Electronics Guide

Error Types and Calibration Scope

Understanding which errors calibration can address is essential for setting realistic accuracy expectations:

• Offset errors: Constant additive errors present when the input is zero; directly correctable through calibration
• Gain errors: Multiplicative errors that scale with signal amplitude; correctable with a single scale factor
• Nonlinearity: Signal-dependent errors where the transfer function deviates from a straight line; requires multi-point calibration
• Temperature-dependent errors: Errors that vary with operating temperature; require temperature measurement and lookup tables or polynomial correction
• Time-dependent drift: Slow changes due to aging; may require periodic recalibration
• Random noise: Not correctable through calibration; must be addressed through averaging or filtering

Effective calibration strategies focus resources on the dominant error sources. A system limited by noise gains nothing from elaborate linearity calibration, while a system with significant nonlinearity requires more than simple offset and gain correction.

Calibration Accuracy Requirements

The calibration reference must be more accurate than the target accuracy by a comfortable margin, typically a factor of four to ten. This ratio ensures that reference uncertainty contributes negligibly to the overall error budget.

For a system requiring 0.1% accuracy:

• Calibration reference accuracy should be 0.01% to 0.025%
• Reference stability during calibration must exceed measurement repeatability
• Environmental conditions during calibration should match or be recorded for correction

When suitable references are unavailable, transfer standards can propagate accuracy from a primary standard through intermediate measurements, though each transfer adds uncertainty.

Calibration Interval Determination

The time between calibrations depends on component drift rates and accuracy requirements. Setting appropriate intervals balances the cost of calibration against the risk of operating with excessive errors:

• Initial characterization: Measure drift over temperature and time to establish baseline behavior
• Guard-banding: Set calibration intervals so that maximum expected drift stays within acceptable limits
• Trend analysis: Track calibration corrections over time; increasing corrections may indicate component degradation
• Risk assessment: Critical applications may require shorter intervals or redundant measurements

Calibration Cycle Implementation

A foreground calibration cycle typically follows a structured sequence:

1. Initialization: Switch signal path from normal input to calibration reference
2. Settling: Allow time for transients to decay and thermal equilibrium to establish
3. Measurement: Acquire multiple samples at each calibration point for averaging
4. Calculation: Compute correction coefficients from measured data
5. Storage: Save coefficients in appropriate memory for use during operation
6. Restoration: Return signal path to normal operation

The calibration cycle duration depends on the number of calibration points, settling times, and averaging requirements. Simple offset calibration may complete in milliseconds, while comprehensive multi-point linearity calibration might require seconds or longer.

Triggering Strategies

Different applications require different approaches to initiating calibration:

• Power-on calibration: Automatically performed at startup before normal operation begins; ensures fresh calibration but extends startup time
• Periodic calibration: Triggered at fixed time intervals; simple to implement but may interrupt during critical operations
• Temperature-triggered: Initiated when temperature changes exceed a threshold; adapts to environmental conditions
• User-initiated: Performed on command; provides operator control but requires discipline to execute regularly
• Idle-triggered: Automatically performed during detected idle periods; minimizes operational impact

Reference Switching Considerations

Switching between normal input and calibration reference introduces potential error sources:

• Switch resistance: Analog switches have non-zero on-resistance that may differ between paths
• Charge injection: Switch transitions inject charge that can cause transient errors
• Leakage current: Off-state switch leakage may affect high-impedance nodes
• Thermal settling: Self-heating changes between calibration and normal operation may shift errors

Careful switch selection and circuit design minimize these effects. Using the same switch type for both paths maintains consistency, and adequate settling time after switching allows transients to decay.

Advantages and Limitations

Foreground calibration offers several benefits:

• Complete signal path coverage: Calibration exercises the entire signal chain from input to output
• High accuracy potential: Extended settling time and averaging enable precise measurements
• Simple implementation: Straightforward control logic compared to background methods
• Known reference conditions: Calibration occurs under well-defined reference conditions

Limitations include:

• Dead time: System unavailable during calibration
• Missed events: Transient signals occurring during calibration are lost
• Thermal disturbance: Switching to different operating conditions may shift thermal equilibrium
• Latency: Errors accumulate between calibration cycles

Redundant Channel Techniques

One background calibration approach uses redundant signal processing channels. While one channel processes the input signal, another performs calibration measurements. The channels then switch roles, with calibration data from the idle channel updating the correction applied to the active channel.

This technique requires:

• Matched channels: Both channels must have sufficiently similar characteristics that calibration of one applies to the other
• Seamless switching: Transitions between channels must not introduce discontinuities
• Thermal tracking: Both channels should experience similar thermal conditions
• Timing coordination: Switching must be synchronized to avoid sample gaps or overlaps

The doubled hardware cost is offset by continuous operation without calibration interruptions, making this approach attractive for high-reliability applications.

Interleaved Calibration

Interleaved calibration inserts calibration samples between normal signal samples. If the sampling rate exceeds the Nyquist requirement by a sufficient margin, some samples can be devoted to calibration without affecting signal reconstruction.

Implementation considerations include:

• Sample allocation: Balance between signal samples and calibration samples based on required bandwidth and calibration update rate
• Reference settling: Calibration reference must settle within the interleaved time slot
• Digital filtering: Signal processing must account for missing samples during calibration
• Timing precision: Sample timing must be precise to maintain signal integrity

Correlation-Based Calibration

Sophisticated background calibration techniques use statistical correlation to extract error information from the signal itself. By injecting small pseudorandom perturbations and correlating the output with the known perturbation sequence, the system can measure its own errors while processing normal signals.

The perturbation must be:

• Small enough: Not to significantly degrade signal quality
• Uncorrelated: With the input signal to enable separation
• Known: Precisely characterized for accurate error extraction
• Broadband: To characterize frequency-dependent errors if present

Correlation-based methods require significant digital processing but achieve truly continuous calibration without dedicated calibration references in the signal path.

Adaptive Calibration Algorithms

Adaptive algorithms continuously update calibration coefficients based on statistical properties of the processed signal. These techniques assume that certain signal properties are known or constrained, enabling detection of errors that violate these assumptions.

Examples include:

• DC offset tracking: If the signal is known to be AC-coupled, any measured DC component indicates offset error
• Gain tracking: If the signal has known statistical properties, amplitude scaling can be detected
• Histogram analysis: Nonlinearity distorts the amplitude distribution of random signals
• Spectral analysis: Harmonic distortion reveals nonlinearity in frequency domain

These methods work best with signals having known statistical properties and may converge slowly or inaccurately with pathological inputs.

Sources of Offset Error

Understanding offset sources helps in both correction and prevention:

• Amplifier input offset voltage: Inherent imbalance in differential input stages appears as equivalent input offset
• Input bias current: Current flowing into input terminals creates voltage drops across source impedance
• Thermoelectric voltages: Temperature differences at junctions between dissimilar metals generate Seebeck voltages
• ADC offset: Comparator offset and reference mismatch create digital code offset
• Leakage currents: Stray currents through insulation resistance create voltage offsets

Single-Point Offset Correction

The simplest offset calibration measures the output with zero (or known) input and subtracts this value from all subsequent measurements:

Corrected_Output = Measured_Output - Offset_Measurement

Implementation options include:

• Input grounding: Short the input to ground and measure the resulting output
• Reference input: Apply a known reference voltage and measure the difference from expected output
• Auto-zero: Periodically sample and subtract the offset using sample-and-hold techniques

For analog correction, a DAC can generate a compensating voltage that cancels the offset. For digital correction, software simply subtracts the stored offset value from each measurement.

Temperature-Dependent Offset Compensation

Offset drift with temperature often exceeds initial offset as a source of error. Compensation approaches include:

• Characterization tables: Measure offset at multiple temperatures and store in lookup table; interpolate during operation
• Polynomial correction: Fit offset versus temperature to polynomial and compute correction from measured temperature
• Matched components: Use components with tracking temperature coefficients so offsets cancel
• Chopper stabilization: Modulate the signal to separate it from DC offset, then demodulate

Effective temperature compensation requires accurate temperature measurement at the location of the offset source, which may differ from the ambient temperature.

Offset Adjustment Circuits

Hardware circuits for offset adjustment include:

• Potentiometer trim: Traditional approach using manual adjustment; simple but not suitable for automatic calibration
• DAC injection: Digital-to-analog converter adds programmable offset correction; enables automatic calibration
• Current source injection: Programmable current into summing node creates offset; useful for current-output sensors
• Switched-capacitor offset storage: Sample and hold the offset on a capacitor for continuous correction

The correction circuit itself contributes noise and potentially its own offset, so careful design ensures the cure does not become worse than the disease.

Sources of Gain Error

Common sources of gain error include:

• Resistor ratio tolerance: Amplifier gain depends on feedback resistor ratios, which have manufacturing tolerances
• Reference voltage error: ADC and DAC gain depends on reference accuracy
• Component drift: Resistors and references change value with temperature and time
• Loading effects: Finite input impedance of subsequent stages attenuates the signal
• Frequency response: Gain may vary with signal frequency due to parasitic capacitance

Two-Point Gain Calibration

Basic gain calibration requires measurements at two known input levels to determine both offset and gain:

1. Measure output Y1 with known input X1 (often zero)
2. Measure output Y2 with known input X2 (near full scale)
3. Calculate gain: G = (Y2 - Y1) / (X2 - X1)
4. Calculate offset: O = Y1 - G * X1
5. Apply correction: Corrected = (Measured - O) / G

The calibration points should span as much of the measurement range as possible to minimize the effect of measurement noise on the calculated gain.

Ratiometric Gain Correction

When a precision reference resistor is available, ratiometric techniques can provide gain correction without an accurate voltage reference:

Gain_Correction = Rref_nominal / Rref_measured

By measuring the reference resistor with the same signal chain used for the actual measurement, gain errors cancel in the ratio. This technique is particularly effective for resistance measurement systems like RTD interfaces.

Temperature Coefficient Matching

For temperature-stable gain, matching temperature coefficients is as important as matching nominal values:

• Use resistor networks: Integrated resistor networks track better than discrete resistors from different batches
• Same technology: Choose all gain-setting resistors from the same technology (all thin-film or all metal-foil)
• Thermal coupling: Mount matched resistors close together on the same substrate
• Ratio stability specification: Select components specified for ratio temperature coefficient, not absolute

Resistors specified at 25 ppm/C individually might achieve 2 ppm/C ratio tracking when properly selected and mounted.

Digital Gain Correction

Digital gain correction multiplies each measurement by a stored correction factor:

Corrected = Measured * Gain_Correction_Factor

Implementation considerations include:

• Numerical precision: The correction factor must have sufficient resolution to achieve the target accuracy
• Multiplication resources: Hardware multipliers enable real-time correction at high sample rates
• Combined correction: Offset and gain correction can be combined into a single multiply-accumulate operation
• Range management: Gain correction changes the numerical range; subsequent processing must accommodate this

Sources of Nonlinearity

Nonlinear behavior arises from:

• Sensor inherent nonlinearity: Many sensors have nonlinear response to the physical quantity being measured
• Amplifier nonlinearity: Gain compression at large signals, crossover distortion in output stages
• ADC differential nonlinearity: Variation in code transition widths causes step size errors
• ADC integral nonlinearity: Cumulative deviation from ideal transfer function
• Component voltage coefficients: Resistor and capacitor values that change with applied voltage

Multi-Point Calibration

Characterizing nonlinearity requires measurements at multiple points across the input range. The number of calibration points depends on the complexity of the nonlinearity and the accuracy requirement:

• Three-point calibration: Measures at zero, mid-scale, and full scale; detects simple curvature
• End-point plus midpoints: Adds intermediate points to detect higher-order nonlinearity
• Full characterization: Measurements at every code (for ADCs) or fine grid; maximum correction accuracy

More calibration points enable more accurate correction but require more measurement time and storage for correction tables.

Lookup Table Correction

The most flexible nonlinearity correction uses lookup tables that store the correction for each input value or range of values:

• Direct lookup: Each possible input code indexes a correction value; fast but memory-intensive
• Segmented tables: Divide range into segments with separate correction for each; balances memory and accuracy
• Interpolated tables: Store corrections at sparse points and interpolate between them; reduces storage requirements

For a 16-bit ADC, direct lookup requires 65,536 entries. Segmented or interpolated approaches might achieve similar accuracy with hundreds or thousands of entries.

Polynomial Correction

When nonlinearity follows a smooth curve, polynomial correction provides an efficient alternative to lookup tables:

Corrected = a0 + a1*x + a2*x^2 + a3*x^3 + ...

The polynomial coefficients are determined by fitting to calibration measurements using least-squares or similar techniques. Advantages include:

• Compact storage: Only the coefficients need storage, regardless of resolution
• Smooth correction: No discontinuities at segment boundaries
• Physical basis: Many nonlinearities have physical origins that produce polynomial behavior

Limitations include potential oscillation with high-order polynomials and inability to correct sharp nonlinearities that require many terms.

Piecewise Linear Correction

Piecewise linear correction divides the range into segments, each with its own linear approximation:

1. Identify the segment containing the current input value
2. Retrieve the slope and offset for that segment
3. Apply linear correction: Corrected = slope * (Input - segment_start) + offset

This approach combines the simplicity of linear correction with the flexibility of multi-segment approximation. Segment boundaries should be placed where the nonlinearity changes most rapidly.

Advantages of Digital Correction

Digital correction provides significant benefits:

• No additional analog errors: Digital processing does not introduce offset, gain error, or drift
• Flexible algorithms: Correction can be arbitrarily complex without hardware changes
• Easy updates: Calibration coefficients can be updated in firmware without hardware modification
• Perfect repeatability: Digital operations produce identical results every time
• Diagnostic capability: Calibration data can be logged and analyzed for trends

Architecture Considerations

Effective digital correction requires appropriate system architecture:

• ADC resolution overhead: The ADC must have enough resolution to capture the signal plus the maximum expected error to be corrected
• Processing word length: Internal calculations need extra bits to avoid quantization errors during correction
• Latency tolerance: Digital processing introduces delay; real-time control systems may have latency constraints
• Processing throughput: Correction must keep pace with sample rate

Real-Time Correction Implementation

Real-time correction applies corrections to each sample as it is acquired:

• Hardware implementation: FPGAs or ASICs provide deterministic timing and high throughput
• DSP implementation: Digital signal processors offer programmability with good performance
• Microcontroller implementation: Suitable for lower sample rates where processing time is not critical
• Pipelined architectures: Break complex corrections into stages that process different samples simultaneously

Post-Processing Correction

When real-time correction is not required, post-processing applies corrections to stored data:

• Batch correction: Apply corrections to accumulated data sets
• Iterative refinement: Multiple correction passes can improve accuracy
• Computationally intensive algorithms: More sophisticated corrections become practical without real-time constraints
• Historical data correction: Apply improved calibration to previously acquired data

Coefficient Storage and Management

Calibration coefficients must be stored reliably and retrieved efficiently:

• Non-volatile memory: EEPROM or flash memory preserves calibration across power cycles
• Checksum protection: Detect corrupted calibration data before use
• Version control: Track calibration dates and firmware versions for traceability
• Default values: Maintain safe defaults if calibration data is invalid
• Multiple calibration sets: Store different calibrations for different operating conditions

Calibration DAC Requirements

DACs used for calibration must meet stringent requirements:

• Resolution: Fine enough to achieve the target calibration accuracy; typically 10-16 bits
• Accuracy: DAC errors appear directly in the calibration; select DAC accuracy to be small relative to correction range
• Stability: DAC drift adds to system drift; use low-drift types or re-calibrate the DAC itself
• Monotonicity: Missing codes or non-monotonic behavior can cause calibration instability
• Low noise: DAC noise adds directly to the signal path when used for offset correction

DAC Injection Points

Where the calibration DAC connects affects both the correction range and the impact on signal path performance:

• Input summing: Add correction at the amplifier input; correction is amplified along with signal
• Reference adjustment: Scale the ADC or DAC reference to correct gain errors
• Output summing: Add correction after amplification; requires larger DAC range
• Feedback modification: Adjust amplifier feedback to trim gain; interacts with frequency response

Input injection minimizes the required DAC range but makes the DAC noise contribution critical. Output injection requires more DAC range but relaxes DAC noise requirements.

Auto-Calibration Algorithms

Automatic calibration algorithms systematically search for optimal calibration settings:

• Successive approximation: Binary search for the calibration setting that minimizes error; fast convergence
• Gradient descent: Iteratively adjust in the direction that reduces error; handles multiple parameters
• Exhaustive search: Test all possible settings and select the best; guarantees optimal result but slow
• Correlation search: Use signal statistics to detect and correct errors without explicit references

Successive Approximation Calibration

Successive approximation efficiently finds the calibration setting that nulls an error signal:

1. Set DAC to mid-scale
2. Measure error signal (difference from target)
3. If error is positive, reduce DAC; if negative, increase DAC
4. Adjust by half the previous step size
5. Repeat until step size reaches one LSB or error is within tolerance

This algorithm converges in N steps for an N-bit DAC, making it very efficient for high-resolution calibration.

Multi-Parameter Calibration

When multiple parameters interact, calibration becomes more complex:

• Sequential calibration: Calibrate parameters one at a time, iterating if they interact
• Orthogonal calibration: Choose calibration order and methods to minimize interaction
• Simultaneous optimization: Use multi-dimensional optimization to find globally optimal settings
• Decoupling networks: Design calibration injection points to minimize parameter interaction

Offset calibration is typically performed first since it affects gain measurements. Gain calibration follows, and linearity calibration comes last since it depends on accurate offset and gain.

Reference Error Sources

Precision references have their own imperfections:

• Initial accuracy: Manufacturing tolerance on the nominal output voltage
• Temperature coefficient: Output variation with temperature, typically specified in ppm/C
• Long-term drift: Gradual change over months and years, often specified as ppm/1000 hours
• Load regulation: Output change with load current
• Line regulation: Output change with supply voltage
• Noise: Random variations that limit measurement resolution

Reference Characterization

Thorough reference characterization provides the data needed for correction:

• Multi-temperature measurement: Characterize output versus temperature to determine actual temperature coefficient
• Aging tests: Monitor output over extended periods to establish drift rate
• Load testing: Measure output at various load currents to quantify regulation
• Line testing: Verify output stability over the operating supply voltage range

Calibration Transfer

Reference calibration typically involves transferring accuracy from a higher-level standard:

• Primary standards: National metrology laboratories maintain the ultimate references
• Transfer standards: Portable, stable references calibrated against primary standards
• Working standards: Laboratory references used for routine calibration
• Production references: References in actual products, calibrated against working standards

Each transfer adds uncertainty, so the calibration chain should be as short as practical while meeting accuracy requirements.

Reference Trimming Techniques

Several techniques adjust reference output to the desired value:

• Resistor trimming: Adjust a resistor in the reference circuit using laser trimming or zener zapping
• Fuse programming: Blow fuses to select among preset output levels
• Digital adjustment: Some references include integrated trim DACs for fine adjustment
• External scaling: Use a precision resistor network to scale reference output

Self-Calibrating References

Advanced reference designs incorporate self-calibration features:

• Temperature compensation: Internal temperature sensor and correction circuitry reduce temperature coefficient
• Heater stabilization: Maintain constant die temperature to eliminate temperature variations
• Burn-in acceleration: Elevated temperature operation accelerates initial drift before final calibration
• Redundancy: Multiple reference cells with voting logic detect and compensate for failures

Temperature Characterization Process

Building a temperature calibration table requires systematic characterization:

1. Temperature range definition: Determine the expected operating temperature range
2. Temperature point selection: Choose calibration temperatures spanning the range; more points provide better accuracy
3. Thermal stabilization: Allow adequate time for thermal equilibrium at each temperature
4. Calibration measurement: Perform full calibration at each temperature point
5. Data validation: Verify measurements are consistent and physically reasonable
6. Table construction: Organize data for efficient lookup and interpolation

Typical temperature steps range from 5 to 25 degrees Celsius depending on the nonlinearity of the temperature response and accuracy requirements.

Table Structure and Organization

Temperature tables can be organized in various ways:

• Direct indexing: Temperature (quantized) directly indexes the table; fast but potentially large
• Sorted tables: Store temperature-correction pairs sorted by temperature; binary search for lookup
• Multi-dimensional tables: Index by temperature and signal level for corrections that vary with both
• Coefficient tables: Store polynomial coefficients that vary with temperature

Interpolation Methods

Operating temperatures rarely fall exactly on calibration points, requiring interpolation:

• Linear interpolation: Simple and fast; adequate when calibration points are closely spaced
• Quadratic interpolation: Uses three surrounding points for smoother curve fitting
• Cubic spline: Smooth interpolation with continuous first and second derivatives
• Lagrange interpolation: Exact fit through multiple points; can oscillate between points

The interpolation method should match the expected behavior of the correction. Most temperature effects are smooth enough that linear interpolation suffices with adequate point spacing.

Temperature Sensor Requirements

Accurate temperature compensation requires accurate temperature measurement:

• Sensor location: Place sensor where it measures the temperature of the components being compensated
• Sensor accuracy: Temperature measurement error translates directly to compensation error
• Response time: Sensor must track temperature changes fast enough to maintain accurate compensation
• Self-heating: Sensor excitation should not significantly raise its temperature above ambient

For systems with distributed components, multiple temperature sensors may be needed to adequately characterize the thermal environment.

Hysteresis and Thermal History

Some components exhibit hysteresis, where the calibration depends not just on current temperature but on thermal history:

• Mechanical stress effects: Thermal cycling can cause permanent changes in component values
• Solder joint stress: Different expansion coefficients create stress that varies with temperature history
• Piezoelectric effects: Mechanical stress in some components generates voltages

Hysteresis effects are difficult to compensate fully. Minimizing them through careful component selection and mounting is usually more effective than attempting to calibrate them.

Field Calibration Challenges

Field environments differ significantly from controlled laboratory conditions:

• Limited equipment: Portable calibration standards may have lower accuracy than laboratory equipment
• Environmental variations: Temperature, humidity, and interference vary unpredictably
• Time pressure: System downtime for calibration has operational cost
• Access limitations: Physical access to calibration points may be restricted
• Documentation requirements: Calibration records must be maintained for traceability

Designing for Field Calibration

Systems intended for field calibration should be designed with this in mind:

• Accessible calibration points: Provide convenient connections for reference signals
• Built-in references: Include stable on-board references that need less frequent external calibration
• Guided procedures: Software-guided calibration sequences reduce errors and training requirements
• Verification capability: Enable verification of calibration success before returning to service
• Calibration data storage: Automatically record and store calibration results

Field Calibration Equipment

Portable calibration equipment balances accuracy against portability:

• Handheld calibrators: Compact sources and meters for basic calibrations
• Transfer standards: Precision portable references calibrated against laboratory standards
• Multifunction calibrators: Generate and measure multiple signal types from a single instrument
• Documentation systems: Electronic systems that record calibration data and generate reports

The calibration equipment itself must be calibrated and certified, adding another layer to the traceability chain.

Simplified Calibration Procedures

Field calibration procedures are often simplified compared to factory procedures:

• Single-point verification: Check at one point to verify calibration is still valid
• Reduced point count: Calibrate at fewer points than full factory characterization
• Abbreviated warm-up: Shorter stabilization times when full accuracy is not critical
• Reference substitution: Use available process signals as de facto references when appropriate

Calibration Verification

Verification confirms that calibration achieved its intended result:

• Functional verification: Confirm the system responds correctly to test inputs
• Specification verification: Measure actual performance against published specifications
• Cross-checking: Compare readings with redundant sensors or reference instruments
• Trend analysis: Compare current calibration with historical data to detect anomalies

Verification should catch calibration errors before the system returns to service, preventing incorrect measurements from affecting process control or data quality.

Documentation and Traceability

Proper documentation maintains the value of calibration:

• Calibration certificates: Record what was calibrated, when, by whom, and against what references
• As-found/as-left data: Document the condition before and after calibration
• Uncertainty statements: Quantify the expected accuracy of the calibration
• Reference traceability: Document the calibration status of all equipment used
• Deviation handling: Record any anomalies and their resolution

Choosing Between Analog and Digital Correction

The choice between analog and digital calibration correction involves multiple tradeoffs:

• System architecture: Pure analog systems require analog correction; mixed-signal systems can use either
• Dynamic range: Digital correction requires ADC headroom for the worst-case error
• Real-time requirements: Analog correction has zero delay; digital correction adds latency
• Complexity: Simple corrections favor analog; complex corrections favor digital
• Flexibility: Digital correction enables field updates; analog is fixed

Production Calibration Efficiency

High-volume production requires efficient calibration:

• Parallel calibration: Calibrate multiple units simultaneously
• Minimized points: Use only as many calibration points as necessary
• Automated systems: Reduce labor through automated test equipment
• Self-calibration: Design products to calibrate themselves when possible
• Statistical process control: Monitor calibration data to detect process drift

Calibration Data Security

Calibration data represents significant investment and must be protected:

• Access control: Limit ability to modify calibration to authorized personnel
• Data integrity: Detect accidental or malicious corruption of calibration data
• Backup: Maintain copies of calibration data to enable recovery from failures
• Audit trail: Log all calibration changes for accountability

Failure Mode Considerations

Design calibration systems to fail safely:

• Corrupted data detection: Checksums identify invalid calibration data
• Default values: Safe defaults enable operation if calibration is lost
• Out-of-range limits: Refuse calibration settings outside physically reasonable bounds
• Verification checks: Confirm calibration produces reasonable results before accepting