an accurate air temperature measurement system based on an

An accurate air temperature measurement system based on an envelopepulsed ultrasonic time-of-flight technique

Y. S. Huang and Y. P. HuangDepartment of Electrical Engineering, National Cheng-Kung University, Tainan, 701 Taiwan,Republic of China

K. N. HuangDepartment of Electronic Engineering, I-Shou University, Kaohsiung, 840 Taiwan, Republic of China

M. S. Younga�

Department of Electrical Engineering, National Cheng-Kung University, No. 1 University Road 70101Tainan, Taiwan, Republic of China

�Received 26 August 2007; accepted 6 October 2007; published online 9 November 2007�

A new microcomputer based air temperature measurement system is presented. An accuratetemperature measurement is derived from the measurement of sound velocity by using an ultrasonictime-of-flight �TOF� technique. The study proposes a novel algorithm that combines both amplitudemodulation �AM� and phase modulation �PM� to get the TOF measurement. The proposed systemuses the AM and PM envelope square waveform �APESW� to reduce the error caused by inertiadelay. The APESW ultrasonic driving waveform causes an envelope zero and phase inversionphenomenon in the relative waveform of the receiver. To accurately achieve a TOF measurement,the phase inversion phenomenon was used to sufficiently identify the measurement pulse in thereceived waveform. Additionally, a counter clock technique was combined to compute the phaseshifts of the last incomplete cycle for TOF. The presented system can obtain 0.1% TOF resolutionfor the period corresponding to the 40 kHz frequency ultrasonic wave. Consequently, with theintegration of a humidity compensation algorithm, a highly accurate and high resolution temperaturemeasurement can be achieved using the accurate TOF measurement. Experimental results indicatethat the combined standard uncertainty of the temperature measurement is approximately 0.39 °C.The main advantages of this system are high resolution measurements, narrow bandwidthrequirements, and ease of implementation. © 2007 American Institute of Physics.�DOI: 10.1063/1.2804115�

I. INTRODUCTION

Many methods have been introduced to measure thetemperature of a gas. Electronic transducers such as the ther-mistor, thermocouple, or thermopile can detect and measuretemperature with a relatively good resolution. All of thesetransducers require physical contact with the gas being mea-sured. Over the past several decades, ultrasonic thermometryhas evolved as a new temperature measurementtechnology.1,2 Ultrasonic thermometry is based on the prin-ciple that sound velocity in any material is a function oftemperature. In an ideal gas, at a constant pressure, the soundvelocity c is given by3,4

c =��RT

M, �1�

where �, R, T, and M are the specific heat ratio, universal gasconstant, absolute temperature �in kelvin�, and molar mass,respectively. As can be seen from Eq. �1�, the sound velocityis directly proportional to the square root of the absolute

temperature. Therefore, the sound velocity measurement canbe used to determine temperature.

The common method to measure sound velocity is de-rived from the time-of-flight �TOF� measurement.5 For ex-ample, the distance between an ultrasonic transmitter and areceiver when divided by the ultrasonic pulse travel timebetween them yields the average sound velocity. Generally, amore accurate distance measurement can be obtained bymeasuring the phase shift quantity between the ultrasonicallytransmitted and the received waves.6 The distance d betweenthe transmitter and receiver is evaluated by

d =c

TF= �N +

�

2�� c

f, �2�

where c is the sound velocity, TF is time of flight, N is theinteger number of the wavelengths �c / f� counted, � repre-sents the phase angle of the last pulse, which is smaller than2�, and f is the ultrasonic frequency. Nevertheless, whenusing TOF to measure sound velocity, the system error isprimarily due to the inertia phenomenon of amplitude delayand the uncertainty caused by environmental factors such astemperature and humidity.3 The errors related to humiditycan be satisfactorily compensated for by adding a humiditysensor circuit to the ultrasonic transducers. The root cause of

a�Author to whom correspondence should be addressed. Electronic mail:[email protected]

REVIEW OF SCIENTIFIC INSTRUMENTS 78, 115102 �2007�

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the amplitude delay inertia phenomenon is the echo wave-form’s relatively long rise time. The starting vibration causedby an ultrasonic piezoelectric transducer induces a relativelylong echo waveform rise time.7 Figure 1 shows the emissionand echo waveforms from a pair of ultrasonic transducers.Inertia delay is included in the measured TOF and the delaytime is dependent on the detection threshold level of the echowaveform. The above combination makes the accurate TOFhard to predict. The errors related to the inertia delay are themost difficult to overcome when the TOF method is used.

Different techniques exist to determine the time of flight.The simplest procedure is the threshold-crossing method.When using this technique, the arrival time is calculatedonce the echo signal exceeds the threshold level. However,the threshold-crossing method has two major measurementproblems. One is that the low signal-to-noise ratio �SNR�will result in substantial measurement errors. Additionally,the use of narrowband piezoelectric transducers will also re-sult in significant measurement errors.8 The errors related tothe threshold-crossing method can be reduced by making thethreshold level variable or using the automatic gain con-trolled technique. However, this procedure still has difficultyin providing a highly accurate measurement.9,10 Digital-signal-processing �DSP� methods are based on the use of across-correlation function to determine TOF.7,11 Although theuse of DSP techniques can improve TOF accuracy, they re-quire complex hardware and long computing time. Addition-ally, the binary-frequency shift-keyed �BFSK� signal is an-other alternative method to measure TOF.12 However, theBFSK method estimates TOF by phase-digitized informationfrom the received signal, which is often influenced by noiseand will likely increase measurement errors. Furthermore,the BFSK method requires a complex circuit and two orthree different waveform frequencies.6

In a previous study, titled “Envelope pulsed ultrasonicdistance measurement system based upon amplitude modu-lation and phase modulation,” a new driving algorithm for anultrasonic transmitter was proposed.13 This algorithm canovercome the inertia delay problem and achieve a more ac-curate TOF measurement. The amplitude madulation �AM�and phase modulation �PM� envelope square waveform�APESW� experiment’s results confirmed the accuracy ofthis method as a tool for distance measurement. The objec-

tive of the present study is to use the accurate TOF to obtaina more precise air temperature measurement. The proposeddriving algorithm produces an envelope zero and a phaseinversion in the echo waveform. This is caused by the self-interference phenomenon and can be used to derive an accu-rate TOF calculation.8 The proposed method only requires asingle 40 kHz signal. Additionally, the proposed driving al-gorithm benefits from noise resistance and ease of imple-mentation. Furthermore, the proposed TOF measurementsystem can be used in conjunction with a humidity sensorand a compensation algorithm. The above combination pro-duces a highly accurate and high resolution temperaturemeasurement.

II. METHOD

A. Ultrasonically transmitted signals and receivedsignals

Ultrasonic waves produced by piezoelectric transducerscan be modeled as a damped sinusoid by7,8

f�t� � Atne−�t sin��t + �� , �3�

where n, �, �, and � are transducer dependent parameters, Ais the wave amplitude, and � is the angular resonance fre-quency of the transducer. Additionally, t represents time. Thesupply of two sequential pulse trains to a piezoelectric trans-ducer will generate two waves f1�t� and f2�t�, respectively, as

f1�t� = Atne−�t sin��t + ��u�t� �4�

and

f2�t� = A�t − td�ne−��t−td� sin��t − �td + ��u�t − td� , �5�

where td is the time interval between the starting points ofthe two pulse trains and u�t� represents the unit step function.The output of the transmitter is a self-interference signalf int�t� and can be expressed as8

f int�t� = f1�t� + f2�t� = Ae−�t�tn sin��t + ��u�t�

+ �t − td�ne�td sin��t − �td + ��u�t − td�� . �6�

If td is smaller than the effective signal length, the two waveswill coexist during a period of time and create a new easilyidentifiable combined ultrasonic wave. When td is chosensuch that f1�t� and f2�t� have a phase difference of �, or

td =�2k + 1��

��k = 0,1,2, . . . � , �7�

then Eq. �6� becomes

f int�t� = Ae−�ttn1 − �1 −td

t�n

e�tdsin��t + �� t � td� .

�8�

The envelope is zero for t= tz, satisfying

tz =td

1 − e−��/n�td. �9�

The phase of the receiver waveform before and after tz aredominated by f1�t� and f2�t�, respectively. Consequently,there will be a phase difference �� before and after theenvelope zero.

FIG. 1. The emission and the echo waveform from a pair of ultrasonictransducers. Accurate TOF is hard to predict because inertia delay is in-cluded and the measured TOF is dependent on the echo waveform’s detec-tion threshold level.

115102-2 Huang et al. Rev. Sci. Instrum. 78, 115102 �2007�


Figure 2 shows the proposed ultrasonic driving wave-form. The APESW is proposed to drive the ultrasonic trans-mitter for TOF measurement. The APESW wave is based onthe envelope zero principle and phase inversionphenomenon.13 One APESW wave has three components.First it transmits ten low-amplitude pulses, which are fol-lowed by two high-amplitude pulses. Subsequently theAPESW transmits another ten low-amplitude pulses. Theamplitude and phase of the measurement waves are modu-lated to enhance TOF measurement’s envelope zero andphase inversion phenomenon. The measurement waves aremodulated to have higher amplitudes. Additionally, they startwith a double-width pulse, which is used for phase modula-tion. As a result, the phases of the measurement waves andthe following ten low-amplitude waves �pulse train 2, phaseII� are significantly different from the first ten waves �pulsetrain 1, phase I�. According to the 40 kHz clock, there is aphase difference of 180° �� between the two pulse trains.This will cause an envelope zero and phase inversion phe-nomenon, both of which sufficiently identify the pulse as themeasurement pulse in the ultrasonic received waveforms.

Figure 3 shows the system block diagram which is usedfor generating the APESW signal and processing the re-ceived signal. The APESW signal is originally generated,with phase modulation, from a complex programmable logicdevice �CPLD�. The signal is then processed by a level-shifter and amplitude modulation circuit. The modulated sig-nal, transmitted signal ST, is then sent to the driving circuitand forms the driving waveform TX. The driving waveform

TX drives the ultrasonic transmitter to transmit the waves.The signal received, by the ultrasonic receiver, is processedby a preamplifier circuit and forms the received sinusoidwaveform RX. By using a clamping and a Schmitt-triggercircuit, the received signal SR is transformed from a sinusoidwave to a square wave, which is also known as a transistor-transistor logic �TTL� signal. Lastly, the signal is sampled bya CPLD for analysis.

When an APESW wave is transmitted to the ultrasonictransmitter, there is a resulting echo pulse wave that is pro-duced by the receiver. This process is shown in Fig. 4. Thetransmitter and receiver are placed directly in front of eachother. The waveforms are measured by a mixed signal oscil-loscope �54622D, Agilent, USA�. The proposed wave ST, asseen in Fig. 2, is used to drive the transmitter and then formsthe driving waveform TX. The two pulse trains of the drivingwaveform TX have a phase difference of �, which causes theenvelope zero and phase inversion phenomena in the re-ceived waveform RX. The received waveform RX is thenconverted into a TTL square waveform SR after being pro-cessed by a clamping circuit and a Schmitt-trigger circuit.The measurement pulse is easily identified via the phasemodulation characteristic. Two phase modulation detectors�PM detectors 1 and 2� are used to detect the phase changingphenomenon of the transmitted and received signals, respec-tively. The PM detectors determine the phase according tothe 40 kHz counter clock at each rising edge of the ST andthe SR signals. PM detector 1 produces an output voltage thatchanges from low to high at the rising edge of the measure-ment pulse of ST. The amplitude of the received waveformRX is relatively low during the envelope zero phase changeperiod. During the envelope zero phase, it is normal for theSR to have no output at all. As a result of the zero outputfrom SR, during the envelope zero phase, the first phasechange that is detected by PM detector 2 is the relative mea-surement pulse. Consequently, the measurement of TOFstarts from the rising edge of the measurement pulse, as de-tected by PM detector 1, and stops when the relative pulse inthe received signal is as detected by PM detector 2.

FIG. 2. The proposed APESW wave has three components. First it transmitsten low-amplitude pulses. Second, it transmits two high-amplitude pulses.Lastly, the APESW transmits another ten low-amplitude pulses. Pulse train2, which is the measurement pulse and the following ten low-amplitudepulses, has a phase difference of � when compared to pulse train 1.

FIG. 3. The APESW signal generation, transmission, and processing systemblock diagram.

FIG. 4. APESW waves ST are supplied to an ultrasonic transmitter. Thecorresponding receiver generates echo waves RX. Echo waves RX are trans-formed from an analog signal to received digital signal SR. Two phasemodulation detectors �PM detectors 1 and 2� are used to sense the transmit-ted measurement pulse and the received relative pulse. The measurement ofTOF is derived from the time difference between the outputs of PM detec-tors 1 and 2.

115102-3 Ultrasonic temperature measurement Rev. Sci. Instrum. 78, 115102 �2007�


B. Computation of TOF and sound velocity

As shown in Fig. 5, TOF is the sum of the full clockcycles and the last incomplete cycle. The TOF of the mea-surement �TF� can be expressed as

TF = �N +�ST

2��Tperiod, �10�

where N represents the integer of the full clock cycles, �ST isthe phase shift quantity between emission and echo waves,and Tperiod is the time period of the counter clock.

To calculate the value of the integer N, the system usesthe counter clock �f =40 kHz�, which is derived from thesystem clock �fclk=40 MHz� divided by 1000. The ultrasonictransmitter driving waveform ST is also aligned with the40 kHz counter clock. Therefore, the integer N can be esti-mated by N=int �TF /Tperiod�=int�TFf�=int �TF�40�103�,where TF is the actual traveling time of the ultrasonic waves,Tperiod represents the period of the counter clock, and intrepresents the integer of the given number. As shown inFig. 5, N is counted from the falling edge of the 40 kHzcounter clock that corresponds to the rising edge of the mea-surement pulse �the rising edge of PM detector 1�. Addition-ally, the counter clock stops at the rising edge of PM detector2, which rises once it detects the phase inversion of the re-ceived signal.

A counter clock technique is used to compute the phaseshift of the last incomplete cycle. This is done to avoid thelimitations caused by the amplitude of the signal and thefinite bits of the analog to digital �A/D� converter.13,14 Asshown in Fig. 6, the phase shift between transmitted andreceived signals ��ST� is calculated from the last incompletecycle. The phase shift quantity is calculated by the originalsystem clock �fclk=40 MHz�. Therefore, the system’s theo-retical maximum TOF resolution is 0.025 s 1 / fclk

=1/40�106 s=0.025 s�. This represents 0.1% of the pe-riod corresponding to the 40 kHz ultrasonic wave frequency.The 40 MHz counter clock phase shift measurement is acti-vated when the system senses the phase inversion of thereceived signal �the rising edge of PM detector 2�. Thecounter clock is deactivated once the next falling edge of the40 kHz counter clock is detected. The phase quantity �� canbe derived from the counting number �m� by

� = m40 kHz

40 MHz2� =

m

10002� . �11�

The phase shift quantity ��ST� between transmitted signal ST

and received signal SR can then be obtained by

�ST = 2� − � . �12�

The following is the algorithm for computing sound ve-locity. If distance d is constant, then the average velocity ofsound c between the transmitter and receiver can be calcu-lated by

c = d/TF = d��N +�ST

2��Tperiod , �13�

where N is the counted integer of the given wave periods, �ST

is the phase shift quantity of the incomplete cycle, and TF isthe TOF. The sound velocity measurement algorithm can beeasily programed into a digital microprocessor system toprovide highly precise measurements.

C. Calculation of temperature

According to Eq. �1�, when everything else remains con-stant, an increase in absolute temperature will cause an in-crease in the speed of sound. The specific heat ratio � isdependent on the gaseous molecule’s degree of freedom.4

The degree of freedom is dependent on the complexity of themolecule. Since air is composed primarily of diatomic mol-ecules, � is equal to 1.4 when the air is dry �0% humidity�. Rand M are also constant in dry air. The universally acceptedvalue for sound velocity c, at 0 °C and 1 atm �760 mm Hg�with 0.03 mol% of carbon dioxide, is 331.45±0.05 m/s foraudio frequencies.4 The formula below shows the unit con-version of Eq. �1�, from kelvin to centigrade, simultaneouslyincorporating the universally accepted value for sound veloc-ity c,

FIG. 5. The TOF calculation is the sum of the 40 kHz counter clock integer�N� and the last incomplete cycle’s phase shift ��ST� quantity. The transmit-ted signal ST is aligned with the 40 kHz counter clock’s rising edge.

FIG. 6. The phase shift quantity is counted by the original system clock�fclk=40 MHz�. The counter clock is activated when the system senses thephase inversion of the received signal �the rising edge of PM detector 2�.The counter clock is deactivated once the next falling edge of the 40 kHzcounter clock is detected. The phase shift quantity ��ST� between the trans-mitted and received signals can be obtained by calculating the phase quan-tity �� from the equation �ST=2�−�.



c�t� = 331.45�1 +t

273.15�14�

or

t = 273.15� c�t�331.45

�2

− 1 , �15�

where t is the temperature in °C. Note that Eqs. �14� and �15�are only suitable under the specified dry environment air.Additionally, to compensate for air with moisture �water va-por�, the formulas require correction.

D. Correction of humidity effects

To accurately account for the effects of humidity onsound velocity, the specific heat ratio � and molar mass M ofEq. �1� must be modified.2,4 The specific heat ratio � is de-pendent on the degree of freedom of the gaseous moleculeand can be expressed as

� =d + 2

d, �16�

where d is the air molecules’ number of degrees of freedom.The degree of freedom depends on the complexity of themolecule. Since the composition of air is primarily two atommolecules �diatomic�, it has five degrees of freedom �d=5�.Therefore the dry air calculation for � is �=1.4. If humidityh is defined as the fraction of water molecules, with six de-grees of freedom, then the average number of d per moleculewill increase to 5+h for moist air. Therefore Eq. �16� can berewritten as

�h =7 + h

5 + h, �17�

where �h represents the specific heat ratio which includes theeffect of moisture. The average molecular weight M of dryair is equal to 29 g/mol, which will decrease with the pres-ence of water �with a molecular weight of 18 g/mol�. Thetotal average molecular weight of moist air Mh can be ex-pressed as

Mh = 29 − �29 − 18�h = 29 − 11h . �18�

The fraction of water molecules h in Eqs. �17� and �18�can be derived from the relative humidity �RH� �expressed asa percentage� by4

h =0.01RH � e�t�

p, �19�

where p equals ambient pressure which at 1 atm air pressureis 1.013�105 Pa. Additionally, e�t� is the vapor pressure ofwater at temperature t. Representative values of e�t� aregiven below in °C:

e�5� = 872 Pa, e�10� = 1228 Pa, e�15� = 1705 Pa,

e�20� = 2338 Pa, e�30� = 4243 Pa, e�40� = 7376 Pa.

Since the universal gas constant R and the absolute tem-perature T of Eq. �1� remain the same in moist and dry air,the ratio of sound velocity �correction factor CFh� in moistair �ch� and dry air �cd� can be expressed as

CFh =ch

cd=

��h/Mh

��d/Md

=��h/Mh

�1.4/29= 4.5513� �h

Mh. �20�

Equations �18�–�20� can be used to correct the effects ofhumidity on the sound velocity c measurement. Figure 7shows the variations in the sound velocity ratio CFh whenhumidity is present under six temperature values. Figure 7demonstrates that CFh increases with humidity. Therefore,Eq. �15�, which computes temperature t, can be revised as

t = 273.15� cd

331.45�2

− 1 = 273.15� ch/CFh

331.45�2

− 1 ,

�21�

where CFh is the correction factor for the humidity effect,and ch and cd are the sound velocities at relative humidity hand dry air, respectively.

III. SYSTEM IMPLEMENTATION

A. Description of the hardware system

The hardware implementation is shown in Fig. 8. Theultrasonic transmitted signals are generated in a digital for-mat by a CPLD �FLEX10K10, Altera Corporation, USA�. To

FIG. 7. The effect of humidity on sound velocity ratio �ch /cd� for six tem-perature values.

FIG. 8. The system’s hardware circuit, including the driving circuit for theultrasonic transmitter and the amplifier circuit for the ultrasonic receiver.



generate the proposed APESW signal, an AM signal and aPM signal are separately generated and sent to an amplitudemodulation circuit and a level-shift circuit. The amplitudemodulation circuit consists of a voltage regulator �7805,Fairchild Semiconductor, USA�, a NPN transistor �2SC1815,Toshiba, Japan�, three resistors �R1, R2, R3�, and a capacitor�C1�. The output amplifier’s �CD4069, National Semicon-ductor, USA� supplied voltage is altered by the AM signalfrom the CPLD. To modulate the amplitude of the transmit-ter’s driving waveform, the supplied voltage is switched be-tween +5 and +12 V. When the AM signal is at the +5 Vlevel, the NPN transistor will work in the saturation regionand the voltage regulator will bypass the R3 resistor andconnect to the ground �0 V�. As a result, the regulator’s out-put voltage will be +5 V. When the control signal level is0 V, the NPN transistor will work in the cut-off region andthe R3 and R2 resistors are combined shifting the outputvoltage to +12 V. The voltage levels of the output amplifierCD4069 are +5 and +12 V. However +3.3 V is required forthe CPLD signals. Therefore a level-shift circuit is added toshift the transmitter’s PM signal. The level-shift circuit con-sists of a buffer �CD4050, National Semiconductor, USA�and an open-collector buffer �74HC07, ST Microelectronics,USA�. Figure 9 shows the relative waveform and the voltagelevel of the AM signal, PM signal, the supplied power for theCD4069, and the APESW. After amplitude modulation, theAPESW has two signal levels, +5 and +12 V. Additionally,the phase modulation can be achieved by controlling thepulse width of the transmitted signal from the CPLD�PM signal�.

The ultrasonic transmitter/receiver �400ST160/

400SR160, Pro-Wave Electronics Corporation, Taiwan� isspecified to have a 55° beam angle, 40 kHz center frequency,and 2 kHz bandwidth. The receiving sensitivity is specifiedas −60 dB at 40 kHz �0 dB=1 V/bar�. The receiver circuitconsists of three main components, a preamplifier �uA741,Texas Instruments�, followed by a clamping circuit, andlastly an inverting Schmitt trigger �74HC14, Texas Instru-ments, USA�. The clamping circuit consists of a diode�1N4148, Fairchild Semiconductor, USA� and a capacitor�C4�. It clamps the receiver signal and limits it to a positivelevel between 0 and 2 V. The clamped signal is then trans-formed from a sinusoid to a square wave by an invertingSchmitt trigger. Finally, the received signal SR is thensampled by the CPLD.

The CPLD measuring system is equipped with anAPESW signal generator and a phase detector. Therefore theCPLD can be used to govern the operation of the entire sys-tem and compute the measured TOF. Figure 10 shows theblock diagram of the programed circuit inside the CPLD.The 40 MHz system clock is divided by 1000 to generate the40 kHz clock. The 40 kHz signal is used as a reference clockfor both the 40 kHz clock counter and phase quantity counterblock. The 40 kHz clock counter is used as a reference forthe driving waveform controller and the N counter block.The driving waveform controller block transmits the AM andPM control signals to the amplitude modulation and level-shift circuits, respectively. After the PM signal is modulated,the pulse width phase change is detected by PM detector 1.PM detector 1 then sends a signal to the N counter blockinitiating the start of the measurement pulse. The relativemeasurement pulse of the received signal is analyzedthrough PM detector 2. As soon as the relative measurementpulse is detected, the phase modulation detector 2 sends asignal to deactivate the N counter. Simultaneously, the phasequantity counter block, which uses 40 MHz clock to calcu-late the phase shift quantity �ST, is activated by PM detector2. Finally, the time of flight TF calculator computes TOFfrom N and �ST, which is then sent to a computer for tem-perature calculation.

B. Software block of the CPLD

The ultrasonic TOF measurement system’s softwareblock diagram is shown in Fig. 11. The TOF measurementsignal ST is transmitted from the ultrasonic transducer andthe reflex signal SR is received by the ultrasonic receiver. The

FIG. 9. The amplitude modulation �AM� is achieved by modulating thesupplied power for the output amplifier CD4069. After amplitude modula-tion, the APESW has two signal levels, +5 and +12 V. Additionally, thephase modulation can be achieved by controlling the pulse width of thetransmitted signal from the CPLD �PM signal�.

FIG. 10. The CPLD programed circuit block diagram.



TOF data value TF can be obtained by calculating the timedifference between ST and SR using the N and phase quantitycounters. The N value is measured by a 40 kHz clock and thephase quantity is measured by a 40 MHz clock. Upon acti-vation, the transmitter’s control algorithm resets the timecounters and sends out the first ten pulses. Next, the AM andPM waves are transmitted to the ultrasonic transmitter. TheN counter will be activated once PM detector 1 senses thephase modulation in the transmitted waveform ST. The Ncounter will be stopped as soon as the phase inversion of SR

is detected by PM detector 2. As PM 2 detects the phaseinversion of SR, the � value phase quantity counter initiatesand counts until the next falling edge of the 40 kHz counterclock. The phase shift quantity �ST is derived from the �value. The system calculates the TOF TF from N and �ST.Lastly, the TOF calculation is sent to a computer for tem-perature calculation.

IV. EXPERIMENTAL RESULTS

A. Temperature measurement

The experiment is conducted in a programmable tem-perature and humidity chamber �GTH-800-00-CP-ST, GiantForce Instrument, Taiwan�. Figure 12 shows the experimentsystem’s block diagram. The experimental temperature mea-surement system consists of a transmitting acoustic trans-ducer, a receiving acoustic transducer, a driving circuit, alevel-shifter and amplitude modulation circuit, and a pre-amplifier and clamping circuit system. The system utilizes a

microprocessor-based controller CPLD to govern the opera-tion of the measurement system. The CPLD also sends thetime-of-flight TF data to a computer for analysis. A calibratedoptical linear scale was used to guarantee that the ultrasonictransmitter and receiver are installed at the exact distance d.The environmental temperature t and relative humidity h canbe controlled via the experiment chamber’s control panel.The actual temperature and relative humidity of the chamberare sensed and recorded by a thermal/humidity meter �TES-1365, TES Electrical Electronic Corporations, Taiwan�. Themeter’s temperature and relative humidity readings are sentto the computer via an RS-232 cable. As a result of the aboveconditions, the computer can calculate and display the mea-sured temperature via the received TF and relative humidityfor a given environment. The temperature measurement thatwas derived from TOF can be compared to the thermal/humidity meter’s reading to determine the measurementerror. This error can then be used for recalibration andexamination.

Three separate experiments were conducted to examinethe effects of temperature t, relative humidity h, and distanced on the temperature measurement that was derived fromTOF. Table I lists the conditions of the three separate experi-ments. In the first experiment, temperature t was the inde-pendent variable. During this experiment relative humidity hwas controlled at 50% and distance d was fixed at 100 mm.The temperature range during the temperature measurementexperiment was from 0 to 80 °C. The second experiment

TABLE I. Experimental conditions of three separate experiments.

Experiment 1 Experiment 2 Experiment 3

Independent variable t h dTemperature t �°C� 0–80 20 20Relative humidity h �%� 50 20–90 50Distance d �mm� 100 100 50–200

FIG. 11. The system’s software block diagram.

FIG. 12. The block diagram of the experiment system.



used humidity h as the independent variable and controls fordistance d and temperature t. In this experiment, temperaturet is fixed at 20 °C and distance d is set at exactly 100 mm. Inthe humidity experiment, the relative humidity h is regulatedover the range of 20%–90%. The final experiment measuredthe effects of variation in the distance between the ultrasonictransducers on the temperature measurement that was de-rived from TOF. In this experiment the independent variabledistance d ranged from 50 to 200 mm, relative humidity hwas controlled at 50%, and temperature t was fixed at 20 °C.A graph of the actual temperature versus the temperaturemeasurement that was derived from TOF from 0 to 80 °C isshown in Fig. 13�a�. The plot of temperature deviation versusactual temperature is shown in Fig. 13�b�. Regarding tem-perature, the experimental standard deviation of the linearitywas 0.33 °C. In addition, the humidity and distance uncer-tainty effects produce standard deviations of 0.12 and0.18 °C, respectively �see Figs. 13�c� and 13�d��.

B. Estimation of the measurement uncertainty

The functional relationship in Eq. �15� states that tem-perature, in °C, is directly proportional to the square ofsound velocity. Equation �21� states that the sound velocitymeasurement needs to be corrected to compensate for rela-tive humidity. Additionally, sound velocity is calculated fromthe ultrasonic transmitted distance d and TOF TF as seen inEq. �2�. As a result, the temperature computing equation�Eq. �21�� can be revised as

t = 273.15� ch/CFh

331.45�2

− 1= 273.15� d/TF

CFh � 331.45�2

− 1 , �22�

where CFh is the correction factor for the humidity effect andch is the sound velocity at relative humidity h. The correctionfactor CFh varies with air humidity h and can be expressed as

FIG. 13. �a� The actual temperature vs the derived temperature measurements from TOF at 0 to 80 °C. �b� The plot of temperature deviations vs actualtemperature. �c� Humidity effect on fixed temperature measurements. �d� Measured distance effect on fixed temperature measurements.



CFh = f�h� . �23�

Under the experiment’s defined parameters, the measuredquantities d, TF, and h are uncorrelated. Therefore the uncer-tainty contributions u�d�, u�TF�, and u�h� can be combined ina square-root-sum method as

u�t� = �c2�d�u2�d� + c2�TF�u2�TF� + c2�h�u2�h� , �24�

where u�t� is the combined standard uncertainty of tempera-ture. Additionally, c�d�, c�TF�, and c�h� are all sensitivitycoefficients derived from Eq. �22�.

The experimental uncertainty budget is outlined inTable II. In each of the three temperature experiments therespective independent variable, temperature t, relative hu-midity h, and distance d, followed established parameters.The respective ranges for the three experiments were dis-tance d from 50 to 200 mm, temperature t between 0 and80 °C, and relative humidity h between 20% and 90%. Un-der the above conditions, the combined standard uncertaintyof temperature u�t� is approximately 0.39 °C.

V. DISCUSSION

Table II shows that the experimental uncertainty is domi-nated by u�TF�. The major u�TF� contributor is the tempera-ture linearity deviation. The uncertainty associated with thethermal meter, noise, the measuring path’s thermal gradient,and wind velocity are the root causes of deviation in thetemperature linearity. The accuracy of the thermal meter is±0.5 °C. If the error is considered to be a random variablewith uniform distribution, then it corresponds to a tempera-ture uncertainty of about 0.28 °C. Noise and the measuringpath’s thermal gradient significantly affect the experimentchamber’s temperature measurement uncertainty. Using thesquare-root-sum method, this temperature uncertainty is es-timated to be approximately 0.26 °C. Lastly, the averagewind velocity is approximately 0.8 m/s with a standard de-viation of 0.05 m/s. This corresponds to a temperature un-certainty of about 0.08 °C.

As stated above, wind velocity affects measurement er-ror. If the wind direction is parallel to the waveform’s direc-tion, it will cause the measured sound velocity to accelerate.Conversely, when wind direction is going in the opposite

direction, it will cause sound velocity to slow down. Theeffect of wind velocity should be considered and compen-sated for when measuring distance and temperature. Addi-tionally, with the integration of a temperature and humiditycompensation algorithm, the error caused by wind velocitybecomes measurable. Therefore, future research may focuson using the proposed TOF measurement system to accu-rately measure wind velocity.

VI. CONCLUSION

The proposed ultrasonic temperature measurement algo-rithm is based on both TOF and phase shift techniques. Inorder to eliminate the TOF errors caused by inertia delay andamplitude attenuation, we proposed using the APESW todrive the ultrasonic transmitter. The APESW uses amplitudeand phase modulation to make specific pulses easily identi-fiable in the received signal. In addition, a counter clocktechnique is used to compute the phase shifts of the lastincomplete cycle. This is done to avoid the limitationscaused by the amplitude of the signal and the finite bits ofthe A/D converter. Therefore, the system’s theoretical maxi-mum TOF resolution can be reduced to 0.025 s. The ex-perimental results indicate that the proposed ultrasonic tem-perature measurement system can accurately measuretemperature. With humidity compensation, the combinedstandard uncertainty of the temperature measurement isabout 0.39 °C. Furthermore, the algorithm is simple to useand can easily be adapted for use with other microprocessors.The main advantages of this system are high resolution mea-surements, narrow bandwidth requirements, and ease ofimplementation.

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TABLE II. Experimental uncertainty budget.

Relative quantity Value �°C�

Time-of-flight uncertainty u�TF� 0.33Relative humidity uncertainty u�h� 0.12Distance uncertainty u�d� 0.18

Combined uncertainty u�t� 0.39



an accurate air temperature measurement system based on an

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