A mechanical radio filter converts an electrical signal into vibration, passes that motion through coupled metal resonators, then converts it back to an electrical signal. The cutaway shows a disc-and-wire arrangement with transducer coils at the ends. The calculator estimates how a small resonator diameter error shifts its resonance.
Mechanical Filter Interactive Calculator
See the resonator discs, coupling wires and electrical transducers. Estimate resonance shift using a measured local diameter sensitivity.
Equation Used
- Sensitivity must be measured or supplied for the actual resonator.
- Negative diameter error raises frequency for positive entered sensitivity.
- Visible flexure is magnified and slowed.
- Disc phases are illustrative, not a solved coupled vibration response.
The calculator estimates local resonance shift from an entered diameter sensitivity. The slowed, enlarged disc vibration illustrates coupling, not the complete filter response.
Discs and wires inside the filter
In the Collins 75A-3 description, the input transducer excites a disc and coupling wires transfer vibration to succeeding discs. The output transducer recovers an electrical signal. The animation shows a five-disc explanatory assembly, with disc bending strongly enlarged so it can be seen.
The discs do not spin or travel through the housing. Fine coupling wires remain attached as the discs flex. The exact disc modes, number of elements and electrical terminations depend on the filter design.
Applications
The Collins 75A-3 receiver used mechanical filtering for signal selectivity. Its manual describes the transducers, vibrating discs and coupling wires that motivate this cutaway. Filter bandwidth and termination depend on the particular filter; this calculator only estimates a local resonance shift.
Local resonance tuning estimate
Let ΔD be diameter error in micrometres and k be a positive frequency sensitivity in Hz/µm. The selected local approximation is Δf=−kΔD. Add Δf to the nominal frequency and divide by nominal frequency to obtain fractional error, or multiply that fraction by one million for ppm.
This sensitivity is an input, not a universal material constant. It cannot establish the complete filter response or predict a notch from one dimensional error alone.
Example: a 455 kHz resonator
At an assumed measured sensitivity of 20 Hz/µm, a −10 µm diameter error gives +200 Hz frequency shift. The resulting resonance is 455.200 kHz, approximately +439.56 ppm. These are example values, not a tolerance recommendation for a Collins filter.
What the view does and does not show
The visible motion explains flexural discs and coupling. It is deliberately slowed and magnified; at radio frequency the actual vibration is not visible to the eye. Relative phases are illustrative. Electrical loading, coupling stiffness, damping and mode shapes would be required for a quantitative multi-resonator response model.
Questions
Are the discs rotating?
No. Their elastic deformation transmits vibration.
Does this calculate the passband?
No. It estimates a local resonance shift from an entered machining sensitivity.
Where should sensitivity come from?
Use the resonator design data, a validated mode calculation or measurements near the nominal dimension.
Technical references
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