Characterization ================ The ``5.characterization`` directory contains the measurement notes, lab photographs, and modeling tools used to characterize the quartz resonator across temperature, orientation, and vibration mode. The characterization work is the empirical input to the DSP and tracking algorithms: it identifies the useful resonant modes, estimates their movement over temperature, and provides a multi-mode equivalent circuit model for simulation. Measurement Dataset ------------------- Measurements were taken with a Vector Network Analyzer and stored as Touchstone ``.s2p`` files. The analysis focuses on ``S21`` insertion loss: frequency is read from column 1 and ``S21`` magnitude from column 4. The raw data is organized as: .. code-block:: text 5.characterization/ ├── 0.doc/ lab images and orientation diagrams ├── 1.raw_data/ raw VNA .s2p measurements ├── 2.analysis/ generated plots and summaries └── 3.model/ BVD extraction and crystal model scripts Temperature and Modes --------------------- The measurements cover 20 C to 65 C in 5 C steps. The expected vibration modes are: .. list-table:: :header-rows: 1 * - Mode - Approximate frequency * - C100 - 3.333 MHz * - B100 - 3.660 MHz * - A100 - 6.224 MHz * - C300 - 10.000 MHz * - B300 - 10.981 MHz Orientation ----------- The board was measured in six orientations to expose gravity and packaging effects. The orientation name identifies which side of the enclosure points upward. .. image:: ../../../../5.characterization/0.doc/OrientationDiagram.png :width: 420 :align: center Lab Setup --------- .. image:: ../../../../5.characterization/0.doc/VNA--1.jpg :width: 620 :align: center .. image:: ../../../../5.characterization/0.doc/TempChamber--1.jpg :width: 620 :align: center .. image:: ../../../../5.characterization/0.doc/XTAL-Enclosure-1.jpg :width: 420 :align: center Multi-Mode BVD Model -------------------- The ``5.characterization/3.model`` scripts extract a Butterworth-Van Dyke equivalent circuit from the measured data. The model keeps a static shunt capacitance in parallel with one motional RLC branch per measured vibration mode. .. image:: ../../../../5.characterization/3.model/bvd_single_mode.png :width: 420 :align: center The extracted model currently uses five motional branches. The model scripts report a globally averaged shunt capacitance of about 8.36 pF and median branch parameters for C100, B100, A100, C300, and B300. .. image:: ../../../../5.characterization/3.model/crystal_model.png :width: 700 :align: center Scripts ------- ``bvd_extractor.py`` Walks the raw ``.s2p`` dataset, finds resonant peaks, fits BVD branch parameters, and writes the extracted parameter set. ``crystal_model.py`` Instantiates the multi-mode quartz model and plots impedance magnitude over the measured frequency span. Run the model scripts from ``5.characterization/3.model``: .. code-block:: bash python bvd_extractor.py python crystal_model.py