FAST IMPEDANCE SPECTROSCOPY METHOD USING SQUARE PULSE EXCITATION

2th IMEKO TC & TC7 Jont Symposum on Man Scence & Measurement September, 3 5, 2008, Annecy, France FAST IMPEDANCE SPECTROSCOPY METHOD USING SQUARE PULSE EXCITATION Jerzy Hoja, Grzegorz Lentka 2 Gdansk Unversty of Technology, Gdansk, Poland, hoja@et.pg.gda.pl, 2 lentka@et.pg.gda.pl Abstract: The paper presents a fast mpedance spectroscopy method for objects wth very hgh mpedance Z x GΩ modeled by mult-element two-termnal RC networks. The method s based on analyss of the object response n the tme doman after square pulse exctaton. The object mpedance spectrum was obtaned usng contnuous Fourer transform. Smulaton tests were performed for dfferent exctaton pulse wdths. Measurements n the realzed system proved the usefulness of the method for parametrc dentfcaton of equvalent crcuts of the objects. Keywords: mpedance spectroscopy, voltage pulse, tme doman response. INTRODUCTION Impedance spectroscopy (IS) s an unversal and effectve tool used for testng of electrcal propertes of techncal and bologcal objects. It allows fndng an object s equvalent crcut n the form of mult-element two-termnal networks. IS s used n many areas, e.g. n research of corroson, protectve coatngs, fuel cells and mpedance measurement of membranes, solaton and bomedcal materals. In order to perform IS, measurement systems generatng the exctaton sgnal wth a specfed shape and smultaneously analyzng the object response sgnal are used. Instruments avalable nowadays use an mpedance measurement technque based on object exctaton wth a SST (sngle sne technque) harmonc sgnal and vector measurement of two sgnals: voltage across and current through the object under measurement [, 2]. By repeatng measurements at dfferent frequences, the mpedance or admtance spectrum can be obtaned as a functon of frequency n a range of several decades. The spectrum allows the analyss of measured object s propertes usng the Complex Nonlnear Least Square Fttng (CNLS) algorthm [3] whch makes parametrc dentfcaton of object equvalent crcut components possble. The man dsadvantage of the SST technque s the very long measurement tme, especally for very low measurement frequences (mhz, μhz). The use of low frequences for IS s necessary n the case of component dentfcaton of objects wth a very hgh mpedance modulus Z x GΩ. Such a case appears when performng IS of e.g. hgh-thckness antcorroson coatngs, delectrc materals and t causes that the mpedance spectrum measurement lasts even a few hours and s possble manly n the laboratory. In the above case, even the use of MST (mult sne technque) acceleratng IS [4] does not allow to shorten meanngfully the spectroscopy tme. The authors, searchng for a method makng fast mpedance spectroscopy possble (lastng not more than a few mnutes) for an object drectly n the feld, lke antcorroson coatngs on brdges, ppelnes etc., have used a method based on an analyss of the response sgnal n the tme doman when exctng the object wth a square pulse sgnal. The proposed method can be counted to a new class of IS technques, whch use non-harmonc exctaton sgnals lke a voltage or current [5] unty step sgnal or pseudorandom whte nose [6]. Unfortunately, the above-mentoned methods were not used n commercally avalable IS nstrumentaton. So, after smulaton tests and verfcaton n a laboratory system, the authors plan to mplement the developed method nto a portable IS analyzer, whch wll be put nto producton. The paper presents the theoretcal background of the method and an analyss of smulated mpedance spectra of the tested object. The method was evaluated for dfferent pulse tmes and dfferent response samplng parameters (samplng frequency, acquston tme and AD converter resoluton were taken nto account). 2. IMPEDANCE MEASUREMENT METHOD In order to meanngfully shorten the tme of classcal IS, realzed by sequental mpedance measurement at selected frequences of a harmonc sgnal, the sngle square pulse exctaton was used. The measurement of tested mpedance Z x response amounts to samplng and quantzng sgnals proportonal to the voltage across and current through Z x, usng AD converters. The measurement system to verfy the presented concepton s presented n Fg.. The system conssts of a personal computer wth an nstalled DAQ card and nput crcutry connectng the measured object (Z x ). The exctaton sgnal for the measured mpedance Z x s prepared wth the ad of a DA converter placed on the DAQ card. In order to lmt the maxmum value of current flowng 97

through the measured object, the programmed resstor R o has been used at the output of a buffer supplyng the exctaton sgnal u o. Current x s converted to voltage u n a current-to-voltage converter realzed usng amplfer A. A change of the current range s realzed wth the ad of the programmable resstor R R. Ths allows to match the sgnal u to the nput range of the ADC converter exstng on the DAQ card. The generated exctaton sgnal u o s not an deal square pulse, addtonally t s deformed by parastc capactance. Due to these facts, a measurement amplfer was used n the system for real voltage u x appearng across Z x. The amplfer output sgnal u 2 s quantzed by the ADC2 converter. Decoder Drver Buffer Dgtal I/O 8-bt uo Ro DACOUT 6-bt DAC DAC FIFO x Z x u x Control crcut Bus (PCI) nterface - A PCI Bus Personal Computer RR - SH68-68EP Shelded Cable u 2 2V -2V - 2-bt ADC2 u ACH0 2-bt ADC ADC's FIFO Power supply DIO0-7 ACH 5V DAQ card PCI-6E Fg.. Block dagram of a measurement system realzng the method of fast IS Current u and voltage u 2 responses contan nformaton about the mpedance of the tested object as a functon of frequency. Ths nformaton can be extracted by usng Fourer transformaton, after approxmatng tme responses usng lnear functons and calculaton of transform usng formulas: 0 () t exp( jωt) U ( jω ) = u dt, where: =, 2 () To calculate the classcal dscrete Fourer transform t s necessary to sample voltages u and u 2 wth a constant tme step. Assumng a maxmum measurement tme equal to 00 s and a samplng frequency equal to 0 khz, the requred number of samples of each sgnal should be equal to 000000. Transform calculaton usng such a number of samples would last even dozens of mnutes. Therefore, n the presented soluton, the acquston tme was dvded nto tme segments n whch samplng s performed wth a dfferent frequency. A maxmum number of 6 tme segments was assumed wth hgh lmts as follows: 0.0 s, 0. s, s,..., 000 s, and a constant number of 000 samples n each segment. For the assumed condton, the maxmum number of samples collected durng the acquston tme s equal to N = 6000. In ths case the transform can be calculated usng the defnton, t means that () can be wrtten: N U ( jω ) u ~ ( t) exp( jωt) dt, (2) n= where u ~ ( t) and u ~ 2 ( t) are lnear approxmatons of each response sgnal (current and voltage) between samples. After approxmaton and ntegral calculaton we obtan: ( ( ) ( ) ) u sn sn N ω u ω ω ReU ( ω ) (3) = u ( ) ( ) cos cos n u ω ω 2 ω ( ( ) ( ) ) u cos cos N ω u ω ω ImU ( ω ) (4) = u ( ) ( ) sn sn n u ω ω 2 ω Determnng from (3) and (4) the spectra of the sgnal proportonal to the voltage across and current through the measured object, on the bass of mpedance defnton, the mpedance spectrum can be calculated usng formula (5): Z ReU j ImU =, (5) ReU j ImU 2 2 RR 3. ANTICORROSION COATINGS SPECTROSCOPY The developed method for the fast spectroscopy method s amed at hgh-mpedance objects, as mentoned at the begnnng. The method s partcularly dedcated to mpedance measurement of antcorroson coatngs, whch allows to evaluate the condton of the antcorroson protecton. Due to safety and economcal reasons t s necessary to determne the qualty of a protectve coatng n order to estmate the renovaton tme. Ths leads to the need of mpedance measurement of antcorroson coatngs and as the result to dagnose ther condton, also performed n the feld, drectly on the protected object. Fgure 2a presents a photograph of a typcal cell for mpedance measurement of the antcorroson coatng on a hgh-voltage power lne pylon, and Fg. 2b presents a crosssecton of the coatng [7]. When the coatng s new and the protecton reles on the barrer mechansm and there s no electrolyte penetraton n the coatng, the equvalent crcut contans only two elements: capactance C c (of an order of tens hundreds pf) and resstance R p (several hundreds GΩ) modelng the propertes of the coatng materal. After the frst perod of explotaton, the coatng loses ts protecton barrer and the electrolyte penetrates the coatng, but adhesve propertes are stll actve and there s no undercoatng corroson. At ths stage, the resstance of the electrolyte n the coatng pores nfluences R p, whose value decreases the more the electrolyte penetrates the coatng. 98

Addtonally, the electrolyte penetraton causes an ncrease of the delectrc constant and as a result the ncrease of the capactance C c. In the next stage, the contnuty of the coatng s broken, undercoatng corroson appears, and the equvalent crcut contans new elements; double-layer capactance C dl and charge-transfer resstance R ct. As the corroson expands, the value of R p stll decreases, untl fnally the coatng s destroyed and the equvalent crcut contans only R ct and C dl. Fgure 4 presents tmngs of sgnals u and u 2 when exctng a two-termnal RC network wth a square pulse wth V ampltude and pulse wdths 0.5 s and 2 s (the assumed pulse wdth results from the estmaton of the object s tme constant on the level of s). For a shorter pulse, the voltage u 2 on the measured two-termnal network Z x does not reach the maxmum value resultng from the voltage dvder created by resstor R o = GΩ and the maxmum value of the mpedance modulus Z x 5 GΩ. Resstor R o has lmted the current flowng through Z x to na, so a range resstor R R = GΩ was used n the currentto-voltage converter, matchng voltage u to the AD converter operatng range. a) b) Slcon sealngs Electrolyte Coatng R p R Undercoatng ct Cdl corroson Coated metal Frst electrode (Ag-AgCl) Coatng Protected metal structure Electrolyte (3% NaCl) C c Polamd cover Polamd rng Second electrode Fg. 2. a) Photograph of the cell for mpedance measurement of antcorroson coatng on the hgh-voltage power lne pylon b) Crosssecton of the coatng For smulaton tests and practcal verfcaton of the method, the four-element two-termnal RC network shown n Fg. 3 was used. The confguraton and the values of the components are a typcal example of the equvalent crcut of hgh-thckness antcorroson coatng n the early stage of undercoatng corroson nducton. Ths s a very mportant moment n coatng dagnostcs, as the fast renovaton of the coatng can prevent the expanson of corroson. Fg. 4. Current (contnuous lne) and voltage (dashed lne) sgnals on the tested two-termnal RC network For the values of resstors R o and R R determned above, usng formulas (3-5), the shape of the mpedance spectrum of the two-termnal RC network was analyzed dependng on a changng square pulse wdth τ and samplng frequency, assumng a total acquston tme equal to 00 s. The smulaton results are presented n Fg. 5, where mpedance spectra were shown n the Nyqust plot, for frequences n range of 0.0 Hz khz. The contnuous lne n the graph presents the mpedance spectrum calculated theoretcally usng nomnal values of RC components (Fg. 3). R p 9.935GΩ C c 34.6pF R ct 4.969GΩ C dl 2.22nF Fg. 3. Schematc dagram of the object under test 4. EVALUATION OF THE METHOD BY SIMULATION To compare the calculated and real mpedance spectra for dfferent parameters of the exctaton sgnal and response samplng, the algorthm of the method presented n Secton 2 was evaluated by smulaton. The smulaton was performed usng Matlab for the object presented n Fg. 3. Fg. 5. Impedance spectra n the Nyqust plot 99

When analyzng curves t can be noted that the spectra obtaned from measurement wth constant samplng frequency (00 Hz) dffer meanngfully from the theoretcal one. Much better results were obtaned (the spectrum s closest to deal) n case of samplng wth a varable frequency. Due to ths fact, n the system presented n Secton 2 and n followng smulatons, the samplng frequency changng n decades n each segment s used. The presented spectra, due to the wde range of changes of real and magnary parts of mpedance, do not allow to evaluate precsely the qualty of ther fttng to the theoretcal characterstc. Because of ths, t was decded to perform the evaluaton on the bass of an error of dentfcaton of components of the equvalent crcut of the tested object. For parametrc dentfcaton of components the computer program LEVM [3] was used. LEVM uses the teratve CNLS method to fnd the functon descrbng a two-termnal RC network wth a known structure well ftted to the mpedance spectra calculated from (3-5). Relatve errors of four dentfed elements were calculated n relaton to square pulse wdth when samplng wth an ADC converter wth 6-bt resoluton (Fg. 6). Fg. 7. Error of dentfcaton of elements of a two-termnal RC network when samplng wth a 2-bt AD converter The sgnfcant ncrease of dentfcaton errors of components C dl and R ct for pulse duraton tmes above 7 s s surprsng. Ths effect can be caused by a too low samplng frequency n the tme segment above 0 s. Due to ths, the sgnals u u 2 samplng tme segments selecton was modfed. The three tme segments durng pulse duraton were assumed, and the same segments were repeated mmedately after the pulse, then two segments were added wth the duraton tme equal to 0 t mp and 00 t mp. Addtonal samplng segments were entered n order to extend the measured mpedance spectrum n the range of low frequences (from 0.0Hz). The total number of samples collected n modfed measurement s equal to 8000. The modfcatons caused the change of relatve error curves (Fg. 8) for pulse duraton tme greater than s. The graphs show that the optmal pulse duraton should not be shorter than the tme constant of the measured object. Fg. 6. Error of dentfcaton of elements of a two-termnal RC network when samplng wth a 6-bt AD converter The graphs shown the sgnfcant nfluence of the exctaton pulse wdth on determned mpedance spectra whch were the bass to dentfy components of the equvalent crcut of the two-termnal network. Relatve errors for all dentfed components reach a clear mnmum for a square pulse of τ = s wdth. Ths s a tme comparable to the tme constant of the tested two-termnal RC network. The resoluton of the AD converter assumed n the smulaton s not always possble to assure. The verfcaton of the method s performed n the system wth a DAQ card equpped wth 2-bt AD converters (Fg. ), so the smulaton was repeated for a 2-bt converter. The graphs of errors presented n Fg. 7 show agan that the optmal exctaton pulse wdth s equal to s. The accuracy of component determnaton s worse, especally for C dl and R ct, whch are placed deeper n relaton to termnals of the two-termnal RC network. A smulaton performed wth a longer acquston tme (000 s) has not shown a sgnfcant accuracy mprovement. Fg. 8. Relatve error of component dentfcaton of a two-termnal RC network for a modfed measurement To compare the obtaned dentfcaton results, optmal results are shown n Table for both resolutons and dfferent methods of tme segment selecton. For each component value, the standard uncertanty was gven as a standard devaton calculated by the LEVM program. 200

Table. Identfcaton results for smulaton tests of the object. ADC 6bt Basc ADC 2bt Basc ADC 2bt Modfed C c R p C dl R ct [pf] [GΩ] [nf] [GΩ] Value 34.4 9.968 2.238 4.972 Err [%] -0.9-0.32 0.8-0.56 StDev 0.2 0.007 0.008 0.00 Value 33.4 9.922 2.5 5.02 Err[%] -0.5-0.78-3. 0.24 StDev 0.5 0.02 0.022 0.027 Value 33.6 9.965 2.77 5.088 Err[%] -0.44-0.57 -.94.76 StDev 0.4 0.06 0.06 0.022 The analyss of Table shows that the proposed method of fast mpedance spectroscopy usng square pulse exctaton allows the dentfcaton of components of the tested two-termnal RC network n a tme of approx. 00 s, wth an uncertanty level comparable to SST spectroscopy. But the measurement tme for an mpedance spectrum usng the SST method performed for frequences n the range 0.0 Hz khz, wth 3 ponts per decade (-2-5 steps) s equal to 900 s. The measurement tme was calculated assumng that at each frequency the measurement lasts for 0 perods of the sgnal [8]. A sgnfcant (9 tmes) shortenng of the measurement tme was obtaned, whch s extremely useful especally n case of measurements performed drectly n the feld. 5. EXPERIMANTAL VERIFICATION Takng nto account the conclusons arsng form performed smulatons, the algorthm of measurement process was developed and mplemented n the realzed measurement system (Fg. ). The algorthm contans automatc range selecton, exctaton pulse generaton wth optmal tme and selecton of an approprate samplng frequency n partcular tme segments of the measurement. Fgure 9 presents a block dagram of the algorthm whch s realzed n three steps. In the frst step, the one of 8 range resstors R R s chosen (also concurrently R o ) startng from the hghest value R R = GΩ (next R R : 00 MΩ, 0 MΩ,... 00 Ω). In order to do ths, a test pulse wth mnmal duraton tme (t mn = 0. s) s generated and the voltage across the measured object u 2 s sampled. If the value of the voltage u 2, at the end of the test pulse s greater than 0.U o (U o ampltude of test pulse u o ), the range resstor s accepted. START =; t mp =t mn R R =R Rtab []; Test pulse generaton and u 2 samplng u 2 (t mp )>0.U o? YES u 2 (t mp )>0.9U o? Generate pulse and sample u 2 and u R Rtab =[G,00M,0M,M,00k,0k,k,00] NO NO t mp = t mp * (log(u x (t mp ))/log(0.9u o ))) Calculate samplng zones and frequences Calculate mpedance spectrum STOP YES = <8 YES Fg. 9. Algorthm of the measurement process mplemented n the system In the second step, the optmal measurement pulse duraton tme s selected. The pulse duraton s ncreased by a coeffcent arsng from an exponental curve to ncrease the voltage across the object above 0.9 U o. In the thrd step, on the bass of the pulse duraton obtaned n the second step, tme segment lmts are calculated as shown n Fg. 0 (the tme axs values are gven for an exemplary pulse duraton of s). Assumng 000 samples n each tme segment, samplng frequences are then determned for each segment (for the presented example n the frst segment the samplng frequency s 00 khz). Then the pulse s generated and the voltage u x and current x response of the object s acqured (total number of samples s equal to 8000). Fnally, the mpedance spectrum s calculated at requred frequency ponts usng (3-5). NO Fg. 0. Tme segments of the samplng process n the proposed modfed method and the curve of the voltage across the object 20

The presented algorthm mplemented n the measurement system allowed expermental verfcaton of the method. The measurements were performed for the twotermnal RC network (Fg. 3). Sgnals proportonal to voltage (u 2 ) across and current (u ) through the measured mpedance Z x, at the output of the nput crcutry are shown n Fg.. A seres of ten measurements of u and u 2 was performed for square pulse exctaton wth an ampltude of U o = V and duraton tme t mp = 2 s. The mpedance spectra were calculated allowng parametrc dentfcaton of the object usng LEVM software. Table 2 presents mean values of the determned parameters, ther relatve errors and standard devaton for the measurement seres. Fg.. Oscllograph of u 2 (Ch) and u (Ch2) n the realzed system Table 2. Identfcaton results from measurement of the object. ADC 2bt Modfed C c [pf] R p [GΩ] C dl [nf] R ct [GΩ] Meas. 33,9 9,84 2,09 4,84 Err [%] -0,45 -,00-5,64-2,55 StDev 0,35 0,0 0,0 0,02 The dentfcaton errors calculated from measurements are 2-3 tmes greater (dependng on the locaton of the component n the structure of the two-termnal network) than those obtaned from smulatons. The error ncrease s caused by non-deal parameters of the nput crcutry whch were not taken nto account durng smulaton. The error sources are dffcult to elmnate (e.g. parastc capactances) n case of very hgh mpedance measurements. The second cause of the ncrease of the dentfcaton error s the powerlne-nduced nose wth a frequency of 50 Hz whch s added to sampled sgnals u (Fg. ) extracted n the nput crcutry, n spte of careful sheldng of the tested object. The obtaned accuracy fulfls requrements for measurements carred out drectly n the feld. Ths can be also useful n some cases n the laboratory, when the most mportant s shortenng of the measurement tme. So the developed method can be an alternatve to classcal IS. 6. CONCLUSIONS A method and the measurement system for fast mpedance spectroscopy of objects modeled by multelement two-termnal networks was developed. The method s based on analyss of the tme doman response of the object Z x after square pulse exctaton. The mpedance spectrum of Z x was determned by transformaton of the tme doman response of the tested object to the frequency doman usng contnuous Fourer transformaton. The proposed algorthm of transform calculaton usng a selected samplng frequency for each segment of the acquston tme has shortened the calculaton tme as well as made possble much better fttng of the obtaned spectrum to the theoretcal one. The performed smulaton test for a 4-element twotermnal RC network has proved the usefulness of the method for parametrc dentfcaton of the object s equvalent crcut. The relatve error of component determnaton does not exceed 0.2%-0.8% dependng on the placement of the element n the structure of the two-termnal RC network n case of the use of a 6-bt AD converter and has ncreased to a maxmum value of ca. 2% n case of a 2- bt ADC when usng a modfed selecton of tme segments n whch the response sgnals are sampled. In the practcal verfcaton of the method n the realzed measurement system, a 2-3 tmes ncrease of the dentfcaton errors was obtaned. Ths s caused by nondeal parameters of the nput crcutry connected to the measured object wth very hgh mpedance, and the nose nduced n the object manly by power lnes. The obtaned accuracy s acceptable for the measurements performed drectly n the feld. The man advantage of the proposed method s meanngful shortenng of the measurement tme n relaton to classcal IS. For the tested object, the measurement tme was shortened from approx. 3 mn. n the case of the Solartron set (Impedance Interface 294 and Frequency Response Analyzer 255) to approx. mn. 40 s. The good results of smulaton and verfcaton drected the authors to further mprovements of the method (e.g. ncrease of samplng frequency to average samples to elmnate nose) and to realze a system usng 6-bt ADCs. REFERENCES [] E. Barsoukov, J. R. Macdonald, Impedance Spectroscopy: Theory, Experment and Applcatons, J.Wley&Sons, 2005. [2] J. Hoja, G. Lentka, Vrtual nstrument usng blnear transformaton for parameter dentfcaton of hgh mpedance objects, Meas. Sc. Tech., Vol. 4, No. 5, pp. 643, May 2003 [3] J. R. Macdonald: LEVM Manual ver.7.. CNLS Immttance Fttng Program. Solartron Group Lmted 999. [4] R. Bragos, R. Blanco-Enrch, O. Casas, J. Rosell, Charactersaton of Dynamc Bologc Systems Usng Multsne Based Impedance Spectroscopy, Proceedngs of the IEEE IMTC, pp. 44-47, Budapest, Hungary, 200. [5] E. Barsoukov, S. H. Ryu, H. Lee, A novel mpedance spectrometer based on carrer functon Laplace transform of the response to arbtrary exctaton, J. Electroanal. Chem. Vol. 536, pp. 09-22, 2002 [6] J. Smulko, K. Darowck, A. Zelnsk, On electrochemcal nose analyss for montorng of unform corroson rate, IEEE TIM., Vol. 56, No 5, pp. 208-2023, 2007. [7] J. Bordzlowsk, K. Darowck, S. Krakowak, A. Krolkowska, Impedance measurements of coatng propertes on brdge structures, Progress n Organc Coatngs, Vol. 46 pp. 26-29, 2003. [8] Solartron: Frequency Responce Analyser 255 Operatng Manual, Dec. 2000. Hgh Impedance Interface 294 Operatng Manual, Dec. 200 202