Position & Acceleration Sensing

Critical Design Constraint: Loading Error

Connecting a load resistance R_L in parallel distorts ideal linearity

Null Position Behavior

At core center: V_sl = V_s2 $\implies$ Output voltage is exactly 0.

Frictionless Design

Infinite resolution & rugged core with zero mechanical contact wear.

Quadrature Phase Shift

Channels A and B are shifted by 900. Phase relation indicates CW vs CCW motion.

Index Channel Z & Power State

Outputs 1 pulse/rev for homing. Positional state lost on power interruption.

Standard Binary Flaw

Multiple bits flip simultaneously across state boundaries.

Gray Code Advantage

Only 1 single bit changes between any adjacent position steps

Rotary Resolvers

with 900 stator coils. Extreme rating against vibration, radiation, and dirt

Rotary Resolvers

Transverse voltage produced by magnetic field B. Used for BLDC commutation & proximity limit switches.

Natural Frequency

$\omega_n = \sqrt{k / m}$ limits operational upper bound

Flat Response Band

At $\omega \omega_n$, mass deflection $x \approx a / \propto a$

Damping Factor

Optimal $\zeta \approx 0.707$ minimizes resonance peaking

CRITICAL EXAM RULE: AC-Coupled only

Charge leaks across internal resistance. CANNOT measure static (O Hz) acceleration or gravity (lg)!

High Dynamic Bandwidth

High stiffness ($>10\text{ kHz}$) ideal for shock, impact, and vibration analysis

DC Capable Sensing (O Hz)

Measures static gravity ($lg$), inclination tilt, and steady linear motion.

On-Chip ASIC Integration

Integrated readout amplifier & SPI/12C digital output on miniature IC.

Piezoresistive / Strain Gauge

• Flexure beam strain measures DC acceleration

• Requires Wheatstone bridge signal conditioning

• Prone to thermal drift (requires temperature comp)

Servo (Force-Balance)

Closed-loop coil drives mass back to null point

Eliminates spring non-linearities and hysteresis

Gold standard for inertial navigation systems (INS)

Rule 1: Static Gravity / Tilt

Rule 2: Absolute vs Incremental

Rule 3: Loading Impedance

Essential Rules for System Engineers