MEASURING DIELECTRIC PROPERTIES OF SIMULANTS FOR BIOLOGICAL TISSUE

Transcription

1 MERIT BIEN 11 Fnal Report 1 MEASURING DIELECTRIC PROPERTIES OF SIMULANTS FOR BIOLOGICAL TISSUE Margaret E. Raabe, Dr. Chrstopher Davs Abstract We strve to measure the delectrc propertes of bologcal smulants, specfcally the value of the delectrc constant for varous uds, and examne the dependency of the delectrc constant on frequency n the range 1 MHz to 1 MHz. Ths value s determned by usng an open-coax technque, n whch an -flled, open-ended coaxal lne s mmersed n the materal of whch the delectrc constant s desred. By usng the known depth of the ud partally fllng the coaxal lne and the dmensons of the nner and outer conductors, the delectrc constant can be determned. The calculatons nvolve modelng the mpedance of a ud-flled coax lne. Relable values of delectrc constants of bologcal smulant materals are mportant to determne, n order to support theoretcal analyss and complex numercal modelng of the energy absorbed from wreless devces that are placed close to, or worn on the human body. Index Terms Bologcal materals, Delectrc constant, Delectrc measurements, Impedance measurement A I. INTRODUCTION delectrc materal s one whch s a poor conductor of electrcty but a very effcent supporter of electrostatc felds. A common example of a delectrc s the electrcally nsulatng materal between the metallc plates of a capactor. Every delectrc materal has a delectrc constant, whch descrbes the extent to whch the materal concentrates electrostatc lnes of flux. One of the most mportant propertes of a delectrc materal s how the value of the materal s delectrc constant vares wth the frequency of the appled electromagnetc feld. Relable values of delectrc constants of bologcal smulant materals are mportant to determne, n order to support theoretcal analyss and complex numercal modelng of how the human body absorbs the energy absorbed from wreless devces that are placed close to, or worn on t. Cell phones are a prme example of ths, as well as n medcne, where the Manuscrpt receved August 1, 11. Ths materal s based upon work supported by the Natonal Scence Foundaton under OCI Grant No Margaret E. Raabe, s wth the Department of Physcs, College of Wooster, Wooster, OH USA (e-mal: margaret.e.raabe@gmal.com). Dr. Chrstopher Davs, s wth the Department of Electrcal and Computer Engneerng, Unversty of Maryland, College Park, MD 74 USA (e-mal: davs@ umd.edu). number of wreless devces that can be mplanted drectly nto the human body s contnung to ncrease, n order to montor condtons lke blood pressure constantly, whle stll beng unobtrusve to the patent [1]. Devces even just held next to the body, radate electromagnetc energy and the electromagnetc waves ht the body and partly penetrate t. As a result, the human tssue absorbs a slght bt of the penetrated electromagnetc energy. The measurement technque n ths research wll help n further determnng the delectrc constants of bologcal smulants and can later be appled to modelng how the human body absorbs ths radated energy. II. THEORY The system we are usng to examne the propertes of a delectrc materal s treated as a cylndrcal capactor. A cylndrcal capactor conssts of an nner cylndrcal conductor of radus R1, surrounded by an outer coaxal cylndrcal shell of nner radus R. The length of both of these cylnders s l, whch s chosen to be much larger than the separaton between the two shells (R - R1) so that edge effects can be neglected. The basc theory we are usng throughout ths experment begns wth the permttvty of a cylndrcal conductor. In general, for a coaxal cylndrcal capactor, the permttvty ε s wrtten as ( ) o r, (1) where ε o s the electrc permttvty of free space x 1-1 F m 1 and ε r s the relatve permttvty, otherwse known as the delectrc constant, whch s a complex number that can be wrtten as ε1 - j ε. The real part of ε r should be much larger than the magnary part, whch s essentally nsgnfcant at the low frequency level. For cylndrcal geometry lke a coaxal cable, capactance s usually stated as a capactance per unt length. The capactance of a coaxal cylndrcal conductor per unt length s C l ln o r R R1. ()

2 MERIT BIEN 11 Fnal Report Snce we are lookng at the capactance per unt length, ths elmnates the length l of the capactors from the above equaton. Equaton () s the capactance of the ud flled lne. To fnd the delectrc constant for the delectrc under test (DUT), we must fnd the capactance of just the ud C, as opposed to the capactance of the entre system wth the ud nsde. The capactance of the ud can be wrtten as L ( ) C, (3) We begn by assemblng the system, as shown n Fg., and screwng t nto the desgned holder so that the coax wll not move durng calbraton or whle takng measurements. We then take our coax system and connect t to one port of an E8364B PNA Network Analyzer. We connect a cable wth an adapter to the analyzer whch wll eventually connect to the coax system as shown n Fg.. where L s the nductance of the lne and s the mpedance of the delectrc materal. The nductance L of the lne s known, snce t only depends on the geometrcal factors of our system, and we can solve for by usng a network analyzer to output the system s mpedance. Ths process s explaned n the analyss secton n further detal. When C s calculated, we can nsert ths nto () and solve for ε r resultng n r C ln R R1 o, (4) whch s a complex number and the desred delectrc constant. III. EXPERIMENT The system we are usng to take measurements was desgned n 9 by Peter Solman and s shown n Fg. 1 []. In ths fgure, the system s not assembled, but whle takng measurements, the nner brass conductor fts nsde the outer alumnum conductor and the system s screwed together. The nner cylndrcal conductor has radus R1 = mm. The outer cylndrcal shell has radus R = mm. Both have length l = 435 mm. Fg 1. Cylndrcal capactor used for measurements. The nner cylndrcal conductor s made of brass and has radus R1 = mm. The outer cylndrcal shell s made of alumnum and has radus R = mm. Both have length l = 435 mm. Fgure. Assembled coax system connected to PNA Network Analyzer. We connect a cable and adapter to the analyzer whch wll eventually connect to thee coaxal lne. Next, we set the frequences on the analyzer to range from 1 MHz to GHz. We are only nterested n dong fnal analyss at the low-frequency range of 1 MHz to 1 MHz; however, we wll take data over a greater range so that we can extract nformaton about the length of the coaxal lne. Ths s descrbed n greater detal n the analyss secton, as well. Before startng any tests, t s crucal we calbrate the network analyzer as precsely as possble to mnmze error. After expermentng wth the E-Cal calbraton method and the Open-Short-Load (OSL) calbraton method, we determned an OSL calbraton was the best method. Ths method conssts of calbratng the end of the connectors (n our case the end of an adapter whch s on the end of a cable connected to the analyzer) as an open lne (nfnte resstance), a short lne (zero resstance), and wth a 5 ohm load on the end of the lne. Ths s an unguded, manual calbraton. The Cal-kt we use s an APC 7mm 855A Cal-kt, but snce there s no APC 7 855A opton to choose n the Calbraton Wzard, we select the 855B APC 7 wth sldng load Cal-kt n the Vew/Select Calkt opton, snce the constants are smlar to the ones n the 855A kt we are usng. After the calbraton s done as accurately as possble, we connect the coax system to the network analyzer by connectng the newly-calbrated cable and adapter to the

3 MERIT BIEN 11 Fnal Report 3 coax. The technque we use to take measurements s known as an open-coax technque. We use ths technque because t has shown to be very promsng when takng measurements of the delectrc propertes of bomaterals [3]. When usng a cylndrcal capactor, ths technque provdes hgh-precson measurements because the magnetc and electrc felds are confned entrely between the nner and outer conductors. Ths provdes less stray felds and less power loss whch allows us to obtan hgh-precson measurements. We begn by mmersng our -flled, opened coaxallne n a transparent contaner flled wth the delectrc materal under test (DUT). The beaker s very tall and sknny and has just a slghtly larger radus than the coax allowng t to ft nsde but wth a very small separaton between the two, mnmzng the menscus effect of the ud. There s a ruler wth.1 m accuracy on the sde of our coax system so we are able to see through the contaner and read the exact depth that the coax system s mmersed nto the DUT. The nner brass conductor s set up nsde the coaxal shell slghtly n order to prevent stray feld effects, so we must mmerse the system n a sgnfcant amount of the DUT, preferably an amount greater than 4mm. We record the depth the system s mmersed n a frst length of ud and save the Smth Chart data as a.prn fle as well as a.ct fle. The.prn fle s read easly by programs such as Matlab, MathCAD, and Excel. Ths type of fle saves the frequences beng tested and real and magnary parts of the systems measured mpedance wth the delectrc materal nsde. The.ct fle s a fle whch can be recalled on the network analyzer but does not read easly nto other programs. It saves the frequency data and the real and magnary parts of the reflecton coeffcent, but n a format that s not read easly nto other programs. Next, we take another measurement wth the same DUT, but wth more of the DUT n the coax system than was n the prevous measurement. We do ths by addng an addtonal amount of the ud to the beaker. We use ppettes to add the addtonal amount of ud n order to add the ud as slowly and accurately as we desre. We agan record the depth the system s mmersed n ths second length of ud, and save the Smth Chart data as a.prn fle and as a.ct fle. We wll use the data from both of these lengths of the DUT to determne the mpedance of the delectrc materal, and use that to determne the materal s capactance, and then fnally extract the delectrc constant from the capactance of the DUT. Ths s explaned n further detal n the analyss secton. IV. ANALYSIS All analyss takes place usng programs wrtten n Matlab. A. Length Analyss It s mportant to determne the exact length of the lne that s flled wth whle the DUT s nsde the system n order to get the most accurate analyss of the materal s delectrc constant. A ruler attached to the sde of the coax system allows us to measure the length of the ud that the lne s mmersed n to an accuracy of 1 mm, but n order to determne the delectrc constant of the DUT, we must know the exact length of the lne that s flled wth durng the tests. To get a rough estmate of the amount of the lne that s flled wth, we could just smply take the total length of the lne, 435 mm, and subtract the length of ud that the lne s mmersed n. However, ths method s not relable enough because we are not clear exactly where nsde the system the measurement begns. We beleve the accuracy of determnng the exact lengths of that the lne s flled wth durng the frst and second measurements of ud s necessary to obtan relable results for a materal s delectrc constant. We must determne lengths L1, L, and L3 shown n Fg.3 for the most accurate calculaton of a materal s delectrc constant. The length L1 represents the amount of Fgure 3. Drawng of the coax system. Determnng lengths L1, L, and L3 to the hghest accuracy s mperatve to get an accurate calculaton for the DUT s delectrc constant. The dotted lnes A and B represent the frst and second lengths of ud, respectvely. that s n our coax system when t s mmersed n the frst length of the delectrc materal, length L3 represents the amount of that s n the coax system when t s mmersed n the second length of ud, and length L s the amount of added ud, n other words, the dfference between L1 and L3. In Fgure 3, dotted lnes A and B represent the frst and second lengths of ud, respectvely. Our method of determnng these lengths nvolves examnng a graph of the real part of the measured mpedance of the system versus the frequency at a range of 1MHz to GHz whle mmersed n the DUT, lke shown n Fg. 4. The graph shown n Fg. 4 s a graph of our system flled wth 1mm of.1 M Salne. We use ths large range of frequences to ensure that we are measurng multple phases of the system. From the graph, we observe a large spke n the

4 MERIT BIEN 11 Fnal Report 4 real mpedance at each frequency where the network analyzer measures a full phase. We take the dfference between two of these peaks, fnd the correspondng wavelength, and then dvde the wavelength by two n order to get the length of the analyzer, 1 s known for every measured frequency f, along wth β as well as L1, whch we determned n the prevous length analyss. Ths leaves L the only unknown n (5) and we can solve (5) for L and result wth an equaton we can use to calculate L every measured frequency that s wrtten as ( 1cos( j sn( ) L. (6) cos( j1sn( Once we solve for each value of L at every correspondng frequency, we need to fnd the test mpedance at the end of the lne wth the second length of ud,. Smlarly, the network analyzer outputs the measured mpedance for the second length of ud, whch we refer to as 3. The expresson for 3 s very smlar to (5) and can be wrtten as Fgure 4. Graph of the systems measured mpedance versus frequency for 1mm of.1 M Salne. We use graphs lke these to determne the length of n the coax system whle each measurement s taken. lne that s flled wth. We have determned usng the later peaks at the hgher frequences s producng more accurate lengths. Because we know the total length of the lne and the amount of water the system s mmersed n, we have an estmate of about how much s n the lne. The peaks at hgher frequences as seemed to produce lengths closest to the expected value. We beleve ths mght be occurrng at hgher frequences because the hgher frequences produce slghtly sharper and as a result, more accurate peaks. We do ths same length analyss for the frst and the second lengths of ud to fnd L1 and L3 and then take the dfference between these two to fnd L. B. Delectrc Constant Analyss The analyss of the delectrc constant of the DUT s based prmarly on the measured mpedance of the coax system. The PNA Network Analyzer outputs the measured mpedance of the coax system when we save the data as a.prn fle. We call the system s measured mpedance wth the frst length of ud 1. From theoretcal analyss that has been done [8], we know ths measured mpedance can be expressed as 1 ( L cos( cos( j sn( jl sn( ), (5) 3 ( cos( cos( j sn( jsn( ), (7) where the only unknown s now. Snce 3 s measured, t s known as well as the rest of the varables, and we can solve (7) for and result n j sn( j3sn( j3 cos(, (8) cos( where L3 s the length of the lne that s flled wth whle the second length of the DUT s n the coax. Agan, from prevous analyss [8], we also know that ( L cos( L) j sn( L), (9) cos( L) jl cos( L) where s the mpedance of the ud n the lne, β s the propagaton constant n the lne wth the DUT at every correspondng test frequency, and L s the dfference between L1 and L3. We also know the mpedance of the delectrc materal n the lne can be wrtten as L, (1) C where L s the nductance of the lne and C s the measured capactance of the ud n the lne per unt length. We also know from theory that capactance can be wrtten as we wrote prevously n (), and (1) can be solved for C to get (3). We can combne equatons (5)-(11), to result n the expresson where s the characterstc mpedance of the lne, L s the test mpedance at the end of the lne wth the frst length of ud, β s the propagaton constant n the lne whle t s flled, L1 s the length of the lne flled wth whle t s mmersed n the frst length of the DUT, and j s the complex unt equal to 1. Because we measure 1 from the network L j tan j tan X L X L 3 j tan( j3tan(, (1)

5 MERIT BIEN 11 Fnal Report 5 where X s a constant characterstc to each frequency and s wrtten as X = ( π f )/c, where c s the speed of lght. Snce every varable n (1) s known except, we use the solve( ) functon n Matlab to extract from (1) and are then able to calculate for every tested frequency. Once we have, we can use (3) to calculate C and then use these values to plug nto (4) and solve for ε r, the delectrc constant. The delectrc constant wll be a complex number ε 1 - jε wth a real part ε 1 and magnary part ε. V. RESULTS AND DISCUSSION range, the real part ε 1 of the delectrc constant of.1 M Salne deally should not vary more than +/-.1 from , whle the magnary part ε of the delectrc constant of.1 M Salne vares over a much larger range, spannng anywhere from 1.8 x 1 to 1.8 x 1 3. Currently, our analyss s producng graphs lke are shown n Fg. 6. Comparng our graphs to the deal results n Fg. 5, t s clear that our current analyss technque s not currently provdng suffcent accuracy. We notce the magnary part of the data looks somewhat accurate, wth most of the data A. Results We nvestgate our current analyss method by comparng our results to prevously measured data for salne solutons ftted to a functon and an analyss program n MathCAD and based on earler work by Stogryn [4, 5]. These results are shown n Fg. 5 and are graphs that we are strvng to acheve wth our system. It s clear from Fg. 5 that n the 1 MHz to 1 MHz Fgure 5. Graphs and are based on prevous work for.1 M Salne and are the results we desre to fnd usng our measurement and analyss technques [4, 5]. Graph shows the real part ε 1 of the delectrc constant versus measured frequency, whle graph shows the magnary part ε of the delectrc constant versus measured frequency. Fgure 6. Results from our current analyss technque of determnng a materal s delectrc constant. Graphs and show the absolute value of real and magnary parts of the delectrc constant versus frequency, respectvely. remanng n the range of 1.8 x 1 to 1.8 x 1 3 and followng a very smlar behavor to that seen n Fg.5. However, the real part of our.1 M Salne data vares largely from the deal values shown n Fg. 5 for what we expect n the low-frequency range. Not only does our data not match the expected value of /-.1, t spans over a sgnfcant range wth the majorty of our data somewhere n between and 8. Ths s not at all what we expect whch leads us to beleve there s a dscrepancy n our analyss. It s also mportant to note Fg 6. shows the absolute value of the real

6 MERIT BIEN 11 Fnal Report 6 and magnary parts of the delectrc constant. Most of all the measured values were negatve and ths s not at all what we expect. We graph the absolute value because perhaps the sgn dfference s a dscrepancy n the analyss. Whle the data for our.1 M Salne strays sgnfcantly from expected values, we beleve our analyss technque s not entrely nconclusve. We also performed tests usng tap water and the resultng data s shown n Fg. 7. the real part of the delectrc should begn to declne [5, 6]. When our data passes about 5 MHz, the real part of the delectrc constant begns to scatter and ncrease n value. Ths behavor s unexpected and shows that there may be some ncrease of nose n the data when t reaches 5MHz. Whle Fg. 7 shows somewhat promsng behavor, the magnary part of the delectrc constant shown n Fg. 7 does not follow expected behavor. Prevous measurements and analyss of the delectrc constant of water says that the magnary part of the delectrc constant should reman very small, very close to but not below zero, untl t reaches the hgh-frequency range [6, 7]. In Fg. 7 we are agan graphng the absolute value of the data because the majorty of the data was below zero. We can see however, that n Fg. 7 as the data approaches 1 MHz, t seems to be somewhat approachng zero, more lke we expect. Fgure 7. Graphs and show the calculated real part and absolute value of the magnary part of the delectrc constant of tap water versus frequency usng our current analyss technque. Ths graph shows our analyss s promsng because we know the expected value of the real part of the delectrc constant of water s 8. at room temperature of about C [7]. When usng tap water, the real part of the data, shown n Fg. 7, ntally appears lke we expect up untl about 5 MHz, remanng relatvely constant at a value of about 8. We beleve 5-Jul and 11-Jul data s slghtly offset from the 19-Jul data because of a slght offset n calbraton, but behavor of these two s exactly the same as the 19-Jul data. We know from prevous work that at room temperature, the delectrc constant of water should reman around 8 whle n the lowfrequency range, and when t reaches about 1 GHz the value of Fgure 8. Graphs and show the calculated real part and magnary part of the delectrc constant of DI water versus frequency usng our current analyss technque. Error n the magnary part of the data s sgnfcantly reduced. Recently, we just began examnng the system wth deonzed (DI) water. We expect DI water to be much purer than the tap water data; however n Fg. 8, t s clear that the real part of the DI water data follows almost the same behavor as the tap water and does not appear to have much reducton of

7 MERIT BIEN 11 Fnal Report 7 nose or any sgnfcant ncrease n accuracy. The real part of the delectrc constant, shown n Fg. 8, s shfted slghtly upward from the expected value of 8, perhaps from an mprecse calbraton, but the behavor of the data appears almost dentcal to the real part of the delectrc constant wth tap water. Comparng the very lttle ncrease n accuracy between tap water and DI water, we can nfer that the error n accuracy s not the data measurements, but the analyss. The one large dfference between the tap water data the DI water data s the magnary part of the delectrc constant. We can see n Fg. 8 that the magnary part of the delectrc constant behaves much more lke we expect, remanng very close to zero but stll becomes sgnfcantly scattered as the frequency ncreases. Wth ths data, we do not need to plot the absolute value of the real or magnary part of the data B. Dscusson It s mportant to note the dfference n the salne data and the tap and DI water data. The tap and DI water data appears noser at the end of the frequency range, whle the salne data appears most nosy rght at the begnnng of the frequency range. Also, we do not expect tap water data to appear cleaner and more accurate than the salne data. Tap water has many mpurtes whle the salne soluton s made wth solely deonzed water and sodum chlorde (NaCl). Ths s made clear when we examne the plots of the complex reflecton coeffcent on the network analyzer. The mpurtes n the tap water create gltches n the data that are very apparent. However, when examnng the plots of the system wth salne 1mm of tap water and nsde. In Fg. 9 wth the tap water, we see wavy lnes and a random unexplaned loop n the mddle. In Fg. 9 wth the salne soluton, we see very smooth data as we expect wth consstent behavor. It s mportant to remember the graphs on the network analyzer are of the complex reflecton coeffcent. When we save the data as a.prn fle, the analyzer takes the data for the reflecton coeffcent and converts t to the measured mpedance of the system. Perhaps whle the analyzer converts the data nto the.prn format, some nose s ntroduced n the process. Ths may explan why the nose reducton between the tap water and salne soluton s not as drastc as t appears on the network analyzer, however t stll does not explan why the end of the tap water data has the most nose and the salne data appears to have the exact opposte behavor. The calbraton method also has the potental to be mproved. Snce we are currently usng the 855A Cal-kt but ths kt s not avalable n the PNA Network Analyzer s Calbraton Wzard, some of the calbraton constants may be slghtly off whch wll produce and offset n the system s measurements. Ths naccuracy s most notceable n the open calbraton. Both the short and the load calbraton look lke very precse dots on the Smth Chart, whle the open calbraton s consstently the most mprecse. Ths may be because the open calbraton constant n the 855B kt s slghtly dfferent than the open calbraton pece we are usng n the 855A kt. Expermentng wth dfferent Cal-kts or even perhaps dfferent calbraton methods could reduce some of ths error n the calbraton. We beleve ths current analyss program s very senstve to nose n the data as well as very senstve to the exact length of n the system durng measurements. Especally f more nose s ntroduced to the data when the analyzer converts from complex reflecton coeffcent to the mpedance, ths senstvty n our analyss program becomes a major complcaton. We beleve the data s not ncorrect, but the analyss program contans certan features that are causng nsuffcent accuracy. The senstvty to nose must be reduced n ths analyss program before we can calculate relable delectrc constants. Fgure 9. Graphs and show the complex reflecton coeffcent for 1 mm of tap water and salne nsde the coax, respectvely. Impurtes n the tap water data s made very apparent compared to the graph of.1 M Salne. nsde nstead of tap water, all the gltches n the data seem to be gone. Ths behavor s shown n Fg. 9, whch shows plots of the complex reflecton coeffcent of the system wth both VI. CONCLUSION AND FUTURE WORK We use an open-ended coaxal lne to nvestgate delectrc propertes of smulants for bologcal tssue. The open-coax measurement technque gves values of nput mpedance that can be analyzed to get the delectrc constant. We desre to determne a relable value of the delectrc constant for varous uds, and examne the dependency of that constant on frequency n the range 1 MHz to 1 MHz. Relable values of delectrc constants of bologcal smulant materals are mportant to determne, n order to support theoretcal analyss and complex numercal modelng of the energy absorbed from wreless devces that are placed close to, or worn on the human body. Before we can measure the delectrc propertes of bologcal smulants, we must get relable data for the

8 MERIT BIEN 11 Fnal Report 8 delectrc propertes of uds whose delectrc propertes are already well-known. We use an open-coax technque whch nvolves takng the -flled, open-ended coaxal lne and mmersng t n the materal of whch the delectrc constant s desred. Ths project has been prmarly workng wth water and salne solutons to determne f our current analyss method s outputtng relable delectrc constants. The analyss program we are usng to calculate the delectrc constant s currently nconclusve. Ths analyss technque takes the measured mpedance of the ud-flled coax lne and uses the known depth of the ud partally fllng the coaxal lne and the dmensons of the nner and outer conductors to determne the delectrc constant. We beleve ths analyss program s extremely senstve to nose n the data. It s also very mportant wth ths analyss that we measure the amount of n the coaxal lne as precsely as possble whle takng measurements to mnmze error. A new analyss program s currently under development that may be less senstve to nose and the exact measurement of n the system. When ths analyss s done, both methods of analyss can be compared to further develop ths project. Ths coaxal system and measurement technque have the potental to be very effectve n determnng the delectrc constant of bologcal smulants wth mproved calbraton technques and a more accurate analyss program. ACKNOWLEDGMENT I would lke to thank Dr. Chrs Davs and Dr, Q. Balzano for all ther help and advsng on ths project. I would also lke to thank the Electrcal and Computer Engneerng department at the Unversty of Maryland along wth the MERIT BIEN staff for the opportunty to partcpate n ths program. Lastly, I would lke to thank Ingy aky, Peter Solman, John Rzasa, and my fellow MERIT BIEN students for all ther help and support. REFERENCES [1] R. Nelson Parrsh, (9, January ). Wreless Implantable Medcal Devces. [Onlne] Avalable: [] P. Solman, Delectrc Materals. Summary of research wth Dr. Chrs Davs. 9, unpublshed. [3] Chrstopher C. Davs, Nasm Vakl, Erc Merdeth. Delectrc Measurements of Bran Phantom and Standard Materals, Unversty of Maryland, unpublshed. Avalable: [4] C.C Davs, "Delectrc propertes of salne solutons", Unversty of Maryland Insttute for Systems Research Report Number 1-11 (1). [5] Stogryn A. Equatons for calculatng the delectrc constant of salne water. IEEE Trans. Mcrow. Theory Techn (1971). [6] Messner, T. and Wentz Frank J. The Complex Delectrc Constant of Pure and Sea Water From Mcrowave Satellte Observatons, IEEE Trans. Geosc. Remote Sensng, 4(9), pp , Sep. 4. [7] Complex Delectrc Constant of Water. 11 May. Onlne delectrc calculator based on models from [6]. [8] C.C Davs, Q. Balzano. Current research at Unversty of Maryland, 11.