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7 Strain, Force, Pressure and Flow Measurements

7 Strain, Force, Pressure and Flow Measurements

Tải bản đầy đủ - 912trang

24.21

A bonded strain gauge consists of a thin wire or conducting film arranged in a

coplanar pattern and cemented to a base or carrier. The basic form of this type

of gauge is shown below:

A bonded strain

gauge



FORCE



Small surface area

Low leakage

High isolation



FORCE



Figure 24.16 – A Bonded Strain Gauge

The strain gauge is normally mounted so that as much as possible of the length

of the conductor is aligned in the direction of the stress that is being measured.

Lead wires are attached to the base and brought out for interconnection.

Semiconductor strain gauges have a greater sensitivity and higher-level output

than wire strain gauges. They can also be produced to have either positive or

negative changes when strained. However, they are temperature sensitive, are

difficult to compensate, and the change in resistance is nonlinear.



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Strain, Force, Pressure and Flow Measurements



Index



24 - Sensor Signal Conditioning



24.22

24.8 High Impedance Sensors

Many popular sensors have output impedances greater than several megohms,

and thus the associated signal-conditioning circuitry must be carefully designed

to meet the challenges of low bias current, low noise, and high gain. A few

examples of high impedance sensors are:

High impedances

sensors…



 Photodiode preamplifiers

 Piezoelectric sensors

 Humidity monitors

 pH monitors

 Chemical sensors

 Smoke detectors

Very high gain is usually required to convert the output signal of these sensors

into a usable voltage. For example, a photodiode application typically needs to

detect outputs down to 30 pA of current, and even a gain of 106 will only yield

30 mV. To accurately measure photodiode currents in this range, the bias

current of the op-amp should be no more than a few picoamps. A high

performance JFET-input op-amp is normally used to achieve this specification.

Special circuit layout techniques are required for the signal conditioning



…require special

interfacing circuits



circuitry. For example, circuit layouts on a printed circuit board (PCB)

typically need very short connections to minimise leakage and parasitic

elements. Inputs tend to be “guarded” with ground tracks to isolate sensitive

amplifier inputs from voltages appearing across the PCB.



Index

24 - Sensor Signal Conditioning



High Impedance Sensors



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24.23

24.9 Temperature Sensors

Temperature measurement is critical in many electronic devices, especially

expensive laptop computers and other portable devices – their densely packed Temperature is an

extremely important



circuitry dissipates considerable power in the form of heat. Knowledge of physical property to

system temperature can also be used to control battery charging, as well as to measure

prevent damage to expensive microprocessors.

Accurate temperature measurements are required in many other measurement

systems, for example within process control and instrumentation applications.

Some popular types of temperature sensors and their characteristics are

indicated in the table below:

Sensor



Range



Accuracy



Excitation



Feature



Thermocouple



-184°C to

+2300°C



High accuracy

and

repeatability



Needs cold

Lowjunction

voltage

compensation



RTD



-200°C to

+850°C



Fair linearity



Requires

excitation



Low cost



Thermistor



0°C to

+100°C



Poor linearity



Requires

excitation



High

sensitivity



Semiconductor



-55°C to

+150°C



Linearity: 1°C



Requires

excitation



10 mV/K,

20 mV/K

or 1A/K

typical

output



Accuracy: 1°C



Popular types of

temperature sensor

and their

characteristics



Table 24.1 – Popular Types of Temperature Sensors

In most cases, because of low-level and/or nonlinear outputs, the sensor output

must be properly conditioned and amplified before further processing can

occur. Sensor outputs may be digitized directly by high resolution ADCs –

linearization and calibration can then be performed in software, reducing cost

and complexity.



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2015



Temperature Sensors



Index

24 - Sensor Signal Conditioning



24.24

Resistance Temperature Devices (RTDs) are accurate, but require excitation

current and are generally used within bridge circuits.

Thermistors have the most sensitivity, but are also the most nonlinear. They are

popular in portable applications for measurement of battery and other critical

system temperatures.

Modern semiconductor temperature sensors offer both high accuracy and

linearity over about a -55°C to +150°C operating range. Internal amplifiers can

scale output to convenient values, such as 10 mV/°C.



Index

24 - Sensor Signal Conditioning



Temperature Sensors



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2015



24.25

24.10 Summary





A sensor is a device that receives a signal or stimulus and responds with an

electrical signal. The full-scale outputs of most sensors are relatively small

voltages, currents, or resistance changes, and therefore their outputs must

be properly conditioned before further analog or digital processing can

occur.







Amplification,



level



translation,



galvanic



isolation,



impedance



transformation, linearization and filtering are fundamental signalconditioning functions that may be required with sensors.





A resistance bridge, or Wheatstone bridge, is used to measure small

resistance changes accurately. There are a variety of different bridge

circuits, and a variety of amplifying and linearizing techniques to suit each

type.







There are a variety of methods for interfacing to remote bridges. Many

integrated bridge transducers are available as “one-chip” solutions to bridge

driving and measurement.







There are many types of sensors – their use in a certain application requires

an understanding of their physical construction and operation, as well as the

required performance and cost demanded by the overall system.



24.11 References

Jung, W: Op-Amp Applications, Analog Devices, 2002.



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2015



Summary



Index

24 - Sensor Signal Conditioning



24.26

Exercises

1.

For temperature measurements only one active transducer is used and so it is

not possible to have a linear output if it is placed in a bridge.

(a)



Show that the output from a single-element varying bridge is given by:



vo 



(b)



VB R

4 R  R

2



Since the active transducer resistance change can be rather large (up to

100% or more for RTDs), the nonlinearity of the bridge output

characteristic (the formula above) can become quite significant. It is

therefore desired to linearize the output of a temperature transducer using

the following circuit:



VB



R1



R 2+ R



vo

R1

R2

Derive an equation for the output voltage.



Index

24 - Sensor Signal Conditioning



Exercises



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2015



25.1

25 System Modelling

Contents



Introduction ................................................................................................... 25.2

25.1 Differential Equations of Physical Systems .......................................... 25.3

25.2 Linear Approximations of Physical Systems......................................... 25.5

25.3 The Transfer Function ........................................................................... 25.8

25.4 Block Diagrams ..................................................................................... 25.9

25.5 Feedback .............................................................................................. 25.16

25.6 Summary.............................................................................................. 25.19

25.7 References ........................................................................................... 25.19

Exercises ...................................................................................................... 25.20



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2015



Contents



Index

25 - System Modelling



25.2

Introduction

In order to understand, analyse and design complex systems, we must obtain

quantitative mathematical models of these systems. Since most systems are

dynamic in nature, the descriptive equations are usually differential equations.

If the system stays “within bounds”, then the equations are usually treated as

linear differential equations, and the method of transfer functions can be used

to simplify the analysis.

In practice, the complexity of systems and the ignorance of all the relevant

factors necessitate the introduction of assumptions concerning the system

operation. Therefore, we find it useful to consider the physical system,

delineate some necessary assumptions, and linearize the system. Then, by

using the physical laws describing the linear equivalent system, we can obtain

a set of linear differential equations. Finally, utilizing mathematical tools, such

as the transfer function, we obtain a solution describing the operation of the

system.

In summary, we:

1. Define the system and its components.

2. List the necessary assumptions and formulate the mathematical model.

3. Write the differential equations describing the model.

4. Solve the equations for the desired output variables.

5. Examine the solutions and the assumptions.

6. Reanalyse or design.



Index

25 - System Modelling



Introduction



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2015



25.3

25.1 Differential Equations of Physical Systems

The differential equations describing the dynamic performance of a physical

system are obtained by utilizing the physical laws – this approach applies

equally well to electrical, mechanical, fluid and thermodynamic systems.

For mechanical systems, Newton’s laws are applicable.

EXAMPLE 25.1 Spring-Mass-Damper Mechanical System

Consider the simple spring-mass-damper mechanical system shown below:



K

f

Friction



Mass

M



y



r (t )

Force

This is described by Newton’s second law of motion (this system could

represent, for example, a car’s shock absorber). We therefore obtain:



M



d2y

dy

f

 Ky  r

2

dt

dt



where K is the spring constant of the ideal spring and f is the friction constant.



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Differential Equations of Physical Systems



Index

25 - System Modelling



25.4

EXAMPLE 25.2 Parallel RLC Circuit

Consider the electrical RLC circuit below:



r (t )



R



L



C



v( t )



This is described by Kirchhoff’s current law. We therefore obtain:

C



dv v 1

 

vdt  r

dt R L 



In order to reveal the close similarity between the differential equations for the

mechanical and electrical systems, we can rewrite the mechanical equation in

terms of velocity:

v



dy

dt



Then we have:

M



dv

 fv  K  vdt  r

dt



The equivalence is immediately obvious where velocity vt  and voltage vt 

are equivalent variables, usually called analogous variables, and the systems

are analogous systems.

The concept of analogous systems is a very useful and powerful technique for

system modelling. Analogous systems with similar solutions exist for

electrical, mechanical, thermal and fluid systems. The existence of analogous

systems and solutions allows us to extend the solution of one system to all

analogous systems with the same describing differential equation.



Index

25 - System Modelling



Differential Equations of Physical Systems



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2015



25.5

25.2 Linear Approximations of Physical Systems

Many physical systems are linear within some range of variables. However, all

systems ultimately become nonlinear as the variables are increased without

limit. For example, the spring-mass-damper system is linear so long as the

mass is subjected to small deflections y t  . However, if y t  were continually

increased, eventually the spring would be overextended and break. Therefore,

the question of linearity and the range of applicability must be considered for

each system.

A necessary condition for a system to be linear can be determined in terms of a

forcing function xt  and a response y t  . A system is linear if and only if:



ax1 t   bx2 t   ay1 t   by2 t 



(25.1)



That is, linear systems obey the principle of superposition, [excitation by



x1 t   x2 t  results in y1 t   y 2 t  ] and they also satisfy the homogeneity

property [excitation by ax1 t  results in ay1 t  ].

It may come as a surprise that a system obeying the relation y  mx  b is not

linear, since it does not satisfy the homogeneity property. However, the system

may be considered linear about an operating point x0 , y0  for small changes

x and y . When x  x0  x and y  y0  y , we have:



y  mx  b

y0  y  mx0  mx  b



(25.2)



and, since y0  mx0  b , then y  mx , which is linear.

In general, we can often linearize nonlinear elements by assuming small-signal

conditions. This approach is the normal approach used to obtain linear

equivalent circuits for electronic circuits and transistors.



PMcL

2015



Linear Approximations of Physical Systems



Index

25 - System Modelling



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