Characterising the Relative Permittivity and Conductivity of Seawater for Electromagnetic Communications in the Radio Band - Summary Report 2012

Transcription

1 Characterising the Relative Permittivity and Conductivity of Seawater for Electromagnetic Communications in the Radio Band - Summary Report 2012 Emma M. O Shaughnessy University of New South Wales at the Australian Defence Force Academy. Electromagnetic wave signalling underwater, while normally restricted to low frequencies because of exponential attenuation, has useful applications at higher frequencies over short ranges. The mathematics of electromagnetic wave propagation shows a close dependence on the permeability, permittivity and conductivity of the transmission medium. Methods of measuring the permittivity and conductivity of typical fresh and salt water media have been studied, as a function of frequency, and field simulations and experimental measurements have been carried out with some success in the validation of theoretical predictions up to a frequency of 1 GHz. Contents I Introduction 2 II Literature Review 2 II.A Underwater Communication Methods II.B Electromagnetic Propagation Theories II.C Methods Available for Measuring Conductivity and Permittivity III Low Frequency Measurements 5 IV High Frequency Measurements - Background Theory 6 IV.A Slabline Construction IV.B Calculating Relative Permittivity (ɛ r ) and Conductivity (σ) IV.C Theoretical Modelling IV.D Modelling in CST V High Frequency Measurements - Results 8 V.A 1 Port Measurements V.B 2 Port Measurements VI Conclusions 10 Nomenclature α β γ ɛ Attenuation factor with distance (db/m) Phase factor with distance (rad/m) Propagation constant (rad/m) Permittivity (F/m) PLTOFF, School of Engineering and Information Technology, ZEIT4500/ of 12

2 λ Wavelength (m) σ Conductivity (S/m) µ Permeability (H/m) u p Phase velocity (m/sec) ω Angular frequency (rad), (ω = 2π f ) E Electric field intensity (V/m) f Frequency (Hz) H Magnetic field intensity (amp-turns/m) t Time (sec) For Seawater the following approximate values were used: ɛ 0 = ɛ r = 81 µ 0 = 4π 10 7 (H/m) σ = 4 I. Introduction WIreless transmission of information through air can use electromagnetic, optical, infrared and ultrasonic carriers. Examples of their use range from a "remote" control transmitting data to a television, to an aircraft navigation system. Comparing propagation underwater, acoustic communications have a large range of applications over ranges of ten s of kilometres, using transmission frequencies in the range of 1 khz - 1 MHz, inversely related to range [1]. Optical systems allow high data transmission rates at short distances, the range being limited by turbidity. The remaining possible form of wireless communication underwater uses electromagnetic propagation. Throughout this project electromagnetic propagation through seawater is being explored to determine the most ideal frequency range for data transmission. II. Literature Review II.A. Underwater Communication Methods Currently the most common source for underwater communications is through acoustic propagation. Sound travels at a speed of 1500 m/s through seawater, which means when sending a signal at this slow speed channel latency can occur and Doppler effects must be managed [1]. The ocean may be referred to as a waveguide for acoustic signals as they are bounded by the upper surface and by the sea floor. Consequently reflections from these surfaces must be considered and shadow zones addressed. The significant advantage of acoustic underwater communications is its ability to propagate over large distances, being a number of kilometres and it is a well known and successful communication technique. Hence it can be summarised that the attenuation of underwater acoustic signals is sourced from spreading loss, absorption loss and scattering loss, while it is beneficial for its long range capacity [1]. Optical signals are also a mode of communication underwater, however is of less common use. They are generally used for short range data transfer and their applications are being explored in littoral waters, as shallow waters are where acoustic communications are least effective [2]. Optical signals can provide higher bandwidth in these areas compared to acoustic signals, being in the approximate ranges of Gigabits per second (Gbps) and 20 kbps respectively [3]. The main limitations for optical signals are they are rapidly absorbed in seawater as well as being subject to the scattering effects of particles suspended in the water [1]. As a result for optical signals to be effective they require line-of-sight and operate best within a matter of metres. Hence high data transmission rates of optical signals is its main advantage despite only working over short distances. Drawbacks from optical signals are that they do not easily cross the water to air boundary while it is not a possibility for acoustic signals. Electromagnetic signals suffer a large refraction loss across the air-water 2 of 12

3 boundary. Is is also not obscured by suspended particles as optical signals are or affected by the waters pressure gradients and turbidity as acoustic signals are [3]. Other significant advantages for electromagnetic propagation underwater include an antenna system can be easily transported in compact units, it is immune to acoustic noise, low visibility areas do not affect its performance and there may be possibilities for the use of the Megahertz carrier for high data transmission rates [4] [5]. Due to the great potential for electromagnetic signals to be ideal short distance data transmitters, acoustic and electromagnetic underwater propagation can be considered as complementary technologies. Over the past decade digital technology has rapidly increased. This has lead to communication systems, such as Bluetooth, that make valuable use of high bandwidth, short range technologies. It has been identified that a range of similar applications can be used underwater over short ranges, including for communications between Unmanned Underwater Vehicles (UUV) and submarines or a surface vessel as well as diving communications and navigation [5]. Hence it can be said that the requirement for underwater communications lies not only with military applications but also with industrial needs as highlighted by Rhodes [5]. Two commonly used systems characterised by underwater wireless communications are Autonomous Underwater Vehicles (AUV) and Remotely Operated Vehicles (ROV). Either of these may be employed for scientific or military purposes and operate via acoustic or optical communications. The possibility of using electromagnetic communications within AUV s is being explored to increase sensor density by employing a large number of small platforms compared to a few large platforms connected via cables [6]. II.B. Electromagnetic Propagation Theories An electromagnetic wave travelling in a medium is governed by Maxwell s equations [7]. If the wave is travelling in the positive z direction, where e γz is the phase and attenuation factor, then its electric field strength (E) and magnetic field strength (H) can be described as follows: E = E 0 e jωt γz (1) H = H 0 e jωt γz (2) The propagation constant, γ, of a medium is dependent on the frequency, conductivity, permittivity and permeability as shown in Eq (3): ( γ water = jω µ 0 µ r ɛ 0 ɛ r j σ ) = α + jβ (3) ω where α is the attenuation factor and β is the phase factor. As the purpose of this project is to determine the most ideal range of frequencies for electromagnetic propagation through seawater, we are then left with the variables µ r, ε r and σ. For water, the relative permeability is always 1 which leaves two variables when analysing the propagation constant.these two variables are defined below: Permittivity, ε, is the property of a material which relates the electric flux density to the electric field. Permittivity is measured in Farads per metre (F/m). Conductivity, σ, is the property of a material which measures the ratio between its current density and electrical field density. Conductivity is measured in Siemens per metre (S/m). Returning to Eq (3) there are two solutions depending on whether the frequency is large or small. The first is a solution for the conduction band where ω σ > ɛ and the second is for the dielectric band where ɛ > σ ω. After applying these conditions, the conduction band the propagation constant can be approximated as follows: and for the dielectric band the following approximation is made: γ CB = (1 + j) π f µσ (4) γ DB = jω µɛ σ µ ɛ (5) 3 of 12

4 While the conduction band is continually dependent on frequency and the (1+j) term indicates the real and imaginary parts increase equally with frequency, the dielectric band has a different effect occurring. Assuming the permittivity and permeability are purely real, the second term in Eq (5) has no ω term indicating the real part of the equation is independent of frequency while the imaginary part varies with frequency. The figure below explicitly shows how the conductivity of water with a relative permittivity of 81 can greatly effect its electromagnetic propagation. Assuming we have ideal conditions where the relative permittivity of seawater is 81 and conductivity is 4, the change over period from the conduction band to the dielectric band occurs around 887 MHz. When considering electromagnetic propagation through seawater is is also necessary to explore Debye s Theory and the Cole-Cole model. Debye s Theory describes the relationship between relative permittivity and frequency of EM waves in a dielectric medium. Debye makes the following assumptions [8]: Figure 1. Electromagnetic propagation through water for a varying range of conductivity. - molecules are free and do not interact with each other - polarization of the dielectric contains induced and orientation components Comparatively, the Cole-Cole model takes into consideration the intermolecular interactions. These models result in two similar but slightly different equations for the relative permittivity for a dielectric. II.C. Methods Available for Measuring Conductivity and Permittivity In the past, conductivity measurements of seawater have have been achieved via inductive conductivity measurements. This has consisted of a single transformer where the primary coil is wrapped around a ring-shaped transformer and the secondary coil is the seawater [9]. The seawater induces a current in the primary coil and the real component of this current is a measure of the seawaters conductivity [9]. Other methods include with double transformer and the double transformer with an additional loop, where both methods also operate inductively. Further information regarding these methods can be found in [9]. Inductive measurements of conductivity have since improved to the invention of the conductivitytemperature-depth (CTD) instruments. As its name implies this is another method for measuring conductivity. Sea-Bird is a reliable manufacturer of CTDs and their design is based upon a three-electrode cell measurement located within a mechanically aspirated duct where water is continuously pumped through the instrument every ten seconds [10]. While CTD s are ideal for measuring conductivity they are expensive and generally operate at a single frequency hence not ideal for this project. Another method investigated was using a single probe coaxial sensor in accordance with Seewattanapon and Akkaraekthalin s work in A Broadband Complex Permittivity Probe Using Stepped Coaxial Line [11]. Their method was based upon retrieving the reflection coefficient from the coaxial sensor connected to a VNA. The frequency range tested with this method was 0.1 GHz to 6 GHz. A similar technique was found in Blanch and Aguasca s Seawater Dielectric Permittivity Model from Measurements at L Band [12]. Blanch and Aguasca s purpose for determining permittivity was heavily reliant on brightness temperature and how it characterises remote sensing. Their technique consisted of a stripline structure that could be filled with liquids and contained a transmission line down the centre. Connecting the structure to a VNA 2-port measurements could be used to obtain transmission and reflection coefficients. These could then be placed through a series of equations as outlined in their paper to derive permittivity and conductivity. It was this method that was chosen to be explored throughout my project. While Blanch and Aguasca s method was investigated for high frequencies, as the VNA begins operating at 300 khz, it was necessary to also investigate a method for the lower frequency range to complement 4 of 12

5 the higher frequencies. This was achieved through the use of a gain phase meter that covered the range 1 khz to 13 MHz and an electrode cell that was already available and ready for use. This method is explained further in the following section. III. Low Frequency Measurements It is known that the Conductivity of a material is related to the materials length (L), cross-sectional area (A) and resistance (R) by the following equation: σ = 1 ρ = L RA (6) Where L is measured in meters (m), R in Ohms (Ω) and A in meters squared (m 2 ). Using this relationship it is possible to determine a materials conductivity given its dimensions. Applying this theory, a cell was acquired that could contain aqueous solutions as is shown in figure 2. Additionally it is known that the relationship between a materials dimensions and capacitance are: C = ɛ 0ɛ r A d (7) Figure 2. Empty Cell for Conductivity Measurements. Inner dimensions: 115 mm x 80 mm x 38 mm. Plates are 0.5 mm thick. Attached to the cell is 1 m of CG58U Coaxial Cable with a BNC to connect to measurement instruments Where A is the cross-sectional area (m 2 ) of the plates and d is the spacing between the plates (m). Hence the relative permittivity can be calculated as follows: ɛ r = Cd Aɛ 0 (8) Once these relationships were known a method was constructed to assist in extracting permittivity and conductivity. The electrode cell was connected to a gain phase meter with an equivalent circuit of the connection shown in figure 3. In figure 3 the resistor and capacitor in parallel can be equated to a single impedance Z which would represent the electrode cell. Circuit analysis of figure 3 shows Z can be equated as follows: R in V a R a V b R b C b Figure 3. Equivalent circuit for determining characteristics of circuit with known values of R and C. V B Z = R a (9) V A V B Prior to completing measurements with the electrode cell connected to the Gain Phase meter, a range of resistor and capacitors of known values were placed in parallel in its place as shown in figure 3. This was to validate the procedure by ensuring accurate resistor and capacitor values were being returned which would then effect the conductivity and permittivity readings. When completing this experimentally it was discovered that the coaxial cable connecting the cell to the Gain Phase meter was effecting the results by adding a parasitic capacitance of 91.7 pf. This value was found using an LCR meter and removing this capacitance throughout calculations enabled a more accurate results set. Figure 4 displays the permittivity and conductivity results obtained from the electrode cell containing tap water, de-mineralised water and an empty cell. It was found that the permittivity of the de-mineralised water was 90 S/m while the tap water was remarkably higher at 95 S/m. The reasons for these rather high permittivity values is expected to be due to unaccounted for capacitance values. The conductivity on the other hand was revealing expected results with the conductivity of fresh judged to be close to 10 2 S/m. 5 of 12

6 (a) Permittivity (b) Conductivity Figure 4. Permittivity and Conductivity results for Electrode Cell IV. High Frequency Measurements - Background Theory Research was conducted into various methods for determining the permittivity and conductivity of seawater, the model designed by Blanch and Aguasca in Seawater Dielectric Permittivity Model from Measurements at L Band [12] was selected to be investigated. This particular model was chosen as it followed a method that had several successful reports by other researchers and enabled the frequency range of the system to be expanded into a higher range then previously examined with the Gain-Phase meter. Additionally, the testing system was capable of being constructed at minimal cost and a vector network analyser was available for use. Other advantages included the ability for it to be simulated on CST s microwave studio. Blanch and Aguasca s purpose for creating an accurate seawater dielectric permittivity model was to improve their knowledge regarding seawater dielectric properties with regards to remote sensing. The process undertaken involves a slabline structure which is a cylindrical structure placed inside two parallel plates as shown in figure IV.D. This structure can then be connected to a Vector Network Analyser to measure the complex permittivity of dielectrics through reflection and transmission coefficients. Figure 5. slabline structure in CST IV.A. Slabline Construction Blanch and Aguasca provided information on how to determine the permittivity and conductivity of the dielectric once transmission and reflection coefficients were obtained, however did not provide information regarding the dimensions or construction of the slabline structure. To construct the slabline, Brian Wadell s work was consulted with his book Transmission Line Design Handbook [13] which details a range of uncommon shaped transmission lines. In accordance with Wadell s work the following relationship between dimensions, relative permittivity and impedance was defined as follows [13]: 6 of 12

7 Z 0 = η ( ) 0 4D 2π ln ε r πd where variables are defined as shown in figure 6. It was selected that the slabline impedance was to be 50 Ω where: µ0 η 0 = = 120π = 377 ε 0 Given d = 1.28 mm D could then be calculated. The final dimensions of the slabline have been included as an Appendix. (10) IV.B. Calculating Relative Permittivity (ɛ r ) and Conductivity (σ) 2 port measurements can be conducted on the slabline by connecting it to a Vector Network Analyser to obtain S-parameters. Once the S-parameters are ob- Figure 6. Basic slabline dimensions tained they can be implemented into a series of equations to determine the complex permittivity and conductivity of dielectrics. This method was based on the model designed by Blanch and Aguasca in Seawater Dielectric Permittivity Model from Measurements at L Band [12]. The data retrieved from the VNA is S 11 and S 21. They are variables then entered into equation 11 leading to the following procedure: From here the reflection coefficient can be calculated as follows: And the transmission coefficient is given by: K = S 11 2 S S 11 (11) Γ = K ± K 2 1 (12) T = S 11 + S 21 Γ 1 (S 11 + S 21 )Γ The Transmission coefficient can also be defined by the following equation: (13) T = e j ω c εr d Hence as the transmission coefficient, frequency and transmission line length (d) are known the relative permittivity can be calculated. d = 200 mm (14) c ε r = j ln(t) (15) 2π f d Additionally, Blanch and Aguasca outlined that the dielectric properties of liquids are described by the Debye model: ε r = ε jε = ε + ε s ε 1 + jωτ j σ ωε 0 (16) where ε is the permittivity at optical frequencies, ε is the static permittivity, τ the relaxation time and σ the ionic conductivity. Relaxation time is the time taken for the dielectric to reach a state of equilibrium and is defined by: τ = ε σ (17) 7 of 12

8 IV.C. Theoretical Modelling Once the slabline method was selected to complete, it was decided to be modelled theoretically. This was completed by beginning with the propagation Eq 3 and assuming the values of 81 for relative permittivity and 4 S/m for the conductivity. Using these values and calculating the slabline impedance using equation 10 ABCD parameters could be obtained. ABCD parameters then allowed conversion to S-parameters as per the methods suggested by Pozar [14]. Once S-parameters were obtained, equations 11 to 16 could be applied to obtain conductivity and permittivity. IV.D. Modelling in CST Microwave studio s CST program was also used to analyse the slabline. The slabline was desisgned in CST in as shown earlier in figure. This has allowed a mathematical calculation of the S-parameters and has proved to be rather valuable in characterising the electric and magnetic fields within the slabline. The disadvantage of CST is that once the permittivity and conductivity values are entered into CST they act as a constant rather than a variable and do not vary with frequency. This contributes to why it was necessary to complete an experimental analysis. V. High Frequency Measurements - Results The slabline testing was to be undertaken in various stages. The slabline was initially constructed with one side wall fixed in place and the second could be removed due to stainless steel screws holding them in place. It was then later sealeda so liquids could be placed within the structure without leaking. Exploiting the advantage of having a removable wall, it was decided that testing would be completed prior to the slabline being sealed as well as after. The advantage of completing measurements prior to sealment is that liquids could be placed within a plastic bag then placed inside the slabline. The purpose of this was so gradual effects of adding water to the confines of the structure could be observed. For both the sealed and unsealed slabline 1-port and 2-port measurements were taken, with each revealing characteristics about the dielectrics contained within. (a) 1-port. (b) 2-port. Figure 7. VNA set up for 1-port measurements (a) and 2-port measurements (b) V.A. 1 Port Measurements One port testing was the first undertaken with the slabline. This report shows one set of results for the sealed data only. 1-port tests were conducted with a short circuit, open circuit, 50 Ω load and a 100 Ω load a The slabline was sealed with Duralac, a sealant commonly used in the aircraft and watercraft industries [15] 8 of 12

9 under each of the following circumstances: Connection to VNA only Connection to empty slabline and VNA Connection to slabline containing de-mineralised water Connection to slabline containing salt water These tests were undertaken with the intention to gradually work up to filling the entire slabline with salt water. This process was chosen to determine if the results follow a pattern and assist in validating results for a full slabline. It should also be noted that salt water was constructed by combining demineralised water with a measured mass of sea salt to combine to give 35 ppt. It possible to predict the behaviour of the reflection coefficient using the following equation: Γ L = Z L Z 0 Z L + Z 0 (18) where Z 0 = 50Ω. 1-port measurement results will be contained in the final report. V.B. 2 Port Measurements The first set of measurements taken was with an empty slabline connected between ports 1 and 2 and the desired final set of measurements to be taken was with salt water filling the slabline in direct contact with the transmission line. Initially Smith chart comparisons were made between the sealed and unsealed raw data results previously obtained. This is shown in figure 8. In all of the figures note that the green diamond represents the starting frequency (300 khz) and the red asterisk represents the end frequency. The initial comparisons show that for an empty slabline there is no significant difference between the sealed and unsealed data sets as they are on top of each other. Differences begin to appear when the demineralised water S-parameters are compared. It is observed that both the sealed and unsealed S 11 parameters begin in the location for a 50 Ω load, being (0,0) while the S 21 parameters begin in the open circuit range. Both data sets then proceed to circulate, however the sealed data follows a smooth line while the unsealed has numerous inner loops. These loops in the unsealed data may be a result of the slabline not being quite as secure or more likely due to the water for the unsealed slabline being located within a plastic bag. As the intermediate stage had the water located within the plastic bag the water is not in direct contact with the transmission line and there would be some air gaps present. This is most likely the source of the smaller loop anomaly s. The salt water comparisons then reveal interesting information in themselves as both S-parameters for each of the data sets begin and end in completely different locations. The circular patterns of the unsealed data suggests a lossy material while the sealed data shows the extreme version and appears to be undergoing a significant amount of attenuation. Figure 8. Smith chart plots comparing 2-port S-parameter data between the sealed (Magenta) and unseald (Blue) raw data measurements. I was becoming rather interested in the process of analysing the different waters that I decided to collect sea water from Clovelly Beach, Sydney and had a willing family member bring me sea water from Yeppoon, 9 of 12

10 QLD to compare to the 35 ppt salt water concoction. Both of these samples of water were processed through the same procedure and smith chart results were congruent with the constructed salt water reinforcing that it was accurately constructed. Following the retrieval of S-parameters it was necessary to de-embed the data to omit parasitics introduced by connections between the VNA and actual transmission line within the slabline. It was found that this introduced a slight translation of the data, however it maintained its general shape and was similar to what was expected from the theoretical modelling. The procedure outlined earlier in eq to extract permittivity and conductivity were then followed for the sealed data sets. Figure 9 shows the current results set for relative permittivity and conductivity for the slabline containing salt water. The results in figure 9 show permttivity varying greatly, however uniformly, with frequency while conductivity asymptotes towards 0. The reasoning for these results is currently under investigation and a greater analysis will be provided in the final deliverable. (a) 1-port. (b) 2-port. Figure 9. Results obtained following the eq for relative permittivity (a) and conductivity (b) To ensure the analysis was being undertaken correctly and accurately a number of checkpoints were conducted. The first was to ensure that the VNA was correctly calibrated before data was collected. This involved calibrating the VNA with an open connector, short connector and broadband load connector contained within the calibration kit over the desired frequency range. The next stage was to ensure the deembedding process was followed correctly and resembled the theoretical model. Once this was confirmed the procedure obtained from [12] was checked to ensure it was understood correctly and this was believed to be the case. My project supervisor, Dr. Robin Dunbar, in parallel conducted the same analysis which resulted in the same findings for permittivity and conductivity. VI. Conclusions Throughout the literature review it was identified that there is a distinct advantage for electromagnetic communications through seawater. Electromagnetic propagation allows high data rates however is limited by its attenuation through seawater. The propagation constant, which governs electromagnetic communications, was analysed and its high reliance on the mediums relative permittivity and conductivity was established. This then proceeded to the various methods that are currently available for measuring conductivity and permittivity. The noticeable difference between papers found was that their areas of interest were focused on varying temperature while mine was to be frequency. Low frequency measurements were conducted on the electrode cell from the range of 1 khz to 10 MHz with the use of a Gain Phase meter. For the high frequency range he method outlined in [12] was chosen to be investigated with varying the frequency from 300 khz to 750 MHz. A stripline structure was successfully built which was referred to as a slabline. The analysis of the slabline was conducted through theoretical modelling, CST and experimental work. The experimental work for extracting permittivity and conductiv- 10 of 12

11 ity has not yet revealed results around the range of and 4 S/m and work is being continued in this area. While the results are currently not what was anticipated a careful and succinct procedure has been followed and closely analysed. Acknowledgements A special thanks must go to both of my project supervisors, Dr. Greg Milford and Dr. Robin Dunbar, who have provided invaluable support continuously throughout the year and guided me through my research. They have also successfully stimulated my interest in the area of underwater communications through their own enthusiasm for this subject. 11 of 12

12 References 1 Preisig, J., Acoustic Propagation Considerations for Underwater Acoustic Communications Network Development, WUWNet 06 Proceedings of the 1st ACM International Workshop on Underwater Networks, New York, USA, 2006, pp Giles, J. W. and Bankman, I. N., Underwater Optical Communications Systems. Part 2: Basic Design Considerations, Military Communications Conference, MILCOM IEEE, Vol. 3, 2005, pp Che, X., Wells, I., Dickers, G., Kear, P., and Gong, X., Re-Evaluation of RF Electromagnetic Communication in Underwater Sensor Networks, IEEE Communications Magazine, Metropolitan University, December 2010, pp Shaw, A., Al-Shamma a, A., Wylie, S., and Toal, D., Experimental Investigations of Electromagnetic Wave Propagation in Seawater, Proceedings of the 36th European Microwave Conference, EuMA, Manchester, UK, September 2006, pp Rhodes, M., Electromagnetic Propagation in Sea Water and its Value in Military Systems, Proceedings of 2nd Annual Conference Systems Engineering for Autonomous Systems Defence Technology Centre, Edinburgh, UK, July, Frater, M., Ryan, M., and Dunbar, R., Electromagnetic Communications within Swarms of Autonomous Underwater Vehicles, ACM Workshop on Underwater Networks, WUWNET 06, Los Angeles, 2006, pp Horvat, V., Handbook of Ocean and Underwater Engineering, chap. Underwater Radio-Wave Transmission, McGraw-Hill, 1969, pp Somaraju, R. and Trumpf, J., Frequency, Temperature and Salinity Variation of the Permittivity of Seawater, IEEE Transactions on Antennas and Propagation, Vol. 54, 2006, pp Striggow, K. and Dankert, R., The Exact Theory of Inductive Conductivity Sensors for Oceanographic Application, IEEE Journal of Oceanic Engineering, Vol. OE-10, 1985, pp Johnson, G., Toole, J., and Larson, N., Sensor Corrections for Sea-Bird SBE-41CP and SBE-41 CTDs, Journal of Atmospheric and Oceanic Technology, American Meteorological Society, Seattle, WA, 2007, pp Seewattanapon, S. and Akkaraekthalin, P., A Broadband Complex Permittivity Probe Using Stepped Coaxial Line, Journal of Electromagnetic Analysis and Applications, Vol. 3, 2011, pp Blanch, S. and Aguasca, A., Seawater Dielectric Permittivity Model from Measurements at L Band, Geoscience and Remote Sensing Symposium, Vol. 2, IEEE International, Spain, Barcelona, 2004, pp Transmission Line Design Handbook, Teradyne, Inc, Boston Massachusetts. 14 Pozar, D. M., Microwave Engineering, John Wiley and Sons, USA, llewellyn Ryland, Birmingham, England, Anti-Corrosive Jointing Compound, ed. 12 of 12