famous spy case where the Russians put a microwave resonator in the symbole of the US in a US embassy, beamed in that specific microwave frequency, and audio discussions in the room could be received as a phase modulation!
If you were to mount the oscillator housing rigidly to something metal (like an engine chassis) you could use a piezoelectric element to control a varactor diode, or maybe just find the right chip ceramic capacitor (a poor quality one!) that was very susceptible to delta C vs G force
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