Active-Clamp Piezo-Driver Charge-Amplifier Drift in Student-Built Engineering Education Nanopositioning Benches: A Laser-Interferometer Evaluation Linking Cable Capacitance to Positioning-Resolution Reliability Bounds

Student-built nanopositioning benches used in engineering education depend on charge amplifiers whose drift is rarely characterised against the cable capacitance that students introduce when they assemble the rig. No observational data are used or claimed: the analysis characterises the estimator under a declared variance structure with between-cluster SD = 6.0, residual SD = 4.5 and intraclass correlation = 0.640, across 2000 replications per design cell for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The analysis indicates that 56 clusters are required to detect a 5-percentage-point effect at 80% power under this variance structure, and that the minimum detectable effect falls steeply as cluster count rises from 8 to 32. A first-order charge-transfer model shows that cable capacitance enters the drift budget multiplicatively, so that a bench whose cable capacitance varies by a factor of two between student assemblies cannot support a fixed resolution specification without capacitance-referenced calibration. The contribution is a bounded, reproducible framework that connects a component-level mechanism (charge-amplifier drift under active clamping) to an institution-level design decision (how many student benches, and how many repeated assemblies per bench, are needed to certify a stated resolution).