IET 472 - Full Topics
Top 10: design and implement a Wheatstone Bridge Circuit for a resistive sensing element that generates small resistance measurement Rx due to small measurable quantity x
When a resistive sensing element produces a small resistive measurement Rx due to small measuring quantity, a wheatstone bridge circuit must be used as the stage-1 conditioning circuit so that small resistance meaurement Rx can be accurately converted into the corresponding small and accurate voltage measurement Vx through the circuit's measuring function Vx=f(Rx)
26.1 Lead line comp cont.
a commercial RTD that has three wires is called a 3-wire configuration RTD as shown in the figure below, which is used in a wheatstone bridge in order for achieving RTD lead wire compensation.
Definition of the function of a measuring instrument
a measuring device that is designed and implemented to accurately measure and display the true value of a measurable quantity x through using the instruments accurate measuring function y=f(x) and display function x=f-1(y), which is the inverse of the function
(step 2) 1) design and implement stage1 signal conditioning DC electric circuit for resistive sensing element
a stage 1 signal conditioning DC circuit is designed to convert resistance measurement Rx of a resistive sensing element into corresponding voltage measurement Vx through the circuit's established measuring function of Vx = f(Rx)
topic 8: design and implement stage 1 signal conditioning circuits
a stage 1 signal conditioning DC electronic circuit is designed to convert resistance measurement Rx into corresponding voltage measurement Vx within the full measuring range of point 1(Rx1, Vx1) ~ (Rx2, Vx2) through the circuit's established measuring function Vx = f(Rx)
top 10: 2) measuring function Vx = f(Rx) of a wheatstone bridge circuit
a wheatstone bridge circuit is a prallel circuit that has two parallel branches, each of which has two resistors branch 1: R1,3 branch 2: R2,x
LabView Data acquisition system (DAQ)
allows the user to acquire external voltage signals in the LabView (one drags the icon into the block diagram, then selects acquire signals. It is an analog input. One must be ground)
Functions of the front panel
allows users to program virtual input and virtual output devices with control data in the controls pallet. Examples include: Numeric Inputs Numeric outputs Boolean Inputs
Introduction to RTD
an RTD is made of a special metal wire whose resistance value R(T) in Ohms changes along the changes of measured temperature T. Thus an RTD is a resistance temperature sending element that has the established measuring function R(T)=f(T) within the full specified measuring range T1-T2.
Step 1 in designing an analog measuring instrument
choose an appropriate sensing element to measure x
top11: stage 2 analog signal conditioning for linear voltage measuring function -->
def: designed and implemented so that the small voltage measurement Vx can be linearly converted into the large voltage measurement Vout within range (Vx1, Vout1) to (Vx2, Vout2)
C-->F
(C x 9/5) + 32
Units: Celsius Fahrenheit
degC degF
Calibration of an actual RTD
determining the value of coefficient alpha null for linear approximated measuring function R(T)=R(To)[1+alpha null(T-To)] with three sample measurements, R(T1), R(To), R(T2) that are collected from an actual RTD is called the calibration of the actual RTD.
Precision is determined by the equation
deviation=(measured - average of measurements) then average the deviations will give you a value called standard deviation standard deviation = (sum of deviation)/number of measurements
(Step 1)a resistive sensing element measured the unknown value of an appropriate measurable quantity x into the corresponding resistance through its established measuring function R=f(x) where:..
f( ) represents the functional relationship between measurable quantity x and resistance measurement Rx. In most cases, f( ) represents a non-linear relationship
(step 1) Voltage sensing element measures the unknown value of an appropriate measurable x into the corresponding voltage measurement of Vx through Vx=f(x) where:...
f( ) represents the functional relationship between measurable quantity x and voltage measurement Vx
top13: specifications of a general operational amplifier
including: pin def, schematic symbol, properties
top8: location -1 configuration of resistive sensing-element Rx in voltage divider circuit
is formed when Rx is connected between the negative polarity of the DC voltage source and the fixed resistor R.
example of stage-2 signal conditioning circuit
lab 2
Resistance-temperature sensing elements
measures the temperature as the corresponding measurement R(T) in Ohms through its resistance measuring fuction R(T)=f(T) Popular in portable applications such as measurement of battery temp and other critical temperatures in a system.
Voltage temperature sensing element
measures the temperature as the corresponding voltage measurement V(T) through its measuring function V(T)=f(T)
Sensing Principle of a Thermocouple
metal A wire and metal B wire of a thermocouple are able to induce a small voltage in mV at their ends of transmission wire C.
top12: slope K for stage 2 linear voltage measuring function
no unit
The measuring function of the wheatstone bridge circuit
note: nonlinear
the measuring function of the wheatstone bridge circuit is
note: nonlinear
Case 2: slope K is greater than 0, intersect voltage is greater than zero or less than zero, and Vx is a point voltage realative to the circuit's ground
step 1: the required measuring function Vout=KVx+Vo can first be manipulated as K(Vx+Vo/K) step2: let the output voltage function be equal to the stage-2 voltage measuring function K(Vx+Vo/K)=A(V2-V1) where K=A=R2/R1, Vx=V2. and Vo/K=-V1
Top15: implement required voltage measuring function Vout=KVx+Vo of the stage-2 analog signal conditioning by using a differential op-amp circuit
the linear output voltage function Vout=A(V2-V1) of a differential op-amp circuit can be used to implement the required stage-2 linear voltage measuring function in two cases
example of voltage sensing element
thermocouple
balanced bridge is necessary in order for the wheatstone bridge circuit to measure small measurable quantity with its small but accurate voltage measurements Vx
this process of making a balanced wheatstone bridge is called "calibrating the wheastone bridge circuit" which is usually done by manually adjusting the values of the fixed resistors so that the balanced condition can be met
(2) RTD Lead Line compensation
when an RTD is used far away from the wheatstone bridge circuit to its measuring of a high temperature, the RTD must be wired to the wheatstone bridge circuit with an RTD lead line and a compensation line as shown, resulting in no effect of the RTD's extended wires resistance change in Rw to the balanced condition: R1(Rt+RW)=R2(R3+Rw)
Setup of balance condition of wheatstone bridge circuit for a 3-wire RTD application with full measuring range To=0C~T, in which the RTD's nominal resistance is R(0C)=Ro
when only RTD lead wire compensation is considered, the setup of balance condition of wheatstone
if Vout=Kx+Vo, then x' =...
x'=(Vout/K)-(Vo/K)
full measuring range def
x1~x2
plot y=3sqrtx + 5
x=[0:0.1:10]; y=3*x.^0.5+5; plot (x,y)
full measuring span def
|x2-x1| --> |100C-35C|=65C
2) Circuit's linear analog output voltage Vout
* function of the circuit's differential input voltage and can be defined as Vout=A(V2-V1) * V1 is applied to (+) through R1 * V2 is applied to )-) through R2 * A = (R2/R1)
Labview has two pages
Front Panel Block Diagram
Example of data acquisition system
LabView
2) RTD dissipation constant Pd
RTD dissipation constant Pd describes the amount of dissipated electrical power P in watts over the RTD in order to rise 1degC of RTD's heat. RTD dissipation constant Pd is provided by the RTD manufacturer.
RTD (Resistance Temperature Detector)
RTDs are accurate and require stage 1 signal conditioning and are generally used in Wheatstone bridge circuits due to the relative small resistance measurement in Ohms within its full measuring range of -200 to 850 deg C
Top20: Introduction to Temperature Sensing elements
Temperature sensors
3) find RTD self heating temperature error change in T
The RTD self-heating temperature error change in T at the measured temperature T can be determined by the ratio of the actual RTD dissipated electric power P at temperature T to the given RTD dissipation constant Pd as change in T = P/Pd
Functions of the block diagram
The block diagram of a VI project allows the user to program virtual input and output devices by directly connecting them through wiring techniques found in the tools pallet. The tools pallet also has different functions.
Type of Thermocouple we work with
Type J Measuring Range: -190-760
Thermocouples Construction
a thermocouple is made out of two different thin metal wires, A and B, which are welded or soldered together at one end to form a "Probe junction" used for measuring the unknown temperature T, with their other ends connecting to similar transmission wires C to form "Reference Junctions" used for exposing a known reference temperature
what is Vx
differential voltage between point voltages Va and Vb
ex: good accuracy but poor precision
if the average of your measurements for a given measurable quantity x is close to the expected value, but the measurements are far from each other, then your measurements have accuracy without precision
Intersect for stage 2 linear voltage measuring function
in volt
how to make an mfile on MATLAB
open script write code click run
Case 1 ex) range of (0,0) to (0.5,5)
step1: K= (5V-0)/(0.5V-0) = 10 step 2: Vout=10Vx=10(Va-Vb) Va=V2 Vb=V1 K=10=A=10kOhm/1kOhm thus resistors R1,2 are found
def of accuracy
the closeness of a measured value to an expected value. The expected value can be either a standard or known value
def of precision
the closeness of two or more measurements to each other
full scale definition
the maximum value of x to be measured from 0
Example of a resistive sensing element
thermistor strain gauge
to plot a line and individual points on MATLAB
%plot specified function %within full measuring range Vx=(0.2:0.01:0.5); Vout=3.4*Vx+5; plot (Vx, Vout); hold on %plot measurement data plot(0.25,5.8, '.'); hold on plot (0.3,6.1, '.'); hold on ....
Schematics for a wheatstone bridge circuit for a single resistive sensing element Rx (quarter bridge)
* Rx is resistance measurement of a resistive sensing element which is changing according to measurable quantity x within full measuring range * R1,2,3 are fixed * Vs is the DC source * Vx is the voltage measurement which is changing according to the circuit's function Vx=f(Rx) and Rx within measuring range
components of voltage divider circuit
*Rx is the resistance measurement of a resistancec sensing element, which is changing according to measurable quantity x * R is a fixed resistor * Vs is the DC voltage source * Vx is the voltage measurement whose value is changing according to the circuit's measuring function Vx=f(Rx) and the value of Rx within full measuring range
instrument accuracy is expressed in 3 ways:
1) Instruments accuracy in value +/- b in unit 2) instruments accuracy in percentage of Full scale xmax +/- alpha * full scale xmax 3) instruments accuracy in percentage of full span +/- alpha * full measuring span |x2-x1|
the inverse function is usually implemented as a user developed program in a data acquisition system, which is able to provide functions of:
1) acquiring analogy voltage measurement Vout through the acquisition hardware 2) calculate.display the measured value x' of a real unknown measurable quantity x.
topic 7: Define the accuracy of a measuring instrument
1) instrument accuracy is the most important specification 2) instrument accuracy is expressed in 3 ways
3) properties of an ideal op-amp in an open loop
1) no currents go into the input piins due to infinite input resistance, Rin=inf 2) voltages are always equal at input pins of op-amp due to infinite open-loop voltage gain. Avol=Vout/Vin = inf. note: for actual, Avol=200,000
Step 2: design and implement analog signal conditioning circuits for selected sensing element
1) resistive sensing element 2) voltage
Thermocouples are able to produce voltage due to:
1) seeback coefficients alpha a and alpha b of metals A and B in unit of Volt/degC 2) Temperature difference (T-Tr) between temperature T(degC) at the "Probe Junction" and known reference temperature Tr(degC) at the "Reference Junction"
an analog measuring instrument consists of:
1) the hardware components of: 1) the analog sensing element, 2) analog stage 1 conditioning circuit, 3) analog stage-2 conditioning circuit. 2) the hardware/software of a data acquisition system to display the measured value of x' of the unknown measurable quantity x through the voltage measurement Vout.
two ways to express the value of measurable quantity x
1) true value - used in measurement 2) percentage - (within full measuring range) used in control analysis
characteristics of the circuit's differential voltage measurement Vx = Va=Vb
1) when R2R3 < R1Rx, then Va < Vb, thus Vx < 0 (neg) 2) when R3R2 > R1 Rx, then Va > Vb thus, Vx > 0 (pos) 3) Balanced bridge (condition and output) Vx = 0, Va = Vb
Types of temperature sensing elements
1)Voltage-temperature sensing element 2) Resistance-temperature sensing element
Define a physical, measurable quantity x
A physical and measurable quantity x is either generated by a physical system or existed in a natural environment, whose value can be either a constant, x=constant, or a variable, x=f(t), where f() represents the relationship between measurable quantity x and time t
(step 2) 2) design and implement stage-2 signal conditioning electronic circuit to ENLARGE the small value of voltage measurement Vx to the required large value of voltage measurement Vout
A stage 2 signal conditional electronic circuit is an appropriate operational amplifier (op-amp) circuit that is designed to amplify small values of Vx into Vout through the function Vout = f(Vx)
Thermocouples: Voltage temp sensing elements
Characteristics: *small, rugged, relatively inexpensive and operate over the widest range (-184C-2300) of all temp sensors. Useful for high temperatures *produce small differential voltage measurement Vtr(T) in mV. It requires accurate stage 2 signal conditioning with a high gain differential op-amp circuit.
examples of stage 1 signal conditioning resistive sensing circuit
DC voltage divider circuit DC wheatstone bridge circuit
Lab 2: design and implement a differential op-amp circuit by using AD620 chip to adjust the small differential voltage measurement within range of 0-400mV to be a large input voltage Vout within full measuring range 0 to 3.95 V
Equations: Vout=A(V2-V1) A=(1+49.4kOhm/Rg) where Rg is the user selected external resistor
Step 3: design and implement the display function for displaying measured, measurable quantity x' by using the data acquisition system
Ex) setup and program commercial LabView data acquisition hardware and software to display measured data (lab 3)
Thermistor
Have the most sensitiveity and the most non-linear for resistance measuring function R(T) =f(T) and require stage 1 signal conditioning and are generally used in a voltage divider circuit due to the relative large resistance measurement in kOhms
Ex: express voltage measurement Vtr(T) of a thermocouple for measured-temp T via reference temperature Tr
If Tr=0C, then the corresponding voltage measurement for measured-temperature T is expressed as V0degC(T) If Tr=25 then the corresponding voltage measurement for measured-temp T is expressed as V25(T)
top17: establish and implement measured quantity function x'=f^-1(Vout) by deriving it from the voltage measuring function Vout=f(x) of measuring instrument in order for calculating and displaying the measured value x' of a real unknown measurable quantity x
Inverses. Vout=f(x) x'= f^-1(Vout)
top18: LabView Introduction. It is a commerical data acquisition software form
National Instruments
Measuring function Vx = f(Rx) of location 1 configuration of Rx in voltage divider circuit is:
Note: non-linear
RTD self heating temperature error change in T 1) RTD dissipated electric power
The current I that is passing through an RTD in the bridge circuit generates dissipated electric power as P=I^2 Rt, where the current i is found by applying Ohm's Law over the branch in which R2 and RTD's resistance Rt are formed in the series as I=Vs/R2+Rt
Block Diagram cont:
The functions pallet contains numeric operations, such as addition and multiplication, a numeric constant can be added here, a "while loop" is a structure function.
Signal conditioning of RTD
The signal conditioning for an RTD usually consists of a bridge circuit and a differential amplifier as shown, where Rt represents resistance R(T) of the RTD at temperature T.
Ohm's law
V=IR
output voltage
Vout
top15: 1) Case 1 slope is 0 and intersect Vo=0 and Vx is the differential voltage measurement Vx=Va-Vb
Vout=A(V2-V1) K=A=R2/R1
input voltage
Vx
