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et438b-4.pptx 1 ET 483b Sequential Control and Data Acquisition

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et438b-4.pptx 2 Static Characteristics Error = (measured value) – (ideal value) Ways of expressing instrument error 1.) In terms of measured variable Example ( + 1 C, -2 C) 2.) Percent of span Example (0.5% of span) 3.) Percent of actual output Example (+- 1% of 100 C)

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et438b-4.pptx 3 The difference between the upper and lower measurement limits of an instrument define the device’s span Span = (upper range limit) – (lower range limit) Resolution is the smallest discernible increment of output. Average resolution is given by: Where: N = total number of steps in span 100 = normalized span (%)

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et438b-4.pptx 4 Example: A tachogenerator (device used to measure speed) gives an output that is proportional to speed. Its ideal rating is 5 V/ 1000 rpm over a range of rpm with an accuracy of 0.5% of full scale (span) Find the ideal value of speed when the output is 21 V. Also find the speed range that the measurement can be expected to be in due to the measurement error.

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et438b-4.pptx 5 Determine the maximum output voltage Where:V max = maximum output voltage n max = maximum speed G = tachogenerator sensitivity (V/rpm) Find ideal value of speed Ideal speed Find V max Accuracy +-0.5% of full scale (5000) = +-25 rpm Speed range = 4225 rpm = 4175 rpm

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et438b-4.pptx 6 A 1200 turn wire-wound potentiometer measures shaft position over a range from -120 to +120 degrees. The output range is 0-20 volts. Find the span, the sensitivity in volts/degree, the average resolution in volts and percent of span.

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et438b-4.pptx 7 Repeatability - measurement of dispersion of a number of measurements (standard deviation) Accuracy is not the same as repeatability Example Not repeatable Not accurate Repeatable Not accurate Repeatable Accurate Ideal Value Reproducibility - maximum difference between a number of measurements taken with the same input over a time interval Includes hysteresis, dead band, drift and repeatability

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et438b-4.pptx 8 Determining the accuracy of a measuring instrument is called calibration. Measure output for full range of input variable. Input could be increased then decreased to find hysteresis. Repeat input to determine instrument repeatability. Increasing Input Measurements 1 Decreasing Input Measurements 2 Plot the data 1 2

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et438b-4.pptx 9 Hysteresis and Dead Band Difference between upscale and downscale tests called hysteresis and dead band Hysteresis & Dead Band

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et438b-4.pptx 10 Linearity Ideal instruments produce perfectly straight calibration curves. Linearity is closeness of the actual calibration curve to the ideal line. Types of Linearity Measure % Input % Output Average up and down scale values Zero-based line Terminal- based line Least-squares line Least-squares minimizes the distance between all data points

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et438b-4.pptx 11 First order instrument response First order model transfer function For step input Step response Where :C m (s) = instrument output C(s) = instrument input G = steady-state gain of instrument = instrument time constant with K = step input size (1 for unit step) Exponentially increasing function time constant

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et438b-4.pptx 12 Time required to reach 63.2% of final value is time constant, =2 Time required to go from 10% to 90% of final value is the rise time, t r t 90 – t 10 = t r 63.2% 90% 10% t 90 = 4.57 S t 10 = 0.22 S t r =4.57 S S=4.35 S

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et438b-4.pptx 13 Typical Instrument time constants Bare thermocouple in air (35 Sec) Bare thermocouple in liquid (10 Sec) Thermal time constant determined by thermal resistance R T and thermal capacitance C T. = R T ∙C T Example: A Resistance Temperature Detector (RTD) is made of pure Platinum. It is 30.5 cm long and has a diameter of 0.25 cm. The RTD will operate without a protective well. Its outside film coefficient is estimated to be 25 W/m 2 -K. Compute: a.) the total thermal resistance of the RTD, b.) the total thermal capacitance of the RTD, c.) The RTD thermal time constant.

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et438b-4.pptx 14 RTD To signal Conditioner a.) Find the surface area of the probe to find R T L=30 cm D=0.25 cm h o = 25 W/m 2 -K

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et438b-4.pptx 15 b.) Find the volume of the probe to find C T Where: = density of Platinum = 21,450 Kg/m 3 V = volume of probe S m = specific heat of Platinum = 0.13 kJ/Kg-K Find volume of cylinder Now find the thermal capacitance

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et438b-4.pptx 16 c.) Find the RTD time constant RTD Response curve

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17 et438b-4.pptx Common mode voltages are voltages that have the same magnitude and phase shift and appear at the inputs of a data acquisition system. Common mode voltages mask low level signals from low gain transducers. Data recording system VsVs V cmn Induced voltage and noise Sensor and signal conditioning source Common mode voltages also appear on shielded systems due to differences between input potentials

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et438b-4.pptx 18 Common mode voltage due to ground - + V+V+ V-V- VoVo VdVd Differential Amp Total common mode voltage V cm = V cmn +V cmg OP AMP differential inputs designed to reject common mode voltages. Amplify only V d = V + - V -.

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et438b-4.pptx 19 Define: A c = gain of OP AMP to common mode signals (designed to be low) A d = differential gain of OP AMP. Typically high (A d = 200,000 for 741) Ideal OP AMPs have infinite A d and zero A c Common mode rejection ratio (CMRR) is a measure of quality for non-ideal OP AMPs. Higher values are better. WhereA d = differential gain A c = common mode gain

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et438b-4.pptx 20 Common Mode Rejection (CMR) calculation CMR units are db. Higher values of CMR are better. Example: A typical LM741 OP AMP has a differential gain of 200,000. The typical value of common mode rejection is 90 db. What is the typical value of common mode gain for this device

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et438b-4.pptx 21 From problem statement V d = 200,000 CMR = 90 db Solve for A c by using the anitlog Raise both sides to power of 10 Solve for A c Plug in values and get numerical solution Common mode gain is 6.32 for typical LM741

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et438b-4.pptx 22 Characteristics of Instrumentation Amplifiers - Amplify dc and low frequency ac (f<1000 Hz) - Input signal may contain high noise level -Sensors may low signal levels. Amp must have high gain. - High input Z to minimize loading effects -Signal may have high common mode voltage with respect to ground Differential amplifier circuit constructed from OP AMPs are the building block of instrumentation amplifiers

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et438b-4.pptx 23 Amplifies the difference between +/ - terminals Input/output Formula To simplify let R 1 = R 3 and R 2 = R 4 Polarity of OP AMP input indicates order of subtraction

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et438b-4.pptx 24 Practical considerations of basic differential amplifiers - Resistor tolerances affect the CMRR of OP AMP circuit. Cause external unbalance that decreases overall CMRR. - Input resistances reduce the input impedance of OP AMP -Input offset voltages cause errors in high gain applications -OP AMPs require bias currents to operate

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et438b-4.pptx 25 To minimize the loading effects of the OP AMP input resistors, their values should be at least 10x greater than the source impedance Example: Determine the loading effects of differential amp Input on the voltage divider circuit. Compare the output predicted by differential amplifier formula to detailed analysis of circuit. Assume no loading effects and use the OP AMP gain formula V R2 + I -

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et438b-4.pptx 26 Find the output ignoring the loading effects that the OP AMP has on the voltage divider. Now solve the circuit and include the loading effects of the OP AMP input resistors. Use nodal analysis and check with simulation. Remember the rules of ideal OP AMPs: I in = 0 and V + =V -

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et438b-4.pptx 27 Solution using nodal analysis

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et438b-4.pptx 28 Solve simultaneous equations and determine percent error due to loading

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et438b-4.pptx 29 Results of operating point analysis in LTSpice V 1 =0.514 V V 2 =0.229 V V 0 =0.286 V

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et438b-4.pptx 30 Dc motor draws a current of 3A dc when developing full mechanical power. Find the gain of the last stage of the circuit so that the output voltage is 5 volts when the motor draws full power. Also compute the power dissipation of the shunt resistor

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et438b-4.pptx 31 Example Solution 2.46 V V + V d -

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et438b-4.pptx k R f = ? Vdc 2.46 V Caution: Note the maximum differential Voltage specification of OP AMP. (30 V for LM741) R f is a non-standard value. Use 8.2 kΩ resistor and 5 kΩ potentiometer. Calibrate with 300 mV source Until 5.00 V output is achieved Compute power dissipation at full load I= 3 A so…. Use 1 Watt or greater Standard value

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et438b-4.pptx 33 Simulated with Circuit Maker (Student Version)

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