Goals for Understanding
Static characteristics of a measurement system
Dynamic characteristics of a measurement system
A typical problem in Biomedical Engineering requires studying the behavior of biological systems under diverse conditions, measuring a parameter of interest from a system and creating a readable output. The tool used for this is a transducer. Transducers transfer signals generated in one system to another system in the same or different form.
Some of the transducers characteristics are determined by the particular application. Ideally, the transducer must not affect the parameter to be measured. Sometimes this is not possible and some error may be generated. The ability to keep the error under acceptable limits will make the system useful.
A measurable parameter of the transducer changes with changes in the studied system. How the transduced signal follows the studied one is determined by comparative methods against a standard. The static and dynamic characteristics can be studied.
The measured variable could be mechanical, thermal, magnetic, electric, optical, or chemical, among others. The sensor will transform the measured variable into a measured signal. This signal typically needs conditioning. The signal conditioning includes amplification, filtering, impedance matching, modulation and demodulation. In most common cases the measured signal is electrical. This makes the conditioning and interfaces easy.
During this lab session you will study the static and dynamic characteristics and conditioning of the signal of temperature transducers.
Transducer: a device for transferring power generated in one system to another system in the same or another form. A measurable parameter of the transducer changes under a change in the studied system.Some typical biomedical measurements:
The transducer transforms a measured variable into a measurable signal. The magnitude of the measured signal will be related to the magnitude of the measured variable. Transducers are calibrated against standards, so a quantification of the measured variable is obtained.
Signal: a function of one or more independent variables. Typically,
signals contain information about the behavior or nature of some phenomenon.
Static characteristics of a measurement system: The transducer influences the characteristics of the measurement system. A transducer is characterized by its accuracy, precision, and sensitivity. Other transducer parameters like repeatability, resolution, hysteresis and linearity may be required to fit a particular application.Static calibration process:
These known inputs values, or standards, should be at least ten times more accurate than that of the sensor being calibrated.
Standard: something setup by an authoritative body to measure quantity, weight, extent, value, or quality. It is an element that gives an established reference value for a specific measurement (time, pressure, weight, etc).
Accuracy: is how close the measured value is to the true value. Accuracy is determined by means of the static calibration process. It provides a confidence level as a percentage of the real value. The discrepancy between the instrument reading and the true value is called error.Different types of error:
Precision: is the instrument ability to give the same reading under the same conditions without regard for the coincidence or discrepancy between the result and the true value. It is a necessary but not sufficient condition for accuracy.
A is more precise than B since the discrepancy between the read values in A is smaller than in B. B is more accurate, however, than A.
Sensitivity: is the slope of the calibration curve.y = f(x)
S(xa) = dy / dx
S = k
S = 2 k x
Repeatability is the ability to reproduce the same output readings when the same value is applied repeatedly under the same conditions and in the same direction in short time intervals. Quantitatively, it is the minimum value that exceeds, with a specified probability, the absolute value of the difference between two successive readings obtained under the specified conditions (if not stated, is assumed 95%).
Resolution is the smallest increment in the input that produces a change in the output. When the input increment is from zero, then it is called the threshold. Transducer resolution is usually limited by the resolution of the element used to quantify the input signal.
Hysteresis: is the difference between two output values that correspond to the same input depending on the direction of successive input values. It is usually expressed in percentage of full scale during any one calibration cycle. Here, the top line represents the output with increasing input while the bottom line is for decreasing input. The difference is the hysteresis.
Linearity describes the closeness between the calibration curve and a specified straight line.Typically, the straight line is defined by the least square criterion. This method gives the best quality. Additional constraints may be added, such that the line passes through the origin. The line may also be defined based on theoretical predictions derived from the design of the sensor.
Dynamic characteristics of a measurement system:Is the measurement system responsive when the input signal is not constant?
The dynamic characteristics are dynamic error and speed of response. One can determine the dynamic characteristics of a measurement system empirically. These systems are usually represented by linear differential equations.
Measuring dynamic characteristics:
Dynamic error: is the difference between the indicated value and the true value for the measured quantity when the static error is zero and shows how the output changes when the input is a constant or variable value.
Speed of response: is how fast the measurement system reacts to changes in the input variable. If the system is linear, one signal is enough to characterize the system. The signal is chosen according to the type of system. For temperature, a step function is easy to setup, but for acceleration an impulse function is easier than a step.
Signal conditioning: To process the form or the mode of a signal so as make it intelligible to, or compatible with, a given device such as displays, recording or processing systems. They are usually electronic circuits performing one or more of the following functions: amplification, conformation, compensating, and linearizing.
Amplification: According to the characteristics of the signal under study and the response of the transducer to the signal changes, operational amplifiers with different characteristics and in several configurations are used to increase the amplitude of the voltage. Later in the course, we will return to this issue.
Conformation: Conformation is necessary in order to make the signal useful. Sometimes the shape of a signal is a thin pulse which could induce errors because it may or may not be detected at the next stage of the circuit (e.g. a pulse at the output of a photomultiplier tube). Sometimes the parameter changing is not itself a signal and an electric supply is needed to obtain a signal (e.g. resistive sensors). Voltage dividers are largely used.
Compensation: Usually the output signal is a combination of a
desired and an undesired signal (interferences). We want to remove the
interference and there are several ways to do that. When using a
transducer, a typical solution is to connect a second transducer to the
same system under the same conditions as the one producing the desired
A Wheatstone bridge is basically two voltage dividers connected in
parallel, where the output signal comes from the difference in their
individual outputs. They have very good sensitivity and are useful for the
measurement of resistance, inductance and capacitance.
Linearization: Analog and digital systems can be used for linearization. The thermistors used in this lab have an exponential variation of the resistance with the temperature. By simply using another resistor in series, the variation of the resistance with the temperature becomes almost linear. The value of the additional resistor can be chosen to make the system linear in a range of interest.
The graph represents Rp as a function of temperature
Rp = R * Rt / (R + Rt )
Signal processing: filtering, digitizing. These topics will be covered in the Biosignal Processing Lab.
Filtering: Sometimes the signal and the noise have different frequencies and a way to improve the signal-to-noise ratio is to keep (pass) certain frequencies and reject (stop) the unwanted frequencies. We will not design filters in this course but we will use them.
Digitizing: The biomedical signal that has been preprocessed (amplified and/or filtered) can be transferred into a computer or microprocessor or any display system by using data acquisition circuitry. This circuitry samples and quantizes the signal into a discrete form suitable for storage and processing on the computer.