# Understanding the performance of measuring systems

### Sensitivity

The sensitivity of a measuring system (sensor, filter, amplifier, analogue-to-digital converter etc) should be sufficient for the planned measurement task. Specifically the aim should be:

• To avoid poor signal-to-noise ratios when measuring low amplitude signals;
• To have sufficient range to avoid clipping and signal saturation for high amplitude signals;
• To ensure linearity, so as not to distort signals.

The sensitivity of the entire measuring system must be known if absolute measurements of the quantity of interest are needed, and this will require a calibration covering the sensitivity of sensors and the gain of any amplifiers, filters and ADCs present in the instrument chain. The sensitivity is typically described in terms of the electrical voltage or charge developed per newton, pascal and so on, depending on the relevant physical unit.

If a system provides a digital output rather than an analogue output, the sensitivity may be expressed in digital counts referred to the quantity of interest. The range of numeric values produced by an ADC depends on the number of bits used in the conversion. The analogue signal is approximated by a number of values/levels equal up to a maximum of 2N where N is the number of bits of the ADC. For example, an 8- bit ADC represents the full scale range with 28 values (256).

### Frequency response

The frequency response of a measuring system is the sensitivity (both amplitude and phase) as a function of frequency. The response should extend to a high enough frequency to record faithfully all frequency components of interest within the measured signals. This requires that the sensor and any amplifier and filter are sufficiently broadband. If the amplitude and phase response of the measuring system cannot be regarded as constant, it will be necessary to correct the measured signal for system effects using the system's calibration information. Any significant resonance behaviour within the frequency interval of interest will tend to distort the measured data, causing amplification of frequency components close to the resonance frequency and potentially distorting the time waveform for any broadband pulses.

In addition, for an unambiguous representation of the signals within the desired frequency range the sampling frequency of any ADC within the measuring chain must be greater than two times the maximum frequency in the signal to be measured (commonly referred to as the Nyquist frequency). It is common for systems to oversample such that the sampling frequency exceeds the minimum defined by the Nyquist criterion.

### System self-noise

The self-noise of the measuring system (often referred to as the “noise floor”) is a key parameter when measuring low amplitude signals, and defines the minimum signal amplitude that can be measured by the system.

This noise within the measuring system arises from two main sources:

• noise generated by sensors and the measuring system itself;
• noise generated by the environment in which the measuring system is being used.

The system self-noise is the noise generated by the system in the absence of a signal arising from an external stimulus. The self-noise varies with frequency and as a result is typically presented as a noise spectral density level versus frequency.

### Dynamic range

The dynamic range of a measuring system is the range of signal amplitudes over which the system can faithfully measure the input signal, i.e., from the noise floor of the system (the lowest measurable signal amplitude) to the highest amplitude of signal that may be measured without significant distortion. The system dynamic range should be sufficient to allow the highest expected signal amplitude to be recorded without distortion or saturation caused by the sensor, amplifier or ADC.

High amplitude signals that are beyond the maximum measurement capability of the measuring system will lead to distortions in the measured data. Clipping of the signal may occur, i.e., the peaks of the signal are missing from the data.  A very high amplitude signal may cause the amplifier electronics to saturate and recovery from saturation may not be immediate.

A measuring system should be linear over its full dynamic range. This means that at any particular frequency the system sensitivity is constant over the full range of the measurable signal amplitudes.  The linearity of components such as amplifiers should be checked, especially for high amplitude signals close to the maximum of the dynamic range.

Note that when measuring low amplitude signals, it is necessary to ensure that the signal amplitude exceeds the noise floor of the system, and also that it is not so low as to be affected from by noise arising from limited poor resolution of the ADC for very small amplitude signals.

### Interaction between conditioning amplifiers and digital acquisition systems: an industry view from HBM

All sensors for kinematic or mechanical quantities, such as force, torque, pressure, acceleration or even angular rate have to be connected to a conditioning amplifier for the signal to be processed further. The sensor and conditioning amplifier, filters etc. together constitute the measuring chain.

For traceability of the measuring chain and to make its components exchangeable, it is necessary to characterise each of the components of a measuring chain (sensor and conditioning amplifier) independently.

As the sensor is the interface to the physical process of interest and interacts with its enviroment, including mountings and suspension systems, it remains nonlinear, at least if universal use is intended. Only the conditioning amplifier – as the interface between sensor and indicator can be fully conditioned for universal use - meaning at any frequency in the required band. In other words the requirement for the conditioning amplifier is that it reacts to a signal of the same magnitude in the same way, no matter at what frequency (up to a certain cut off frequency) it occurs.

Conditioning amplifiers face the expectation of a flat frequency response (up to a certain cut off frequency). On the other hand industry requires DAQ systems to fit into a more and more digital environment.  However such commercially available digital amplifiers do not show flat frequency response.

Thus measurement manufacturer HBM created a DAQ system what can claim to be dynamically suitable. In the attempt to do so, the digital filter functions of a suitable module have been optimized. As a result the MX410B – a four-channel highly dynamic universal amplifier of the QuantumX DAQ series - provides this and is suitable for dynamic calibration.

This conditioning amplifier is compatible with strain gauge transducers in half and full bridge configuration for both direct current (DC) and 4.8 kHz carrier frequency (CF) as well as with inductive half and full bridges and current-fed piezoelectric sensors (IEPE),  normalised voltage or current with active transducer supply and can thus serve a wide variety of input  transducers. For the mechanical quantities considered here such as force, torque and pressure the full bridge configuration plays an important role. The module gives the choice of using it either with DC excitation or with carrier frequency excitation. The main advantage of the carrier frequency excitation is that it gives the equipment an inherent immunity to external noise and excellent long-term stability, as any signal aside from the very narrow CF-band base will be suppressed.

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