Precision Analog Converter Gain Drift under Dynamic Thermal PCB Stress
Dynamic PCB thermal gradients cause substrate flexing that alters converter resistor ladder ratios via piezoresistive strain, driving gain drift.
Strain Tensor
Displacement Matrix
Deformation at a point in a continuum is represented by an array of values describing relative displacement in three dimensions. The strain tensor organizes these values into a symmetric matrix that includes both normal and shear components. This mathematical object remains independent of the coordinate system used to measure the displacement.
Coordinate Transformation
Rotation of the reference axes changes the individual values within the matrix but leaves the physical state of the material unchanged. Invariants of the strain tensor provide quantities like the volumetric change and the maximum shear that are used to predict material failure. These calculations are essential for structural analysis in aerospace and civil engineering.
Principal Direction
Maximum elongation and compression occur when the coordinate system is aligned with specific axes. These values define the principal directions of the strain tensor in the coordinate system.
Small Strain
Small strain approximations simplify the relationships between the tensor components and the measured displacements. Verification of the tensor field often involves multi-axis strain gauges or optical methods that can resolve the direction of the deformation. If the material is isotropic, the strain tensor relates directly to the stress state through the modulus of elasticity and the Poisson ratio.
This relationship forms the basis for finite element analysis in mechanical design.