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