Introduction

The selection of accelerometer sensitivity represents one of the most critical yet frequently overlooked decisions in configuring vibration control systems. While considerable attention typically focuses on accelerometer frequency range, mass, mounting methods, and environmental specifications, the choice of sensitivity in picocoulombs per g (pC/g) or millivolts per g (mV/g) profoundly affects control system performance, achievable dynamic range, and the ability to successfully execute challenging tests.

The accelerometer sensitivity, in combination with the signal conditioning gain settings and the controller's analog-to-digital converter input range, determines the complete signal chain characteristics from mechanical acceleration through electrical signal to digital representation. Improper sensitivity selection can render difficult tests impossible to control, introduce excessive noise that corrupts low-level measurements, or cause signal clipping that invalidates test data. This technical note examines the technical considerations governing transducer sensitivity selection, explains how sensitivity interacts with controller voltage range and gain architecture, and provides guidance for optimizing sensitivity selection across different test types including sine, random, shock, and mixed-mode testing in MISO control applications.

Fundamental Relationships in the Signal Chain
Understanding transducer sensitivity selection requires establishing the relationships between mechanical acceleration, electrical signal levels, and digital representation throughout the measurement and control chain. Each stage of this chain has constraints that must be satisfied simultaneously for successful control.

The accelerometer converts mechanical acceleration into an electrical signal proportional to the applied acceleration. For piezoelectric accelerometers with charge output, sensitivity is specified in picocoulombs per g (pC/g). A 10 pC/g accelerometer produces 10 picocoulombs of charge for each g of acceleration. A 100 pC/g accelerometer produces 100 picocoulombs per g, ten times more signal for the same acceleration. This charge output is converted to voltage by a charge amplifier or integrated electronics in the accelerometer (IEPE type), with the conversion gain determined by the charge amplifier feedback capacitor or the IEPE internal electronics.

For IEPE accelerometers with voltage output, sensitivity is specified directly in millivolts per g (mV/g). A 10 mV/g accelerometer produces 10 millivolts for each g of acceleration, while a 100 mV/g accelerometer produces 100 millivolts per g. The voltage output connects directly to the vibration controller's input circuitry through signal conditioning that may provide additional gain or attenuation.

The signal conditioning stage scales the accelerometer output to match the input range of the analog-to-digital converter (ADC). A typical vibration controller uses a 24-bit ADC with input range of ±10 volts, though some systems use ±5 volts or ±2.5 volts. The signal conditioning provides selectable gain to optimize the signal amplitude relative to this ADC range. Common gain ranges include 0.1x, 0.3x, 1x, 3x, 10x, 30x, and 100x, allowing adjustment over a factor of 1000 from lowest to highest gain.

The ADC converts the analog voltage to a digital number that the controller uses for spectral analysis and control calculations. A 24-bit ADC divides the input range into 16,777,216 discrete levels. For a ±10 volt input range, each bit represents approximately 1.19 microvolts. The effective resolution depends on both the ADC bit depth and the amplitude of the signal relative to the full-scale range. A signal using only 10% of the ADC range loses approximately 20 dB of effective dynamic range compared to a signal optimally scaled to use the full range.

The complete signal chain from acceleration to digital representation can be expressed as:

Digital Value = Acceleration × Sensitivity × Gain × ADC_Scale

Where ADC_Scale relates the voltage at the ADC input to the digital output value. For optimal performance, the product of Sensitivity × Gain should be chosen such that the maximum expected acceleration produces a voltage near the ADC full-scale range, maximizing resolution while avoiding overload.

Dynamic Range Considerations

Dynamic range represents the ratio between the largest and smallest signals that can be simultaneously measured and controlled. In vibration testing, dynamic range requirements vary dramatically depending on the test type and the characteristics of the test article. Understanding these requirements guides sensitivity selection.

The test article's dynamic characteristics determine the required measurement dynamic range. A stiff metal structure with well-damped modes might exhibit a ratio of 30 dB between resonant peaks and anti-resonance valleys in its frequency response. A lightly damped structure with sharp resonances might show 80 dB between peaks and valleys. The vibration control system must measure both the high amplitude at resonances and the low amplitude at anti-resonances within the same test, requiring dynamic range sufficient to span this entire range.

Consider a test article with a sharp resonance where response reaches 50 g, and an anti-resonance where response drops to 0.05 g. The dynamic range requirement is 20*log10(50/0.05) = 60 dB. If a second resonance produces 100 g while another anti-resonance reaches 0.01 g, the requirement increases to 80 dB. Some structures with multiple lightly damped modes can exhibit dynamic range requirements exceeding 100 dB.

The accelerometer sensitivity must be low enough that the maximum acceleration does not exceed the accelerometer's measurement range or overload the signal conditioning electronics. Piezoelectric accelerometers typically have maximum acceleration limits ranging from 50 g for high-sensitivity types to 10,000 g for low-sensitivity shock accelerometers. The sensitivity and maximum acceleration are inversely related: high sensitivity accelerometers generally have lower maximum acceleration capability because the piezoelectric crystal reaches its maximum charge output at lower acceleration.

A 100 pC/g accelerometer might have maximum range of 50 g, producing 5000 pC maximum output. A 10 pC/g accelerometer might handle 500 g, producing the same 5000 pC maximum output. A 1 pC/g accelerometer could measure 5000 g. The choice depends on the maximum acceleration expected during the test, with margin for safety.

The accelerometer noise floor establishes the minimum measurable acceleration. High sensitivity accelerometers typically exhibit lower equivalent input noise because the larger signal from a given acceleration provides better signal-to-noise ratio. A 100 pC/g accelerometer might have noise floor of 0.0001 g RMS, while a 1 pC/g accelerometer might have noise floor of 0.001 g RMS. This ten-fold difference in noise floor corresponds to 20 dB difference in the lower limit of dynamic range.

The combination of maximum acceleration and noise floor determines the accelerometer's inherent dynamic range. A 100 pC/g accelerometer with 50 g maximum and 0.0001 g noise floor provides 20log10(50/0.0001) = 114 dB dynamic range. A 1 pC/g accelerometer with 5000 g maximum and 0.001 g noise floor provides 20log10(5000/0.001) = 134 dB dynamic range. However, this comparison is misleading because these accelerometers are designed for entirely different applications with different maximum acceleration requirements.

The critical insight is that sensitivity should be selected based on the maximum acceleration expected in the test, then the system dynamic range is determined by the ratio of this maximum to the noise floor. For a test expecting maximum acceleration of 20 g, a 100 pC/g accelerometer with 50 g range and 0.0001 g noise floor provides 20log10(20/0.0001) = 106 dB dynamic range. A 10 pC/g accelerometer with 500 g range and 0.0002 g noise floor provides 20log10(20/0.0002) = 100 dB dynamic range. The high sensitivity accelerometer provides better dynamic range when maximum acceleration permits its use.

Controller Voltage Range and Gain Architecture

The voltage range of the vibration controller's ADC inputs and the available gain settings determine how accelerometer sensitivity must be matched to the application. Modern vibration controllers typically use one of several standard input ranges, and understanding these ranges is essential for optimal sensitivity selection.

The most common configuration uses ±10 volt ADC input range with selectable gain from 0.1x to 100x. This provides full-scale acceleration range from 1000 g (at 0.1x gain with a 10 mV/g accelerometer) down to 0.1 g (at 100x gain with the same accelerometer). The wide gain range enables a single accelerometer to serve multiple applications by adjusting gain to match the expected acceleration level.

Some controllers use ±5 volt input range, effectively halving the full-scale acceleration for any given combination of sensitivity and gain. A 10 mV/g accelerometer at 1x gain provides 500 g full scale with ±5 volt input versus 1000 g with ±10 volt input. This difference becomes significant when testing to high acceleration levels or when attempting to maximize dynamic range.

A few specialized controllers offer ±2.5 volt input range, further reducing full-scale capability but potentially offering advantages in noise performance for low-level measurements. The reduced input range means that gain must be lower or sensitivity must be lower to handle a given maximum acceleration, with implications for system noise floor.

The gain architecture in the signal conditioning electronics determines the flexibility available to match accelerometer output to ADC input range. Controllers with discrete gain steps typically offer 0.1x, 0.3x, 1x, 3x, 10x, 30x, and 100x. Each step represents approximately a factor of three, providing seven steps spanning a factor of 1000 in total range. This discrete stepping means that for any given accelerometer sensitivity, there are only seven possible full-scale ranges available.

Controllers with continuously variable gain or finer gain steps provide more flexibility to precisely match the signal to the ADC range. A system offering gain in 1 dB steps from -20 dB (0.1x) to +40 dB (100x) provides 60 distinct settings, allowing much more precise optimization. However, most commercial vibration controllers use discrete gain steps as a practical compromise between flexibility and complexity.

The interaction between accelerometer sensitivity and available gain settings determines whether a satisfactory configuration exists for a particular test. Consider a test expecting maximum acceleration of 25 g with a controller having ±10 volt input and discrete gains of 0.1x, 0.3x, 1x, 3x, 10x, 30x, 100x.

Using a 100 mV/g accelerometer:

•    At 1x gain: Full scale = 10V / 0.1V/g = 100 g (adequate margin)
•    At 3x gain: Full scale = 10V / 0.3V/g = 33 g (marginal margin)
•    At 10x gain: Full scale = 10V / 1.0V/g = 10 g (overload)

The optimal choice is 1x gain, providing 4:1 margin above the 25 g maximum. This margin accommodates unexpected resonances or control overshoots without clipping.

Using a 10 mV/g accelerometer with the same test:

•    At 10x gain: Full scale = 10V / 0.1V/g = 100 g (adequate margin)
•    At 30x gain: Full scale = 10V / 0.3V/g = 33 g (marginal margin)
•    At 100x gain: Full scale = 10V / 1.0V/g = 10 g (overload)

Again 10x gain provides appropriate margin, but now with ten times less signal than the higher sensitivity accelerometer would provide at 1x gain. This difference affects noise floor and dynamic range.

The key principle is that higher sensitivity accelerometers provide more signal for a given acceleration, enabling lower gain settings that generally provide better noise performance. However, high sensitivity accelerometers have lower maximum acceleration limits, so sensitivity must be matched to the expected test levels.

Multiple Gain Ranges and Difficult Test Articles

Vibration controllers with multiple independently adjustable gain ranges provide significant advantages when controlling difficult test articles, particularly those with extreme dynamic range or unusual frequency response characteristics. Understanding when and how multiple gain ranges help enables optimal system configuration.

The concept of multiple gain ranges applies primarily in MISO control systems with multiple control and monitor channels. Each channel can be configured with independent gain settings, allowing optimization for the specific characteristics of that channel. A control channel measuring high acceleration at a stiff mounting point might use low gain, while a monitor channel measuring low acceleration at a compliant location might use high gain. This independent optimization enables simultaneous measurement across a wide range of acceleration levels.

Consider a MISO vibration test with four shakers driving a large flexible structure. Control accelerometer C1 at the primary drive point measures 30 g maximum during resonances but drops to 3 g at anti-resonances, a 20 dB range. Control accelerometer C2 at a secondary location measures 10 g maximum and 0.1 g minimum, a 40 dB range. Monitor accelerometer M1 on a lightweight component measures 80 g maximum and 0.8 g minimum, a 40 dB range. Monitor accelerometer M2 on an isolated section measures 2 g maximum and 0.02 g minimum, a 40 dB range.

Without independent gain adjustment, a single gain setting must accommodate all channels. The system gain must be set conservatively to prevent overload of the highest-amplitude channel (M1 at 80 g), but this causes the lowest-amplitude channel (M2 minimum at 0.02 g) to use a very small portion of the ADC range, sacrificing dynamic range and increasing susceptibility to noise.

With independent gain per channel, each can be optimized:

•    C1: Gain selected for 30 g maximum, providing good resolution at 3 g minimum
•    C2: Higher gain for 10 g maximum, excellent resolution at 0.1 g minimum
•    M1: Low gain for 80 g maximum, adequate resolution at 0.8 g minimum
•    M2: High gain for 2 g maximum, good resolution at 0.02 g minimum

This independent optimization enables each channel to use 50-80% of the ADC range at its maximum signal, maximizing effective dynamic range across all channels simultaneously.

The benefit becomes even more pronounced with test articles exhibiting extreme dynamic range in their frequency response. Some structures with lightly damped modes show resonance amplification factors (Q values) exceeding 100, meaning the response at resonance is 100 times (40 dB) higher than the drive level. If the test specification requires maintaining constant input acceleration while measuring response through these resonances, the control accelerometer at the drive point might see 10 g while the response accelerometer at the resonance location sees 1000 g.

Without independent gain control, the system must be configured to handle the 1000 g maximum at the response location, forcing the control point to use only 1% of the ADC range. This severely degrades control quality as quantization errors and noise become significant relative to the small signal. With independent gain, the control channel uses high gain optimized for its 10 g level while the response channel uses low gain for its 1000 g level, maintaining good measurement quality on both.

The practical implementation of multiple gain ranges requires that the controller firmware maintain separate gain settings for each channel and apply appropriate scaling factors in the control algorithms. When the control channel uses one gain and the response channels use different gains, the control calculations must account for these differences to properly compare measured values to specifications. Well-designed controllers handle this automatically, but operators must understand that changing gain on any channel requires corresponding changes in the control setup.

Some advanced controllers offer automatic gain ranging where the system monitors signal levels during initial surveys or low-level operation and automatically adjusts gain on each channel to optimize usage of the ADC range. This feature simplifies setup and ensures optimal configuration, particularly valuable for complex test articles where manual gain optimization would be time-consuming. However, auto-ranging must be disabled during formal qualification testing to prevent gain changes during the test that could introduce transients or invalidate data continuity.

The disadvantage of multiple independent gain ranges is increased complexity in system setup and documentation. Each channel's configuration must be recorded and verified. Calibration procedures become more complex as each channel may require different calibration factors. Troubleshooting signal quality problems requires checking gain settings on each channel individually. These complexities are manageable with proper procedures but represent real operational considerations.

Sine Vibration Testing Considerations
Sine vibration testing presents specific considerations for transducer sensitivity selection that differ from random or shock testing. The characteristics of sine testing, including resonance tracking, slow sweep rates, and control objectives, influence optimal sensitivity choices.

During sine vibration testing, the instantaneous acceleration amplitude is relatively predictable, determined by the test level specification and the frequency response of the test article at the current frequency. The control system maintains constant amplitude as frequency sweeps through the specified range, with amplitude increasing at resonances and decreasing at anti-resonances according to the test article's frequency response function.

For constant amplitude sine testing, the maximum acceleration occurs at the strongest resonance of the test article. If testing at 10 g input specification and the test article has a resonance with amplification factor of 20, the response at that resonance reaches 200 g. The accelerometer sensitivity must be selected to handle this 200 g maximum, not merely the 10 g specification level. Failure to account for resonance amplification leads to signal clipping at resonances, corrupting control and potentially damaging the test article.

The common practice of conducting a low-level resonance search before qualification testing helps identify maximum response amplitudes. A sweep at 0.5 g or 1.0 g with all response channels monitored reveals where resonances occur and their approximate amplification. If a resonance shows 15 g response during a 1 g search, the full-level qualification test at 10 g will produce approximately 150 g at that location. Accelerometer sensitivity and gain settings can be optimized based on this information before beginning the qualification test.

For control accelerometers in sine testing, sensitivity should be selected to provide good resolution at the specified test level while handling maximum expected acceleration at resonances. A test specification of 5 g to 20 g requires the control accelerometer to accurately measure 5 g, suggesting high sensitivity for good resolution. However, if test article resonances amplify acceleration by a factor of 5, the accelerometer must handle 100 g at 20 g input. This consideration typically drives selection toward moderate sensitivity (10-30 mV/g) rather than high sensitivity (100 mV/g).

For monitor accelerometers at locations remote from the control point, different considerations apply. These accelerometers measure test article response but do not directly control the test level. Their purpose is to verify that response limits are not exceeded and to characterize the test article's dynamic behavior. Since resonances may amplify acceleration dramatically at these locations, low sensitivity accelerometers (1-10 mV/g) are often appropriate, accepting somewhat higher noise floor in exchange for ability to measure very high acceleration without overload.

Resonance tracking and resonance dwell tests require the control system to maintain constant acceleration at a resonance that may shift frequency during the test due to temperature effects, nonlinearities, or progressive damage. The numerical precision requirements for tracking slowly drifting resonances were discussed in the 64-bit architecture technical note, but sensitivity selection also plays a role. The control accelerometer must provide sufficient resolution that small changes in acceleration can be detected and corrected, suggesting higher sensitivity when the control level is moderate and the expected resonance amplification is not extreme.
Phase accuracy in MISO sine control with multiple shakers requires good signal-to-noise ratio on all control channels to maintain precise phase relationships. Lower noise floor resulting from higher sensitivity selection improves phase accuracy, but only if the sensitivity choice does not force gain so low that ADC quantization becomes significant. The optimal balance typically involves selecting the highest sensitivity compatible with the maximum expected acceleration, then using moderate gain settings that provide good noise performance while maintaining adequate headroom for unexpected peaks.

Slow sweep rates in sine testing, typically 1 to 4 octaves per minute, mean that the system spends significant time at each frequency. This extended duration at each frequency allows extensive averaging to reduce noise, partially compensating for lower sensitivity or lower gain settings. However, this averaging cannot recover information lost to ADC quantization if the signal uses too small a fraction of the ADC range. Sensitivity and gain should be set to use at least 20-30% of the ADC range at the typical test level, providing adequate resolution even with limited averaging.

Random Vibration Testing Considerations

Random vibration testing presents fundamental different considerations for sensitivity selection compared to sine testing. The statistical nature of random vibration, the continuous excitation across broad frequency ranges, and the use of spectral analysis for control create unique requirements.

Random vibration consists of broadband excitation where the acceleration varies continuously and randomly with time. The specification defines power spectral density (PSD) rather than instantaneous amplitude, describing the distribution of vibration energy across frequency. The relationship between PSD level and instantaneous acceleration involves the statistical properties of Gaussian random processes.

For Gaussian random vibration, the RMS acceleration equals the square root of the area under the PSD curve. The instantaneous acceleration varies continuously, with peak values reaching approximately 3 to 4 times the RMS value in normal operation, and occasionally reaching 5 times RMS or higher. This statistical variability means that accelerometer sensitivity and gain must be set conservatively to handle peaks significantly higher than the RMS level, or clipping will occur intermittently.

Consider a random vibration test with overall level of 10 g RMS. The PSD specification might be 0.04 g²/Hz from 20 Hz to 2000 Hz, which integrates to approximately 100 g² total, giving 10 g RMS. During the test, instantaneous acceleration typically reaches 30 to 40 g peaks, with occasional excursions to 50 g. The accelerometer and gain settings must handle these peaks without clipping.

If test article resonances amplify the random input, the response at those resonances shows increased PSD level and correspondingly increased RMS and peak acceleration. A resonance with Q of 20 that amplifies a 0.04 g²/Hz input by a factor of 20 produces 0.8 g²/Hz at the resonance peak. If this resonance spans approximately 10 Hz bandwidth, it contributes 8 g² to the total, increasing local RMS significantly. The monitor accelerometer measuring response at this location must handle the increased peak levels.

The control system for random vibration uses spectral analysis, computing FFT of the time data and converting to power spectral density. The control loop adjusts drive signal levels to maintain specified PSD at each frequency bin across the control range. This spectral control approach is relatively insensitive to occasional clipping of individual time domain samples, unlike sine control which is directly disrupted by clipping. However, excessive clipping corrupts the statistical properties of the signal and introduces spectral artifacts that degrade control quality.

The rule of thumb for random vibration is to set accelerometer sensitivity and gain such that the full-scale range is approximately 5 times the RMS level. This provides adequate headroom for typical peaks while using sufficient ADC range for good resolution. For a 10 g RMS test, full scale should be approximately 50 g. Using a 10 mV/g accelerometer with ±10 volt input requires gain of 10/(0.01 * 50) = 20x. If available gains are 10x, 30x, the choice would be 10x, providing full scale of 100 g, or 10 times the RMS level. This conservative setting ensures negligible clipping probability.

The trade-off in random vibration sensitivity selection involves balancing clipping avoidance against noise floor considerations. Using lower sensitivity or lower gain to provide large margins against clipping means the typical signal uses a smaller fraction of the ADC range, reducing effective dynamic range and making the measurement more susceptible to electronic noise. For test articles with flat frequency response and no strong resonances, conservative settings work well. For test articles with sharp resonances and deep anti-resonances, more careful optimization is required.

In MISO random control with multiple shakers, the control accelerometers at different shaker locations may experience different acceleration levels due to mechanical coupling through the fixture and test article. Independent gain settings enable optimization for each control point. A primary control location might measure 12 g RMS while a secondary location measures 8 g RMS. Setting gain independently allows each channel to use 40-60% of ADC range at typical peaks, maximizing resolution while maintaining adequate clipping margin.

The spectral averaging used in random control enables some tolerance for measurement noise that would be problematic in sine control. Averaging 100 or more spectral estimates reduces the noise floor by 10-20 dB relative to single-spectrum noise. This allows use of moderate sensitivity accelerometers (10-30 mV/g) with moderate gain settings even when individual unaveraged spectra would show marginal signal-to-noise ratio. The averaging recovers adequate precision for control purposes.

The dynamic range required in random vibration testing depends on the ratio between the highest and lowest PSD levels across the specified frequency range. A simple flat spectrum from 20 Hz to 2000 Hz at 0.04 g²/Hz requires relatively modest dynamic range. A shaped spectrum with peaks at 0.4 g²/Hz and notches at 0.004 g²/Hz requires 20 dB more dynamic range. Accelerometer sensitivity should be selected based on the peak PSD levels, then relied upon to provide adequate noise floor for measuring the notched regions. High sensitivity accelerometers excel at providing the dynamic range needed for complex shaped spectra.

Shock Testing Considerations

Shock testing presents the most demanding requirements for accelerometer selection and gain configuration. The high peak accelerations, short duration pulses, and critical importance of accurately capturing the shock pulse shape require careful attention to sensitivity selection.

Classical shock testing uses transient pulses such as half-sine, terminal peak sawtooth, or trapezoidal shapes with specified peak acceleration and duration. A typical specification might require 50 g peak, 11 millisecond half-sine pulse. The peak acceleration of 50 g directly determines the maximum that the accelerometer and signal conditioning must handle, but shock testing considerations extend beyond simply avoiding overload at the peak.

The high-frequency content in shock pulses means that accelerometers must have adequate frequency response extending well above the nominal frequency calculated from the pulse duration. A 11 millisecond half-sine pulse has fundamental frequency around 45 Hz, but accurate reproduction of the pulse shape requires measurement extending to 500 Hz or higher. The accelerometer's mounted resonance frequency should be at least 5 to 10 times higher than the highest frequency of interest, typically requiring resonant frequency above 5 kHz for accurate shock measurement.

The trade-off between sensitivity and resonant frequency limits accelerometer choices for shock testing. High sensitivity accelerometers (100 pC/g) typically have resonant frequencies of 2-10 kHz due to the large seismic mass required to generate high charge output. These accelerometers are marginal or unsuitable for shock testing requiring frequency response above 1-2 kHz. Low sensitivity accelerometers (1-10 pC/g) use smaller seismic mass, achieving resonant frequencies of 10-50 kHz suitable for shock testing. The reduced sensitivity means lower signal levels that require higher gain or acceptance of reduced resolution.
For classical shock testing with moderate peak levels (10-100 g), accelerometers in the 10-30 pC/g range (approximately 10-30 mV/g for IEPE types) provide good balance between sensitivity and frequency response. A 10 mV/g accelerometer measuring a 50 g shock produces 500 mV peak. With 1x gain, this signal is well within the ±10 volt ADC range while providing good resolution. The accelerometer's 20 kHz resonant frequency ensures accurate pulse shape measurement.

For high-shock testing with peak levels of 500-10,000 g, low sensitivity accelerometers (1-5 mV/g) become necessary. A 1 mV/g accelerometer measuring 1000 g produces 1 volt, requiring gain of approximately 5-10x to use 50-100% of a ±10 volt ADC range. These low sensitivity accelerometers typically have resonant frequencies of 30-70 kHz, essential for accurate measurement of the high-frequency content in severe shocks.

The test article response to shock excitation often shows amplification at structural resonances, similar to sine testing but with additional complexity due to the transient nature of shock. A structure with resonance at 200 Hz might show significant amplification when excited by a shock pulse containing substantial energy near 200 Hz. The response accelerometer at the resonance location may measure peak acceleration 5-10 times higher than the input shock level. For a 50 g input shock, the response might reach 250-500 g at particular locations.

This response amplification requires careful selection of monitor accelerometer sensitivity based on the expected maximum response, not the specified input level. A resonance search using low-level shocks can identify locations of maximum response and inform accelerometer selection for the full-level qualification test. Alternatively, analysis of the test article's frequency response function can predict response amplification, though this requires detailed structural knowledge often unavailable before initial testing.
Shock Response Spectrum (SRS) analysis, commonly used in shock testing, requires accurate measurement of the entire shock pulse time history. The SRS computation involves numerically integrating the acceleration time history through banks of single-degree-of-freedom systems with different natural frequencies. This computation is sensitive to noise, DC offsets, and any distortion in the measured pulse. Higher sensitivity accelerometers providing better signal-to-noise ratio yield cleaner SRS curves with less noise, particularly at high frequencies where the SRS oscillations become sensitive to measurement noise.

The sampling rate in shock testing must be high enough to accurately capture the shock pulse, typically requiring 5-10 samples during the pulse rise time. For a 1 millisecond rise time, sampling at 5-10 kHz is adequate. For shock pulses with sub-millisecond rise times, sampling rates of 50-100 kHz may be necessary. The combination of high sampling rate and relatively short duration (typical shock record lengths of 50-200 milliseconds) means that data volumes are manageable and extensive averaging is not available to reduce noise. Signal quality depends primarily on selecting appropriate accelerometer sensitivity and gain to optimize signal amplitude relative to ADC range and electronic noise.

In MISO shock testing with multiple shakers, timing synchronization between shakers becomes critical. The shock pulse from each shaker must arrive at the test article with proper phasing to produce the intended combined shock. This synchronization requires accurate measurement of shock timing, which in turn requires good signal-to-noise ratio and adequate sampling rate. Higher sensitivity accelerometers facilitate timing measurements by providing cleaner signals with well-defined pulse onsets.

Mixed-Mode Testing Considerations

Mixed-mode testing, including Sine-on-Random (SoR) and Random-on-Random (RoR), presents the most complex sensitivity selection challenges because the test simultaneously includes characteristics of multiple test types. The accelerometer must handle the combined acceleration from all components while providing adequate resolution for each component independently.
Sine-on-Random testing superimposes one or more discrete sine tones on broadband random vibration. A typical SoR specification might require 6 g RMS random from 20-2000 Hz with three sine tones at 100 Hz, 300 Hz, and 800 Hz, each at 5 g amplitude. The instantaneous acceleration includes the sine amplitudes plus random peaks, which combine in complex ways depending on the phase relationships at each instant.

The peak acceleration during SoR testing approximates the sum of maximum random peaks plus sine amplitudes, though the actual maximum depends on statistical phase relationships. For the example above, the 6 g RMS random produces typical peaks of 18-24 g (3-4 times RMS). Adding three 5 g sine tones could add up to 15 g if all three are in phase, though statistically they average closer to 8-10 g combined. The expected peak acceleration is approximately 24 + 10 = 34 g, with occasional excursions to 40-45 g.
Accelerometer sensitivity and gain must be set to handle these combined peaks. Using a 10 mV/g accelerometer at 3x gain provides full scale of 10V/(0.03V/g) = 333 g, which is extremely conservative and wastes most of the ADC range. Using 10x gain provides full scale of 100 g, appropriate for the expected peaks. Using 30x gain provides full scale of 33 g, which is marginal and will experience some clipping during peak excursions.

The control system must separately track the random PSD level and the sine amplitudes during SoR testing, requiring that both components be accurately measured simultaneously. If gain is set too low (sensitivity too low or multiplier too small), the random component uses a small fraction of the ADC range and suffers from increased noise floor that degrades spectral analysis quality. If gain is set too high, clipping occurs during combined peaks, corrupting both random and sine measurements.

Test article response during SoR testing may amplify the sine components at resonances while showing different amplification of the random component. A structural resonance at 300 Hz might amplify the 300 Hz sine tone by a factor of 20, while also amplifying the random energy near 300 Hz by a similar factor. The monitor accelerometer at this location must handle 100 g from the amplified sine plus elevated random peaks from the amplified random spectrum. This can easily result in peaks of 120-150 g at locations that would measure only 50-60 g during random testing alone or 100 g during sine testing alone.

The need to independently measure both sine and random components suggests using moderate sensitivity accelerometers (10-30 mV/g) with moderate gain settings that provide good signal-to-noise for the random component while preventing clipping on combined peaks. Very high sensitivity (100 mV/g) accelerometers that work well for low-level random testing are generally unsuitable for SoR due to limited headroom for the combined acceleration.

Random-on-Random testing combines two independent random spectra with specified coherence. A typical RoR specification might require a primary random spectrum at 8 g RMS from 20-2000 Hz and a secondary random spectrum at 4 g RMS from 200-1000 Hz. The two spectra are partially correlated, with the degree of correlation specified by coherence.

The peak acceleration during RoR testing depends on how the two random components combine. If the components are completely uncorrelated (zero coherence), they combine as root-sum-square: sqrt(8² + 4²) = 8.94 g RMS, with peaks reaching 27-36 g. If the components are fully correlated (coherence of one) and in phase, they add directly: 8 + 4 = 12 g RMS, with peaks reaching 36-48 g. The actual combination depends on the specified coherence and the instantaneous phase relationships.

Accelerometer sensitivity for RoR testing should be selected assuming worst-case phasing where components add directly, providing margin for the highest possible peaks. This conservative approach prevents clipping during the occasional instances when random phase causes components to add constructively. Using the example above, expecting peaks to 50 g suggests setting full scale to 100 g for 2:1 margin, requiring approximately 10x gain with 10 mV/g accelerometers.

For MISO control in mixed-mode testing, different control locations may experience different combinations of acceleration components. One shaker location might receive strong sine components with moderate random, while another receives strong random with moderate sine. Independent gain settings on each channel enable optimization for the specific combination each channel experiences, maintaining good measurement quality across all control points.

The complexity of mixed-mode testing makes automatic gain ranging particularly valuable if available and if used during setup rather than during formal qualification testing. The automatic system can observe the combined acceleration during a low-level trial run and optimize gain on each channel independently, ensuring that each channel uses 40-70% of the ADC range during peaks while providing adequate resolution during typical operation.

Practical Selection Guidelines and Examples

Synthesizing the considerations discussed throughout this technical note enables development of practical guidelines for transducer sensitivity selection across different applications and test types. These guidelines provide starting points that should be refined based on specific test article characteristics and test requirements.

For general-purpose sine testing with moderate acceleration levels (1-50 g), select accelerometers with sensitivity of 10-50 mV/g for IEPE types or 10-50 pC/g for charge output types. These sensitivities provide good signal levels while handling reasonable resonance amplification. If preliminary resonance surveys indicate amplification factors exceeding 5:1, consider lower sensitivity (1-10 mV/g) for monitor accelerometers at high-response locations.

Example: Sine testing from 5-2000 Hz at 10 g specification level. Control accelerometer: 30 mV/g, expecting peaks to 30 g (assuming 3:1 amplification at some resonances). With ±10V input and 10x gain, full scale = 10V/(0.3V/g) = 33 g. This provides adequate margin while using 30g/33g = 91% of range at maximum, ensuring good resolution. At the 10 g specification level, usage is 30%, providing good resolution even at minimum level.

For high-level sine testing (50-200 g) or testing of stiff structures with minimal resonance amplification, lower sensitivity accelerometers (1-10 mV/g) become necessary to prevent overload. Accept the reduced signal level and compensate with higher gain settings, though recognize that the higher gain may increase noise floor somewhat.

Example: Sine testing from 5-500 Hz at 80 g specification level on a stiff metal structure with maximum observed amplification of 1.5:1. Control accelerometer: 10 mV/g, expecting peaks to 120 g. With ±10V input and 1x gain, full scale = 10V/(0.01V/g) = 1000 g. This provides large margin but uses only 12% of ADC range, acceptable because the high amplitude signal maintains good signal-to-noise despite low ADC usage.

For random vibration testing with moderate levels (1-20 g RMS), select accelerometers with sensitivity of 10-30 mV/g. Set gain to provide full scale approximately 5-8 times the RMS level, balancing clipping avoidance against resolution. Monitor test article resonances during initial setup and adjust if amplification is severe.

Example: Random testing at 10 g RMS with flat spectrum from 20-2000 Hz. Control accelerometer: 10 mV/g. With ±10V input, target full scale of 50 g (5 × RMS). Required gain = 10V/(0.01V/g × 50g) = 20x. Available gains are 10x (100 g FS) and 30x (33 g FS). Select 10x for adequate margin against clipping, using approximately 40% of ADC range at 4-sigma peaks. With extensive spectral averaging (100+ spectra), this provides adequate dynamic range.

For shock testing with moderate peak levels (10-100 g), select accelerometers with sensitivity of 5-20 mV/g and resonant frequency above 10 kHz. Higher frequency response capability is more important than maximum sensitivity in shock applications. Set gain to use 30-60% of ADC range at the expected peak.

Example: Shock testing with 60 g peak, 6 millisecond half-sine pulse. Control accelerometer: 10 mV/g with 30 kHz resonance. With ±10V input, using 3x gain provides full scale = 10V/(0.03V/g) = 333 g, overly conservative. Using 10x gain provides full scale = 100 g, using 60% of range at the 60 g peak. This provides margin for unexpected peaks while ensuring good resolution for accurate pulse shape measurement.
For mixed-mode testing (SoR, RoR), select moderate sensitivity accelerometers (5-20 mV/g) and set gain conservatively assuming worst-case combination of components. Better to sacrifice some resolution than to experience clipping that corrupts both components simultaneously.

Example: SoR testing with 8 g RMS random plus two 6 g sine tones. Control accelerometer: 10 mV/g. Expected peak = 24 g random + 12 g sine = 36 g typical, 45 g occasional. With ±10V input, using 10x gain provides full scale = 100 g, using 45% at occasional peaks. This provides adequate margin while maintaining good resolution for both random spectral analysis and sine amplitude measurement.

For MISO control with multiple shakers and varying acceleration levels across control points, use accelerometers with matched sensitivity on all control channels to simplify system configuration, but set gain independently on each channel to optimize for the local acceleration level. Use higher gain on channels with lower amplitude, lower gain on channels with higher amplitude.
Example: MISO with four shakers, control points measuring 15 g, 12 g, 8 g, and 6 g RMS during random testing. All control accelerometers: 10 mV/g for consistency. Gains: Channel 1 at 10x (full scale 100 g), Channel 2 at 10x (100 g), Channel 3 at 10x (100 g), Channel 4 at 30x (33 g). The higher gain on Channel 4 optimizes resolution for the lower amplitude signal while channels 1-3 use consistent settings. This configuration maintains good measurement quality on all channels.

Verification and Validation

After selecting transducer sensitivity and configuring gain settings, verification testing should confirm that the configuration provides adequate performance before conducting qualification tests. This verification prevents costly test failures or invalid data resulting from suboptimal configuration.

The signal quality check examines the actual signal levels reaching the ADC during a low-level test run. The controller should provide display or logging of signal amplitude relative to full scale on each channel. Ideal operation uses 30-70% of ADC range during typical operation with margin for peaks. If channels consistently operate below 20% of range, increasing gain improves resolution. If channels exceed 80% or show occasional clipping, reducing gain prevents overload.

Dynamic range verification measures the system's ability to simultaneously capture high and low level signals within the same test. During a sine sweep with resonances, monitor both the peak signals at resonances and the noise floor at anti-resonances. The ratio between peak and noise floor should exceed the expected test article dynamic range by at least 10 dB to provide margin for measurement uncertainty and control algorithm requirements.

For random testing, spectral analysis quality can be assessed by examining the spectrum during a trial run. The spectrum should show smooth PSD curves without excessive noise or artifacts. The noise floor in low-PSD regions should be at least 20 dB below the specified PSD level. If the noise floor approaches the specified PSD, increase gain or select higher sensitivity accelerometers.
Clipping detection confirms that selected sensitivity and gain prevent overload. Most controllers provide clipping indicators that flag when input signals exceed the ADC range. Running a trial test at 50-75% of the full qualification level and monitoring for clipping indicators reveals whether full-level testing will encounter problems. If clipping occurs during the trial, reduce gain or select lower sensitivity accelerometers before proceeding.

Phase accuracy in MISO control should be verified by examining the phase relationships between control channels during a sine test. The controller should display or log the phase of each control channel relative to a reference. Deviations from the expected phase (typically zero degrees for synchronized shakers) indicate signal quality problems, possibly resulting from inadequate signal-to-noise ratio that could be improved by increasing gain or selecting higher sensitivity accelerometers.

Conclusion

Transducer sensitivity selection represents a critical system design decision that profoundly affects vibration control system performance across all test types. The interaction between accelerometer sensitivity, signal conditioning gain, and ADC input range determines the achievable dynamic range, measurement resolution, and control quality. Proper sensitivity selection requires careful consideration of maximum expected acceleration including resonance amplification, statistical peak factors for random vibration, and the combined acceleration in mixed-mode tests.

The availability of multiple independent gain ranges in modern vibration controllers provides powerful capability to optimize each measurement channel independently, particularly valuable for MISO control of complex test articles with varying response levels across different measurement locations. High sensitivity accelerometers (50-100 mV/g) excel for low-level testing where their superior signal-to-noise ratio enables precise control and wide dynamic range, but are limited to applications where maximum acceleration remains below approximately 20-50 g. Moderate sensitivity accelerometers (10-30 mV/g) provide versatile performance across a wide range of applications from moderate sine testing through random and mixed-mode testing, handling maximum acceleration to 100-200 g while maintaining adequate resolution. Low sensitivity accelerometers (1-10 mV/g) are essential for high-level testing, shock applications, and monitoring locations with severe resonance amplification, accepting reduced resolution in exchange for ability to measure extreme acceleration levels.

The selection process should begin with careful analysis of test specifications and test article characteristics to determine maximum expected acceleration at each measurement location, then select accelerometer sensitivity appropriate for this maximum while providing adequate signal level for good resolution at typical operating levels. Gain settings should be configured to use 30-70% of the ADC input range at typical operating conditions, providing margin for peaks while avoiding wasteful excess margin that sacrifices resolution. For MISO control with multiple channels, independent gain optimization on each channel maximizes overall system performance. Verification testing at reduced levels before conducting qualification tests confirms that the selected configuration provides adequate performance and prevents costly failures or invalid data from improper configuration.

Organizations operating vibration laboratories should maintain an inventory of accelerometers with various sensitivities to enable optimal selection for each test application. The modest cost of maintaining multiple accelerometer types is repaid many times through improved test quality, expanded test capability, and avoided test failures. Documentation of sensitivity selection rationale, gain settings, and verification test results provides traceability and enables continuous improvement in configuration practices. Understanding the fundamental relationships between sensitivity, gain, dynamic range, and control quality enables test engineers to make informed decisions that optimize vibration control system performance across the full spectrum of challenging test applications.