Digital Capacitance & Inductance Meter_hruskovic

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10.2478/v10048-008-0016-9 MEASUREMENT SCIENCE REVIEW, Volume 8, Section 3, No. 3, 2008 Digital Capacitance and Inductance Meter M. Hruškovic, J. Hribik Dept. of Radio Electronics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovičova 3, 812 19 Bratislava, Slovak Republic, e-mail: hruskovic@kre.elf.stuba.sk; jan.hribik@ stuba.sk A microcomputer-controlled measuring instrument for capacitance and inductance measurement is described. It is based
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  10.2478/v10048-008-0016-9 MEASUREMENT SCIENCE REVIEW, Volume 8, Section 3, No. 3, 200861  Digital Capacitance and Inductance Meter M. Hruškovic, J. Hribik  Dept. of Radio Electronics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology,Ilkovi č ova 3, 812 19 Bratislava, Slovak Republic, e-mail: hruskovic@kre.elf.stuba.sk; jan.hribik@ stuba.sk  A microcomputer-controlled measuring instrument for capacitance and inductance measurement is described. It is based on anoscillator circuit with the oscillation frequency dependent on a measured element. An analysis of the oscillator used is also given.Equations for the oscillation frequency and its deviation from the resonance frequency of a frequency controlling resonance circuit arederived. The measured results can be transferred into a personal computer (PC) which can process and display these results andcontrol the instrument via RS-232 serial interface.Keywords: capacitance and inductance measurement, microcomputer control 1.   INTRODUCTION LECTRONIC METHODS of capacitance and inductancemeasurement are based on different principles [1]-[4].They include bridge methods, vector impedance methods,resonance methods, digital RLC methods, voltage and currentmeasurement methods, and phase shift measurement methods.All of these methods have some advantages but also suffer from some drawbacks.The most precise are bridge methods but the constructionand measurement by such instruments are complicated. DigitalRLC methods use feedback amplifiers and low measurementfrequencies [2], [5]. The measurement circuit in these methodsis simple but the accuracy is relatively low. Resonancemethods use the known dependence of the resonancefrequency on the values of an inductance and capacitanceelements of a series or parallel resonance circuit. For thefinding of resonance frequency, they are inaccurate.. Amodified version of the resonance methods is based on themeasurement of the frequency of an oscillator with themeasured element connected into a frequency controllingresonance circuit. Digital frequency measurement is accurateand yields the desired digital output of the instrument. 2.   PRINCIPLE   OF   THE   PROPOSED   METHOD The method used in the designed instrument is based on theoscillator, the frequency of which depends on the measuredvalue of an inductance or capacitance. A simplified circuitdiagram of the oscillator used is in Fig.1 [6]. A resistor   R  LP   represents the losses in the coil supposing that the capacitor has negligible losses. The condition for the oscillations(Barkhausen criterion), [7], is given by the expression 1)() = ω   j(j ω A β (1)where β (j ω  ) =  β  (  ω  )exp[j φ  FB (  ω  )] is the feedback circuittransfer function, A (j ω  ) = A(  ω  )exp[j φ  A (  ω  )] is the amplifier transfer function, and ω is the complex frequency. From (1),the amplitude and the phase conditions yield theseexpressions: 1)()( = ω ω  β   A (2) 0)()( =+ ω ϕ ω ϕ   A FB (3)From Fig.1, the feedback transfer function can be written inthe form 2222222 2222 )()1( )1()( )(  FB LP  FB LP   FB LP  FB LP  LP   R R L LC  R R  LC  R LR j R R R L  j ++−−++= ω ω ω ω ω ω  β  (4) Fig.1 Simplified circuit diagram of the oscillator   Notice that at the resonance frequency, ω r  , (4) simplifies tothe expression  FBr r  FB LP  LP   R LQ LQ R R R +=+= ω ω ω  β  )( (5) E  MEASUREMENT SCIENCE REVIEW, Volume 8, Section 3, No. 3, 200862and from the amplitude condition (2)  LQ R A r  FB ω ω  += 1)( (6)In these equations the resonance frequency, ω r  , and theQ-factor of the resonance circuit  LC  r  1 = ω  (7)  L RQ r  LP  ω  = (8)were introduced.The phase characteristic of the feedback circuit can now beexpressed from (4). Near the resonance frequency thisexpression is  FB FB FB  R LQ LC QR +−= − ω ω ω ϕ  )1(tan)( 21 (9)and it can be seen that φ  FB (  ω  ) approaches zero. In this case itis possible to express the oscillation frequency in the form ⎟⎟ ⎠ ⎞⎜⎜⎝ ⎛ −−= 1)()(11 2 ω ω ϕ ω   A AQ LC  (10)where φ  A (  ω  ) =  –  φ   is the amplifier phase shift at theoscillation frequency. The relative deviation of the ω 2 fromthe resonance frequency 2 r  ω  is 1)()()( 2 −−= ω ω ϕ ω δ   A AQ (11) 3.   DESIGNED   INSTRUMENT   DESCRIPTION A block diagram of the designed instrument for inductanceand capacitance measurement is in Fig.2 [6]. A measuredvalue-to-digital-value converter contains a measuringoscillator, an amplitude control circuit, input protectioncircuits and a harmonic-to-rectangular signal shaper, Fig.3.The measuring oscillator is composed of an amplifier, aresonance circuit, reference elements and a relay switchcontrolled from a microcomputer part. The rectangular shapedsignal is lead to the microcomputer part which measures theoscillation frequency, calculates the measured value anddisplays the result on the LED display. The microcomputer  part also operates a control keyboard and a serial interface(RS232) to a personal computer (PC) and controls theoperation of the instrument. Fig.2 Block diagram of the designed measuring instrument The measuring oscillator is of the type shown in Fig.1. For capacitance measurement, a reference inductor is connected in parallel into the resonance circuit by a relay switch, Fig.3. Thereference inductor is realized by a capacitive loaded gyrator with two operational amplifiers (OA). Its inductance is 78 mHand is linear up to the current 11 mA. It is enough to measurethe capacitances up to 10 µF. Such high inductance cannot berealized by a coil with a core because of its nonlinearity andtemperature dependence. A coil without a core has highnumber of turns with high DC resistance and high self-capacitance. Fig.3 Block diagram of the measured value-to-digital valueconverter  For inductance measurement, a reference capacitor isconnected in parallel into the resonance circuit by a relayswitch. Its capacitance is selected to be 20 nF and is composedof two 10 nF capacitors. This choice was made to getapproximately the same range of the measured capacitive andinductive reactances.The amplitude of the oscillations is partially controlled byanti-parallel connection of two diodes in a negative feedback which is used to set the amplifier gain. Much more effectiveamplitude control is realized by a control of the feedback resistor. For these purposes the feedback resistor is a photoresistor and is controlled by the rectified and amplifiedoscillator output signal through an LED.  MEASUREMENT SCIENCE REVIEW, Volume 8, Section 3, No. 3, 200863To prevent the damage of the oscillator, e. g. whenconnecting a charged measured capacitor, the high-speedinversely biased diodes with low capacitance are used.Another protection is a connection of resistors into the inputsof the OA with a diode protection inside the OA.The oscillator output signal is shaped to a rectangular form by a comparator with hysteresis. In this way, the TTL/CMOScompatible rectangular signal is obtained for themicrocontroller to measure its frequency. 4.   MICROCOMPUTER    PART   OF   THE   INSTRUMENT The microcomputer part of the instrument must measure thefrequency or period of the oscillator signal, calculate themeasured value, display the measurement results, control thewhole instrument, communicate with a PC and perform someother auxiliary functions. All these requirements can besatisfied by a designed microcomputer circuit and peripheralsshown in Fig.4. A core of this part is a microcontroller. Itschoice came out of the following requirements: minimum of two 16-bit timer/counters to enable to measure the oscillator frequency in the whole range with sufficient accuracy,sufficient number of I/O ports, supporting of a serial interface,sufficient computing power, sufficient capacity of programand data memory (possibly EEPROM type to enable to storecalibration constants). Fig.4 Block diagram of the microcomputer part of the instrument  The microcontroller PIC18F252 has RISC CPU withmaximum clock frequency 40 MHz and maximum speed of operation up to 10 MIPS. This clock frequency can beobtained from 10 MHz crystal oscillator by means of a built-inPLL. This possibility is used in the designed instrument. Themicrocontroller contains three memories: 1.5 Kbytes dataRAM, 32 Kbytes FLASH program memory and 256 bytesdata EEPROM. The FLASH program memory is readable,writable and erasable during normal operation. In the designedinstrument it is possible to change the program in this memorythrough a serial port and to write samples of a voice control of the instrument into it. The data EEPROM is used to storecalibration constants.From the frequency or period measurement point of view itis important that the microcontroller PIC18F252 contains one8-bit and three 16-bit timers/counters with programmable prescalers. Other important peripheral features of themicrocontroller are two CCP (Capture/Compare/PWM)modules, a synchronous serial port module (two modes of operation: 3-wire SPI, I 2 C) and an addressable asynchronousserial port module (supports RS-485 and RS-232). Analoguefeatures of the microcontroller are a 10-bit A/D converter module with 5-channel multiplexed input, programmable lowvoltage detection and other special features such as watchdogtimer with its own on-chip RC oscillator, power savingSLEEP mode, selectable oscillator options, etc.A LED display of the instrument is multiplexed, whichmeans that the power supply voltage of the common anodes isswitched by transistors controlled from port A every 10 ms.The cathodes are controlled from port B of themicrocontroller. The keyboard microswitches are sensedthrough port B and port RC5 of the microcontroller. The relayswitch, which selects L or C measurement, is controlled from port RC1. The oscillator signal is connected to the timer 1input TMR1.A TTL/RS-232 level converter MAX3226E is connected to pins RX and TX (serial port). This circuit supports maximumtransfer speed 250 Kbits/s and has an electrostatic discharge protection. To minimize the interference and power consumption, this circuit is active only if it is connected to theactive RS-232 interface or if it transmits data. In other case itis in SLEEP mode.The instrument also makes use of other supplementaryfunctions. One of them is I 2 L interface. The data and clock lines are electrostatic discharge protected and a +5 V power supply line with current limit and overvoltage protection isadded. A temperature sensor DS1631A and a real time circuitMAX6900 are also connected to this I 2 L line. The A/Dconverter is used to digitize a voice control input signal from amicrophone, which is filtered and amplified beforeconversion. PWM module (pulse frequency 156 kHz, 8-bitresolution) is used to create a voice output from the inputsampled signal with 8-bit resolution and 8 kHz samplingfrequency. A low-pass reconstruction filter at its output hasthe limiting frequency 4 kHz and the signal is next amplifiedand connected to a loudspeaker. Thus, the instrument canannounce some events such as range switching, etc. 5.   EXPERIMENTAL   RESULTS The realized instrument is able to measure capacitancesfrom 1 pF up to 10 µF and inductances from 1 µH up to 15 H(higher values have not been tested). The deviations of themeasured capacitances and inductances from those calculatedfrom the Thomson equation are less than 1 %. Because of lowdispersion of the measured values it is possible to use software  MEASUREMENT SCIENCE REVIEW, Volume 8, Section 3, No. 3, 200864correction in the microcontroller. The deviation of theoscillator frequency is independent on the Q-factor and is verylow for the Q-factors of the resonance circuit higher than 2.The error of measurement caused by temperature changes is0.06%/ o C. The overall accuracy of the instrument after calibration is 0.3% + 1 pF or 0.3% + 1 µH. 6.   CONCLUSION A microcomputer-controlled measuring instrument for capacitance and inductance measurement based on theoscillator circuit with the oscillation frequency dependent onthe measured element was designed. The analysis of theoscillator used yields the equations for the oscillationfrequency and its deviation from the resonance frequency of afrequency controlling resonance circuit. The analogue anddigital part of the instrument are described following block diagrams in Fig.2, Fig.3 and Fig.4. The basic circuit of theanalogue part is the measuring oscillator while the core of thedigital part is a microcontroller. The realized instrument isable to measure capacitances from 1 pF up to 10 µF andinductances from 1 µH up to 15 H (higher values have not been tested). The overall accuracy of the instrument after calibration is 0.3% + 1 pF or 0.3% + 1 µH in the wholemeasuring range. The measured results can be transferred intoa personal computer (PC) which can process and display theseresults and control the instrument via RS-232 serial interface.The instrument equipment includes temperature measurement,real time and date, serial   interface I 2 L, voice control input andvoice output. ACKNOWLEDGMENT This work was partially supported by the Slovak grantagency, GAT, under the grant VEGA No. 2/0107/08   and the project No. AV 4/0012/07. REFERENCES [1]   Helfrick, A.D., Cooper, W.D. (1990).  Modern Electronic Instrumentation and Measurement Techniques .Englewood Cliffs, USA: Prentice-Hall.[2]   Sedlá č ek, M., Haasz, V. (2000).  Electrical Measurementsand Instrumentation. (2nd ed.). Prague, Czech Republic:Vydavatelství Č VUT.[3]   Webster, J. (ed.) (1999). Wiley Encyclopedia of Electrical and Electronics Engineering Online. Instrumentation and  Measurement  . New York, USA: John Wiley & Sons.(http://mrw.interscience.wiley.com/emrw/9780471346081/home/)[4]   Hribik, J. (2002).  Electronic Measurement  . Bratislava,Slovak Republic: Vydavate ľ stvo STU. (In Slovak)[5]   Lentka, G., Hoja, J. (2004). The influence of sampling parameters on accuracy of capacitance measurement inthe method based on DSP. In 13 th InternationalSymposium on Measurements for Research and IndustryApplications and 9 th European Workshop on ADCModelling and Testing, Volume 1, 29 September-1October 2004 (pp. 294–297). Athens, Greece: NTUA andIMEKO TC-4.[6]   Bedná ř  , V., Hruškovic, M. (2004). Capacitance and  Inductance Meter  . Bratislava, Slovak Republic: FEI SUT.(In Slovak)[7]   Sentz, R.E., Bartkowiak, R.A. (1968).  Feedback  Amplifiers and Oscillators . New York, USA: Holt,Rinehart and Winston.
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