Chapter 9 Miscellaneous Measurements by Yixin Ma 15/05/2013 miscellaneous [,mIsa'leInias ]consisting of many different kinds of things that are not connected and do not easily form a group. 混杂的；各种各样的. 235 CONTENTS 9.1 Time,Frequency,and Phase-Angle Measurement 9.2 Liquid Level 9.3 Humidity 9.4 Chemical Composition 9.5 Current and Power Measurement 9.6 Using "Observers"to Measure Inaccessible Variables in a Physical System 9.7 Sensor Fusion(Complementary Filtering)
Chapter 9 Miscellaneous Measurements by Yixin Ma 15/05/2013 miscellaneous【ˌmɪsəˈleɪniəs】: consisting of many different kinds of things that are not connected and do not easily form a group. 混杂的；各种各样的. CONTENTS 9.1 Time, Frequency, and Phase-Angle Measurement 9.2 Liquid Level 9.3 Humidity 9.4 Chemical Composition 9.5 Current and Power Measurement 9.6 Using “Observers” to Measure Inaccessible Variables in a Physical System 9.7 Sensor Fusion (Complementary Filtering) 2/35
3/35 9.1 Time,Frequency,and Phase-Angle Measurement The most convenient and widely utilized instrument for accurate measurement of frequency and time interval is the electronic counter-timer. Time and frequency standard is a piezoelectric crystal oscillator( 电晶体振荡器)； Typical frequency is 107 Hz,drift in frequency may be of the order of 3 parts in 107 Hz; .Quartz crystal clocks use various approaches to deal with the effects of temperature on the clock frequency,which is about 3 ppm (parts per million)for 0~50 C. 4/35 9.1 Time,Frequency,and Phase-Angle Measurement Signal Amplifier and shaper Gate 106 10310103 100 10 回回@回回回回 Decimal-Counting Units Gate control 102 10°6 10-3 10-4 sec sec sec Crystal oscillotor 10 MHZ Time-base dividers Fig.9.1(a)Frequency measurement The signal goes through a gating circuit to the decimal-counting units for a precisely timed interval(EPUT =event per unit time). Use a 2nd signal in place of the crystal oscillator to get the frequency ration of the two signals
9.1 Time, Frequency, and Phase-Angle Measurement The most convenient and widely utilized instrument for accurate measurement of frequency and time interval is the electronic counter-timer. z Time and frequency standard is a piezoelectric crystal oscillator (压 电晶体振荡器); z Typical frequency is 107 Hz, drift in frequency may be of the order of 3 parts in 107 Hz; z Quartz crystal clocks use various approaches to deal with the effects of temperature on the clock frequency, which is about 3 ppm (parts per million) for 0~50 ℃. 3/35 Fig. 9.1(a) Frequency measurement - The signal goes through a gating circuit to the decimal-counting units for a precisely timed interval (EPUT =event per unit time). - Use a 2nd signal in place of the crystal oscillator to get the frequency ration of the two signals. 9.1 Time, Frequency, and Phase-Angle Measurement 4/35
9.1 Time,Frequency,and Phase-Angle Measurement 5/35 Crystal oscillator 10 MHz Gote Decimal-counting units 回回回回回回回 Signal Gote Amplifier open closed Signal Gate and Trigger control shaper level Time Irigger-level control -0.0860314sec+ Fig.9.1(b)Period Measurement The trigger-level control is adjusted so that triggering occurs on the steepest part of the signal waveform to reduce error. Define frequency fo=/fc,fc is the frequency of crystal oscillator,for a 1-s sampling period,when f>fo frequency should be measured and when f<fo,period should be measurement to get better accuracy. 6/35 9.1 Time,Frequency,and Phase-Angle Measurement Crystal oscillator 10 MHz Gate 回回回回回回回 Slope Gate control Input 4 signal 1 Trigger Stop Amplifier and shaper Trigger-level control 路di计 Trigger Slope+、 Amplifier and shoper Trigger-level control 0.0074319sec (c)Time-interval measurement Fig.9.1(c)Time-Interval Measurement Two separate events have been transduced to electrical pulses.One is used to open the gate and the other is used to close the gate
Fig. 9.1(b) Period Measurement - The trigger-level control is adjusted so that triggering occurs on the steepest part of the signal waveform to reduce error. - Define frequency ࢌ = ࢌ , fC is the frequency of crystal oscillator, for a 1-s sampling period, when f>f0 frequency should be measured and when f<f0, period should be measurement to get better accuracy. 9.1 Time, Frequency, and Phase-Angle Measurement 5/35 9.1 Time, Frequency, and Phase-Angle Measurement Fig. 9.1(c) Time-Interval Measurement Two separate events have been transduced to electrical pulses. One is used to open the gate and the other is used to close the gate 6/35
7/35 9.1 Time,Frequency,and Phase-Angle Measurement Crystal oscillator 10MH2 Gate 回回回回回回回 Gate control Start Input Trigger Trigger Amplifier Stop stort stop signal and shaper Amplifier 0.0006478sec and shaper (d)Pulse-width measurement Fig.9.1(d)Pulse-Width Measurement (Only one input signal) 8/35 9.1 Time,Frequency,and Phase-Angle Measurement Reference oscillator 360u 回回回回回回回 中，deg F sin wt Trigger start Gate control Amplifier ↑Stop and shaper Start 5 sin (w =-43 Amplifier and shaper Trigger stop (e) Fig.9.1(e):The phase-angle Measurement between two sinusoidal signals of the same frequency To use this method,the amplitude of the two signals must be made equal and the triggering point of the two channels adjusted to be the same
9.1 Time, Frequency, and Phase-Angle Measurement Fig. 9.1(d) Pulse-Width Measurement (Only one input signal) 7/35 Fig. 9.1(e): The phase-angle Measurement between two sinusoidal signals of the same frequency To use this method, the amplitude of the two signals must be made equal and the triggering point of the two channels adjusted to be the same. 9.1 Time, Frequency, and Phase-Angle Measurement 8/35
9/35 9.1 Time,Frequency,and Phase-Angle Measurement "Clean" “Noisy" input signal input signal Upper hysteresis level Peak-to-peak sensitivity OV Lower hysteresis level Output of Schmitt trigger Figure 9.2 Use of Counter Hysteresis to Reject Noise To prevent false counts as a result of the unavoidable noise on input signals,counter input circuits use a Schmitt trigger type of circuit with a built-in hysteresis effect(迟滞效应). 10/35 9.1 Time,Frequency,and Phase-Angle Measurement The major error sources in counter-timers are categorized as: 1.The士1 count ambiguity(歧义，模糊性)，a random error; 2.The time-base error,resulting from temperature and line-voltage changes, aging,and short-term instability; 3.The trigger error,a random error due to noise that causes early or late crossing of hysteresis level; 4.Channel-mismatch error,a systematic error present in two-channel measurements when input-circuit rise times and/or propagation delays are not identical for the two channels. Frequency measurements are subject only to the +1 count and time-base errors. Period measurements have these two errors plus the trigger error,while time- interval measurements suffer from all four
Figure 9.2 Use of Counter Hysteresis to Reject Noise z To prevent false counts as a result of the unavoidable noise on input signals , counter input circuits use a Schmitt trigger type of circuit with a built-in hysteresis effect (迟滞效应). 9.1 Time, Frequency, and Phase-Angle Measurement 9/35 9.1 Time, Frequency, and Phase-Angle Measurement z The major error sources in counter-timers are categorized as: 1. The±1 count ambiguity (歧义,模糊性), a random error; 2. The time-base error, resulting from temperature and line-voltage changes, aging, and short-term instability; 3. The trigger error, a random error due to noise that causes early or late crossing of hysteresis level; 4. Channel-mismatch error, a systematic error present in two-channel measurements when input-circuit rise times and/or propagation delays are not identical for the two channels. z Frequency measurements are subject only to the ±1 count and time-base errors. Period measurements have these two errors plus the trigger error, while timeinterval measurements suffer from all four. 10/35
11/35 9.1 Time,Frequency,and Phase-Angle Measurement Analysis of the trigger error gives the standard deviation of the timing error as: rms trigger error N+N+N+N (9.2) Where Nc:counter noise,V rms(typically 0.2 to 2.0 mV) No:start-signal noise,V rms N:stop-signal noise,V rms a:slew rate(变化率)of start signal at trigger(触发)point,V小s V:slew rate of start signal at trigger point,V/s 2/35 9.1 Time,Frequency,and Phase-Angle Measurement eole;=0 0360° 90°270° E;sin wt E。sin(wt+φ) +180°，-180° Fig.9.3(a)Phase Angle from Lissajous Figure(利萨如图形) Another common method of phase-angle measurement involves cross-plotting the two sinusoidal signals against each other,by using an XY plotter for very low frequencies and an oscilloscope for high frequencies.The cross plot can be shown to be an ellipse,and suitable measurement on this ellipse give the phase angle
9.1 Time, Frequency, and Phase-Angle Measurement z Analysis of the trigger error gives the standard deviation of the timing error as: rms trigger error ே మାேೞೌ మ ሶ ೌ మ ே మାேೞ್ మ ሶ ್ మ (9.2) Where NC: counter noise, V rms (typically 0.2 to 2.0 mV) Nsa: start-signal noise, V rms Nsb: stop-signal noise, V rms ܸሶ : slew rate (变化率) of start signal at trigger (触发) point, V/s ܸሶ : slew rate of start signal at trigger point, V/s 11/35 Fig. 9.3(a) Phase Angle from Lissajous Figure (利萨如图形) z Another common method of phase-angle measurement involves cross-plotting the two sinusoidal signals against each other, by using an XY plotter for very low frequencies and an oscilloscope for high frequencies. The cross plot can be shown to be an ellipse, and suitable measurement on this ellipse give the phase angle. 9.1 Time, Frequency, and Phase-Angle Measurement12/35
3/35 9.1 Time,Frequency,and Phase-Angle Measurement Ei sin wt E。sin(wt+p 11N11113s1901t11共11/ 180 0 Fosin wt Calibrated phase-shift device Figure 9.3b Phase Angle from Lissajous Figure-Straight line An alternative method employing the same basic principle but a null technique. The calibrated phase-shift circuit is adjusted until the ellipse degenerates into a straight line.Then the phase angle is read directly from the phase-shifter dial. When the "sinusoidal"signal are noisy and/or distorted,special phase meters and tracking filters may be necessary for accurate measurement. 14/35 9.2 Liquid Level Using Motion Force Tx Measurement and/or control of liquid level in tanks is an important function in many industrial processes and in more exotic()applications, such as the operation and fueling of large liquid-fuel rocket motors. Motion Force transducer transducer (o) (61 Figure 9.4 Liquid Level Measurement Strategies -Fig.9.4(a):a simple float is coupled to some suitable motion transducer to produce an electrical signal proportional to the liquid level. -Fig.9.4(b):a displacer which has negligible motion and measures the liquid level in terms of buoyant force by means of a force transducer
Figure 9.3b Phase Angle from Lissajous Figure – Straight line z An alternative method employing the same basic principle but a null technique. The calibrated phase-shift circuit is adjusted until the ellipse degenerates into a straight line. Then the phase angle is read directly from the phase-shifter dial. When the “sinusoidal” signal are noisy and/or distorted, special phase meters and tracking filters may be necessary for accurate measurement. 9.1 Time, Frequency, and Phase-Angle Measurement 13/35 z Measurement and/or control of liquid level in tanks is an important function in many industrial processes and in more exotic(特殊) applications, such as the operation and fueling of large liquid-fuel rocket motors. 9.2 Liquid Level – Using Motion & Force Tx Figure 9.4 Liquid Level Measurement Strategies ▬ Fig. 9.4(a): a simple float is coupled to some suitable motion transducer to produce an electrical signal proportional to the liquid level. ▬ Fig. 9.4(b): a displacer which has negligible motion and measures the liquid level in terms of buoyant force by means of a force transducer. 14/35
9.2 Liquid Level Using Pressure Tx 15/35 Differential Pressure pressure pickup pickup (d) -Fig.9.4(c)&(d)allow measurement of the liquid level in open and pressure vessels,since hydrostatic pressure (is related directly to liquid level. 个 Air Regulator Pressure slightly higher than greatest liquid head Fig.9.4 Liquid Level Measurement Strategies 一Fig.9.4e:a"bubbler'"or purge(净化；清诜)system,the gas pressure downstream of the flow restriction is the same as the hydrostatic head(静水压头)above the bubble-tube end. 16/35 9.2 Liquid Level -Using Capacitance Tx Probe (one "plate Insulotor of capacitor) 00 Insulator- Tank (other "plate" ot capacitor 0 lg) Figure 9.4 Liquid Level Measurement Strategies -Fig.9.4(f):for essentially nonconducting liquids(conductivity <0.1 uS/cm3),the bare- probe arrangement may be satisfactory since the liquid resistance R is sufficiently high. -Fig.9.4(g):For conductive liquids the probe must be insulated to prevent short- circuiting of capacitance by the liquid resistance
▬ Fig. 9.4(c) & (d) allow measurement of the liquid level in open and pressure vessels, since hydrostatic pressure (静液压) is related directly to liquid level. 9.2 Liquid Level - Using Pressure Tx ▬ Fig. 9.4(e): a “bubbler” or purge(净化;清洗)system, the gas pressure downstream of the flow restriction is the same as the hydrostatic head (静水压头) above the bubble-tube end. Fig. 9.4 Liquid Level Measurement Strategies 15/35 9.2 Liquid Level - Using Capacitance Tx Figure 9.4 Liquid Level Measurement Strategies ▬ Fig. 9.4(f): for essentially nonconducting liquids(conductivity < 0.1 uS/cm3), the bareprobe arrangement may be satisfactory since the liquid resistance R is sufficiently high. ▬ Fig. 9.4(g): For conductive liquids the probe must be insulated to prevent shortcircuiting of capacitance by the liquid resistance. 16/35
17/35 9.2 Liquid Level -Using Radioisotopes Detector (ionization chamber) I loe-upx (9.4) where I intensity of radiation falling on detector; lo intensity at detector with absorning material not present; Radioisotope source e base of natural logarithms; u mass absoption coefficient Fig.9.4(h)Liquid Level (constant for given sorce and absorbing material),cm2/g; Measurement Strategies p≌mass Using Radioisotopes density of absorbing material,g/cm3; (放射性同位素) x thinckness of absorbing materialm,cm. -The absorption (of B-ray or y-ray radiation varies with the thickness of absorbing material between the source and the detector. 1835 9.2 Liquid Level Using Hot-wire or Carbon Resistor Elements -The heat-transfer coefficient at the surface of the resistance element Hot-wire element changes radically(急剧地)when the liquid or carbon resistor surface passes it. -This changes its equilibrium temperature and thus its resistance, causing a change in bridge output voltage. -By locating resistance elements at known height intervals,the tank level may be measured in discrete increments. Fig.9.4(i)Liquid Level Measurement Using Hot-wire or Carbon Resistor Elements
9.2 Liquid Level - Using Radioisotopes ▬ The absorption (吸收) of β-ray or γ-ray radiation varies with the thickness of absorbing material between the source and the detector. Fig. 9.4(h) Liquid Level Measurement Strategies Using Radioisotopes (放射性同位素) ܫ=ܫି݁ఓఘ௫ (9.4) where ܫ ≜ intensity of radiation falling on detector; ܫ ≜ intensity at detector with absorning material not present; ݁ ≜ base of natural logarithms; ߤ ≜ mass absoption coefficient constant for given sorce and absorbing material ,ܿ݉ଶ⁄݃; mass ≜ ߩ density of absorbing material,݃ ܿ݉ଷ ⁄ ; ݔ ≜ thinckness of absorbing materialm, ܿ݉. 17/35 ▬ The heat-transfer coefficient at the surface of the resistance element changes radically(急剧地) when the liquid surface passes it. ▬ This changes its equilibrium temperature and thus its resistance, causing a change in bridge output voltage. ▬ By locating resistance elements at known height intervals, the tank level may be measured in discrete increments. Fig. 9.4 (i) Liquid Level Measurement Using Hot-wire or Carbon Resistor Elements 9.2 Liquid Level - Using Hot-wire or Carbon Resistor Elements 18/35
9.2 Liquid Level Using Ultrasound 1935 2立 ) Figure 9.4 Liquid Level Measurement Using Ultrasonic"Range-finding" Techniques -The "radar"liquid level sensors use similar principles but with microwave energy rather than acoustic().Two versions,noncontact and guided wave(导行波)，are available. 9.3 Humidity -Concepts 20/35 Absolute humidity:an amount of water vapor,usually discussed per unit volume.Generally the mass of water vapor,per unit volume of total moist air. Relative humidity:the ratio of the partial pressure of water vapor in the air-water mixture to the saturated vapor pressure of water at those conditions. The relative humidity of air depends not only on temperature but also on pressure of the system of interest. Specific humidity:the ratio of water vapor to dry air in a particular mass, and is sometimes referred to as humidity ratio.Specific humidity ratio is expressed as a ratio of mass of water vapor,per unit mass of dry air. o Partial pressure is the pressure which the gas would have if it alone occupied the volume.The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture. In common use are the relative humidity,dew-point()temperature, mixing ratio or specific humidity,and volume ratio (parts of water vapor per million parts of air)
(j) Figure 9.4 Liquid Level Measurement Using Ultrasonic “Range-finding” Techniques ▬ The “radar” liquid level sensors use similar principles but with microwave energy rather than acoustic(声学). Two versions, noncontact and guided wave(导行波), are available. 9.2 Liquid Level - Using Ultrasound 19/35 z Absolute humidity: an amount of water vapor, usually discussed per unit volume. Generally the mass of water vapor, per unit volume of total moist air. z Relative humidity: the ratio of the partial pressure of water vapor in the air-water mixture to the saturated vapor pressure of water at those conditions. The relative humidity of air depends not only on temperature but also on pressure of the system of interest. z Specific humidity: the ratio of water vapor to dry air in a particular mass, and is sometimes referred to as humidity ratio. Specific humidity ratio is expressed as a ratio of mass of water vapor, per unit mass of dry air. z Partial pressure is the pressure which the gas would have if it alone occupied the volume. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture. z In common use are the relative humidity, dew-point(露点) temperature, mixing ratio or specific humidity, and volume ratio (parts of water vapor per million parts of air). 9.3 Humidity - Concepts 20/35