Material Characterization Using Complementary Split-Ring Resonators
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 61, NO. 11, NOVEMBER 2012
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Material Characterization Using Complementary Split-Ring Resonators Muhammed Said Boybay, Member, IEEE and Omar M. Ramahi, Fellow, IEEE
Abstract—A microwave method based on complementary split-ring resonators (CSRRs) is proposed for dielectric characterization of planar materials. The technique presents advantages such as high measurement sensitivity and eliminates the extensive sample preparation procedure needed in resonance-based methods. A sensor in the shape of CSRRs working at a 0.8– 1.3 GHz band is demonstrated. The sensor is etched in the ground plane of a microstrip line to effectively create a stopband filter. The frequencies at which minimum transmission and minimum reflection are observed depend on the permittivity of the sample under test. The minimum transmission frequency shifts from 1.3 to 0.8 GHz as the sample permittivity changes from 1 to 10. The structure is fabricated using printed circuit board technology. Numerical findings are experimentally verified. Index Terms—Complementary split-ring resonators (CSRRs), material characterization, near-field sensors.
I. I NTRODUCTION
P
ERMITTIVITY is an important material characteristic for electrical engineers. The response of a material to electrical signals depends on the permittivity of materials. Thus, precise determination of the permittivity is an important task for microwave/radio-frequency circuit design and antenna design, and for microwave engineering in general. In addition, characterization of materials or detecting changes in the electrical properties of materials has applications in areas such as quality control in food industry, biosensing, or subsurface detection [1]–[6]. For most of the applications, properties such as the material composition, moisture or water content, etc., of the sample under test carry valuable information. Since electrical properties of materials depend on these properties, quality control in materials science, in food industry, biosensing, or subsurface detection can be conducted based on sensing electrical properties of materials. Many methods have been proposed and used for material characterization. These methods can be classified as free-space methods, transmission-line methods, near-field sensors, and resonant cavity methods. In free-space methods, the classical bistatic measurement setup consists generally of a pair of spotManuscript received January 30, 2011; revised August 12, 2011; accepted August 29, 2011. Date of publication June 29, 2012; date of current version October 10, 2012. The Associate Editor coordinating the review process for this paper was Dr. S. Trabelsi. M. S. Boybay is with the Department of Computer Engineering, Antalya International University, Antalya, Turkey (e-mail: [email protected]). O. M. Ramahi is with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2012.2203450
focusing lens antennas connected to a vector network analyzer (VNA) [7]–[10]. In this configuration, the free-space reflection and transmission coefficients of the sample placed between the antennas are measured. This method has the advantage of being nondestructive and contactless; however, it calls for the use of expensive lenses and horn antennas, and the need of a large sample. Another method for characterization of materials is the transmission-line method. In this method, the sample under test is employed as a filling material for transmission lines. For example, a slab of material can be inserted to a waveguide [11], [12], or the insulating materials of a coaxial line can be replaced by the sample under test [13]. The transmission and reflection from the sample-filled region gives the information needed for extraction of material properties. The method is relatively cheaper than the free-space methods since the use of lenses are eliminated, but the sample preparation remains a challenging task. Microstrip-line and stripline structures are also employed for this method [14]–[16]. Near-field sensors are also used for material characterization [17]–[20]. The most common near-field sensor used for this purpose is open-ended coaxial lines. Since the response of an open-ended coaxial line structure can be analytically obtained, the material properties of the sample under test can be extracted by measuring the reflection coefficient from the open end when the sample under test is placed right at the opening [21]–[23]. Since the technique is not limited by the diffraction limit, the method can be used to extract local material properties. Although the near-field sensors provide an inexpensive method for characterization, irregularities on the sample surface deteriorate the accuracy of the extraction. Additionally, the modeling of the measured reflection coefficient as a function of the dielectric properties remains a difficult task [24]. Among the aforementioned characterization techniques, the most accurate method is the resonant cavity method [25], [26]. In this technique, a cavity resonator is filled with the sample under test, and the shift in the resonance frequency and the change in the quality factor are measured. In addition, partially filled resonators can be used for material characterization. Other than a conventional box resonator, microstrip-line resonators and circular resonators have been used for this purpose [27]– [29]. Although the resonant cavity method is applicable over a narrow band, it is the most precise characterization technique. This method also needs precise sample preparation. In this paper, we present a new method for sensing material properties. The use of electrically small resonators or quasistatic resonators as a near-field probe is introduced and demonstrated. More specifically, the behavior of a complementary
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split-ring resonator (CSRR) as a sensor for material characterization is numerically and experimentally analyzed. The technique combines the accuracy of resonant cavity methods with the ability of the near-field sensors for extracting local material properties with a subwavelength resolution. In addition, the sensor requires simple sample preparation. II. E LECTRICALLY S MALL R ESONATORS FOR D IELECTRIC C HARACTERIZATION A. Resonator Types At the resonance frequency of a resonating structure, the electric field energy and the magnetic field energy stored in the structure must be equal to each other. When a material interacts with the stored magnetic and/or electric field energy or when a material perturbs the field distribution, the resonance frequency changes. The change in the resonance frequency and the material properties of the sample is related to each other by the following formula [30]: (E1 · E0 + μH1 · H0 )dv fr (1) = v 2 2 fr v (0 |E0 | + μ0 |H0 | ) dv where fr is the shift in the resonance frequency fr , and μ are the change in the permittivity and permeability, respectively, and v is the perturbed volume. E0 and H0 are the field distributions without the perturbation and E1 and H1 are the field distributions with the perturbation. If the perturbation is small and the field distribution is assumed unchanged, then (1) reduces to |E0 |2 + μ|H0 |2 dv fr v = . (2) 2 2 fr v (0 |E0 | + μ0 |H0 | ) dv The perturbation approach is used in resonant cavity methods and near-field sensors to extract the properties of materials [31], [32]. In the case of conventional microwave resonators, the structure is not electrically small. The resonance condition is achieved by arranging phase propagation to obtain constructive interference of bouncing waves within the resonator. As an example, at 1.3 GHz, the dimensions of a resonator made of a WR-770 waveguide is 14.27 cm × 19.56 cm × 8.60 cm. Similarly, the length of a λ/2 resonator made of a 50-Ω microstrip line on a 1.56-mm-thick FR-4 substrate is 6.59 cm. (The frequency used in these examples is selected to provide a fair comparison with the sensor designed in this paper, which has a size of 1.2 cm and is analyzed in detail in the succeeding sections.) On the other hand, quasi-static resonators are not based on the proper phase propagations. Usually, a loop is designed to generate a path for current to flow. As shown in Fig. 1, the geometries are designed to generate inductance due to the circulating current and capacitance on the path. Therefore, the structure resonates due to the inductance and capacitance of the path. Most typical electrically small resonators (see Fig. 2) are SRRs [33], spiral resonators [34], Hilbert curves [35], sinusoidal closed loops [36], etc. Similarly, the complementary structures
Fig. 1. Sample quasi-static resonator. The current that circulates around the ring generates a magnetic field passing through the ring, which effectively behaves as an inductance. The gaps on the ring and the separation between the rings behave as capacitance.
Fig. 2. Some example structures for quasi-static resonator concept. (a) SRR. (b) CSRR. (c) Hilbert curves (d) Spiral. All structures are electrically small at their resonance frequencies.
of the same geometries also resonate [37]. The complementary structures are based on Babinet’s principle. For example, in the case of a split-ring resonator, instead of having two conductive concentric rings, two concentric rings are removed from a conductive surface to achieve a CSRR, as shown in Fig. 2(b). B. Sensor Design In this paper, we consider two types of electrically small resonators: the SRRs and CSRRs. In such resonators, the capacitance of the current path has direct dependence on the permittivity of the medium, and the inductance of the current path has direct dependence on the permeability of the medium. Since CSRRs are excited by an electric field polarized in the direction normal to the plane of the resonator, the CSRRs are more sensitive to the permittivity of the medium. Analogously, SRRs are more sensitive to the permeability of the medium. First, we analyze the sensors for their sensitivity to changes in the permittivity of the surrounding medium. For this purpose, SRR and CSRR structures are designed with identical dimensions, as depicted in Fig. 3. In order to have the sensor operating around 1 GHz and to reduce the electrical size of the sensor, the dimensions are selected as s = 0.2 mm, g = 0.2 mm, t = 0.2 mm, and d = 12 mm. Without loss of generality and for the purpose of validating the response of the sensors using
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Fig. 3. To compare SRR and CSRR structures, two resonators are designed. The structures have exact dimensions. Black regions correspond to conductive parts, and white regions correspond to etched-out parts. Dimensions are s = 0.2 mm, g = 0.2 mm, t = 0.2 mm, and d = 12 mm. In order to obtain a high Q resonator, a low loss Rogers substrate is used.
Fig. 5. (a) Sensor is placed on the ground plane of a microstrip line. The microstrip line generates a perpendicular electric field on the ground plane that excites the CSRR. (b) As the sample under test is placed below the ground plane of the microstrip line, the resonance frequency of the CSRR changes.
Fig. 4. Behavior of CSRR and SRR sensors for permittivity change in the surrounding medium. The relative resonance frequency shift is calculated with respect to the resonance frequency when the medium is vacuum. CSRR sensor experiences a higher resonance frequency shift as the permittivity changes.
measurements, the structures are assumed to be printed on a Rogers RO4350 substrate with a thickness of 0.75 mm, a permittivity value of 3.48, and a loss tangent of 0.0031. In the case of an SRR, the electric field is confined between the traces. Therefore, for characterization purposes, it is harder for sample material to interact with the electric field. On the other hand, the magnetic field is spread and can be easily affected by the sample material. In the case of a CSRR, the behavior of magnetic and electric fields are interchanged. As a result for permittivity characterization, a CSRR is expected to behave as a better sensor. In order to investigate this idea, the effect of the permittivity of the surrounding medium is numerically analyzed. The sensors in Fig. 3 are modeled using the full-wave simulator High Frequency Structure Simulator (HFSS). Fig. 4 shows the resonance frequency shift of the CSRR and SRR structures as a function of the permittivity of the medium. The simulation is conducted using the eigenmode solution of HFSS, where the sensor is placed in a box with perfect electric conductor boundaries. Determining the size of the simulation box is important in order not to affect the resonance frequency of the electrically small resonator. In order to prevent the interaction between the electrically small resonator and the boundaries of the box, the size of the box should be around two times (or larger) the size of the electrically small resonator. In addition, having a very large box can also affect the result by having cavity resonance in the frequency range of interest. When the resonator is surrounded by vacuum, the resonance frequency
is considered to be the base (reference) resonance frequency. As the permittivity of the medium is changed, the frequency shift with respect to the base resonance frequency is recorded. Note that, in this procedure, the permittivity of the entire box is changed, except for the substrate of the resonators and the conductive traces. From the simulation results presented in Fig. 4, we conclude that the CSRR is more sensitive to change in permittivity than the SRR structure. Therefore, the CSRR geometry is selected as the sensor to be analyzed further for the purpose of permittivity characterization. C. Excitation of the Sensor In order to excite a CSRR structure, an electric field (E) perpendicular to the CSRR plane is needed. This excitation can be accomplished by using a microstrip transmission line with the CSRR etched out on the ground plane. The structure is presented in Fig. 5(a). This structure resembles a well-known stopband filter [38]. Therefore, as the sample placed at the bottom of the board, as shown in Fig. 5(b), the resonance frequency of the CSRR changes, which results in a shift in the filtering characteristics. The width of the microstrip line is chosen to be 1.68 mm in order to have a 50-Ω characteristic impedance suitable for matching to the internal input impedance of a VNA that will be used later for measurements. This structure also has the advantage of easy integration in microwave circuits. Therefore, a readout circuit that will eliminate the use of bulky and expensive laboratory equipment, such as VNAs, can be designed within the same board that can lead to a compact hand-held sensor. Sample readout circuits that can be designed using commercial components for measuring transmission coefficient and the phase of the reflection coefficient are presented in [39]. However, the readout circuitry and integration with the sensor is beyond the scope of this paper and are the subject of future publication.
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Fig. 6. Magnitude of reflection and transmission coefficients as a function of frequency. The response is plotted for sample = 1 and sample = 3. The minimum transmission frequency is shifted by 14.95%, and the minimum reflection frequency is shifted by 10.23%.
t r t Fig. 7. fmin and fmin values as a function of sample permittivity. fmin r . As the permittivity changes experiences a larger shift compared with fmin t r shifts 37.5%, and fmin shifts 30.2%. from 1 to 10, fmin
III. A NALYSIS OF THE S ENSOR The structure is assumed to be excited by a coaxial panelmount SMA connector from the bottom of the board. The microstrip line is assumed to be 10 cm long, and the width of the ground plane is 5 cm. The reflection and transmission coefficients are computed using full-wave simulation for two values of sample permittivity sample = 1 and sample = 3 (throughout this paper, all full-wave simulations are performed using HFSS). The magnitude of the S-parameters are presented in Fig. 6. The transmission coefficient experiences a minimum value at 1.286 GHz when the sample = 1. In addition, the reflection coefficient experiences a minimum value at 1.052 GHz. These two minimum values change as a function of sample . When the sample = 3, minimum transmission (S21,min ) frequency shifts to 1.106 GHz, and the minimum reflection (S11,min ) frequency shifts to 0.956 GHz. We define the frequency at which the S21 is minimum and the frequency at which the S11 is minimum as t r and fmin , respectively. These frequencies are the measured fmin quantities that will be used to determine the permittivity of t r shifts 37.5% and fmin the sample. Fig. 7 shows that fmin shifts 30.2% when the permittivity of the sample changes from 1 to 10. In order to analyze the sensitivity of the new sensor proposed here, the following method is used to quantify the resolution of the system for determining permittivity. Since, in the meat r and fmin are used as surement procedure, the shift in fmin the data that are related to the permittivity of the sample, the resolution of the sensor depends on the derivative of sample t r with respect to fmin and fmin . In order to achieve expressions t r and fmin , the data for the dependence of sample on fmin presented in Fig. 7 are used. By using curve fitting tools, the polynomials presented in (3) and (4) are obtained as follows: t 3 t 2 + 98.94 fmin sample = − 23.44 fmin t − 147.09fmin + 76.32 r sample = 63.69 (fmin )3
−
(3)
r 124.98 (fmin )2
r + 40.26fmin + 22.88.
(4)
Fig. 8. Permittivity resolution as a function of sample permittivity. The resolution is determined by calculating the required permittivity change to r t . As the sample permittivity increases, generate a 1-MHz shift in fmin and fmin the resolution is reduced.
Using these equations, the derivative of sample with respect r t and fmin are calculated as to fmin t 2 ∂sample t = − 70.32 fmin + 196.48fmin − 147.09 t ∂fmin
(5)
∂sample r r = 191.07 (fmin )2 − 255.96fmin + 40.26. r ∂fmin
(6)
Next, we assume a value for the dynamic range of the system used for measurement. This assumption includes the signal-tonoise ratio and the accuracy of the equipment that is used for excitation of the sensor and the equipment used for measuring the transmission and reflection coefficients. For the purpose of illustration, let us assume that the accuracy of the equipment r t and fmin is or circuit that is being used to measure fmin 1 MHz. Using this assumption and (5) and (6), the change in the permittivity Δ that corresponds to a 1-MHz shift in r t and fmin is calculated. (Note that the assumed accuracy fmin of 1 MHz is a very conservative choice.) Fig. 8 presents the resolution of the sensor as a function of sample permittivity. As the sample permittivity increases, the resolution is reduced. t corresponds to a When sample = 1, a 1-MHz shift in fmin Δ = 0.011. At sample = 10, a 1-MHz shift corresponds to Δ = 0.035.
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Fig. 9. Linear relationship between sample and the minimum reflection/ transmission frequencies is used for the calibration of the sensor.
Fig. 10. Phase of reflection and transmission coefficients as a function of frequency. The response is plotted for sample = 1 and sample = 3. At the minimum transmission frequency, a phase jump of 101◦ is observed, and at the minimum reflection frequency, a phase jump of 138◦ is observed.
A. Extraction of the Sample Permittivity
B. Determination of Permittivity Using Phase Response
In order to extract the permittivity of the sample material, the relation between the permittivity and the S-parameters of the sensor is needed. In [40], a circuit model is presented for a very r t and fmin similar structure. According to the circuit model, fmin are given by
Another method for determining the permittivity of the sample material is based on the phase of the reflection and transmission coefficients. The resolution of the system can be further increased by analyzing the shift in the phase of the transmission r and and reflection coefficients. Fig. 10 shows that, at fmin t , the phase of the reflection and transmission coefficients fmin experiences a drastic shift. Therefore, at these frequencies, the phase of the reflection and transmission coefficients is very sensitive to changes in the permittivity of the sample material. r Compared with the previous method where the shift in fmin t and fmin were the measured quantities for characterization, in the case of the phase detection method, the reflection coefficient provides better sensitivity. Notice that the change in the phase r t and fmin are 138◦ and 101◦ , respectively. at fmin In the phase detection method, the frequency is fixed, and the phases of the reflection and transmission coefficients are monitored. In order to obtain high sensitivity, the operation frequency must be in the region where the phase has a very high slope. As the permittivity of the sample increases, the phase transition shifts to lower frequencies. Although this method provides higher precision compared with the previous method, it is confined to a small permittivity range. This is because if the permittivity change is large so that the operation frequency is no longer in the high slope region, the sensitivity reduces, and a nonlinear behavior is observed. Fig. 11 shows the phase shift as a function of the sample permittivity. The center permittivity is selected to be sample = 4, around the permittivity of an FR-4 laminate. The phase of the transmission coefficient provides an almost linear behavior from sample = 3.9 to sample = 4.1. Assuming that the minimum measurable phase shift is 1◦ , the resolution of the sensor corresponds to 0.005. Using the phase information of the reflection coefficient for the same permittivity interval, a resolution of 0.0042 is obtained. In addition, the phase of the reflection coefficient provides a linear region for wider permittivity range, from sample = 3.8 to sample = 4.2. On the other hand, the method based on the minimum reflection and transmission frequencies provide a resolution of Δ = 0.028
r = fmin
1 2π Lc (C + Cc )
(7)
t = fmin
1 √ 2π Lc Cc
(8)
where C is the capacitance between the microstrip line and the CSRR, and Cc and Lc are the capacitance and inductance of the CSRR, respectively. The sensor uses the change in the capacitance of the CSRR Cc in order to reflect the change in the permittivity of the sample material. We assume that the ground plane of the microstrip line divides the space in to two halfspaces. These two half-spaces provide two parallel capacitance values that form the total capacitance of the CSRR Cc . The first half-space is above the ground plane, which is composed of the substrate, the microstrip line, and the air above the microstrip line. The first half-space has constant capacitance Csubstrate . The second half-space is below the ground plane, which is filled by the sample. This region has a capacitance proportional to the permittivity of the sample, Csample . Since capacitance values Csample and Csubstrate are parallel to each other, the total capacitance can be written as Cc = Csample + Csubstrate . Therefore, the total capacitance and the permittivity of the sample have a linear relationship. Using (7) and (8), and the linear relationship between Cc and sample , it is found that t −2 r sample ∝ (fmin )−2 and fmin
(9)
r This relation is presented in Fig. 9, where (fmin )−2 and are plotted as a function of sample . Since there is a linear relationship, the sensor can be calibrated using two measurements, and permittivity values of unknown materials can be calculated using the relationship presented in (9).
t )−2 (fmin
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Fig. 11. Phase shift as a function of sample permittivity at fixed frequencies. The phase of the reflection coefficient provides a better resolution over a wider permittivity range. Fig. 13. S-parameters of the fabricated sensor without any sample material. As predicted by numerical simulations, the structure possesses a band-stop filter with distinct frequencies at which minimum reflection and minimum transmission are observed.
Fig. 12. Fabricated sensor. (a) Top view. (b) Bottom view. (c) Close-up picture of the CSRR.
for reflection coefficient and a resolution of Δ = 0.0175 for the transmission coefficient around sample = 4. IV. M EASUREMENTS The CSRR-based sensor is fabricated using printed circuit board technology. The fabricated sensor is shown in Fig. 12. All measurements were performed using an Agilent 8722ES VNA. The intermediate frequency bandwidth of the VNA is 3 kHz, the input power is −10 dBm, and the number of points used for the measurement is 1601. A 3.5-mm calibration kit was used. According to the data sheet of the equipment, at a −20-dB transmission, the uncertainty in the magnitude of the transmission coefficient is 0.1 dB, and the uncertainty in the phase of the transmission coefficient is 0.7◦ . The reflection coefficient around −40 dB, on the other hand, has higher uncertainties in both magnitude and phase. Therefore, for this equipment, the transmission coefficient measurement is more accurate. Fig. 13 presents the measured reflection and transmission coefficients of the unloaded sensor. As predicted by the numerical simulations, reflection and transmission coefficients experience minimum values at specific frequencies. The discrepancy be-
Fig. 14. S11 as a function of frequency for different sample materials. The frequency at which the reflection is minimized shifts to lower frequencies as the permittivity of the sample material is increased. The bandwidth of the S11 dip depends on the loss tangent of the sample material.
tween the measured data presented in Fig. 13 and the numerical data presented in Fig. 6 is due to errors in the fabrication process. Measured s and t for the fabricated structure (see Fig. 3) is equal to 0.161 and 0.2627 mm, respectively. As a consequence of this slight change in the design parameters, the minimum S21 frequency is shifted from 1.28 to 1.16 GHz. Three sample materials with permittivity values ranging from 2 to 4 were prepared for permittivity measurements. The copper layer on a Rogers RO3003 board was completely removed using ammonium persulfate solution. Six layers of the copperremoved board were stacked to realize a 4.5-mm-thick medium with a permittivity of 3. Similarly, FR-4 boards are used to realize a medium with a permittivity value around 4.3. Finally, a Teflon block is used to realize a medium with a permittivity value around 2.1. Based on empirical findings, the material thickness for the sensor considered here had to be at least 2–3 mm. In other words, the shift in the resonant frequency converges to a fixed value as the thickness of the sample reaches 2–3 mm. Beyond such thickness, the resonant frequency does not change.
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V. C ONCLUSION
Fig. 15. S21 as a function of frequency for different sample materials. The frequency at which the transmission is minimized shifts to lower frequencies as the permittivity of the sample material is increased. The bandwidth of the S21 dip depends on the loss tangent of the sample material. TABLE I S UMMARY OF THE E XPERIMENTAL R ESULTS
Fig. 14 shows the change in the reflection coefficient when the permittivity of the sample material changes. As predicted using the numerical simulations, increasing the sample permittivity reduces the frequency at which the minimum reflection is observed. In addition, it is observed that when the sample material is FR-4, the dip of the S11 is smaller than when using other materials. This is a result of the high loss tangent of the FR-4 material. The effect of the permittivity of the sample material is more dominant on the behavior of S21 compared with the behavior of S11 . Fig. 15 shows that the minimum transmission frequency shifts by almost 18% when the sample material is FR-4. The experimental results and properties of the sample materials are summarized in Table I. The permittivity resolution of the sensor, which is based on an assumed 1-MHz measurement accuracy, is calculated. By assuming that the relation between the permittivity of the r t and fmin is linear between data points, the sample and the fmin permittivity resolution is calculated. The permittivity resolution t in the interval of sample = 1−2.1 is equal to based on fmin 0.0159, and in the interval of sample = 2.1−3, the resolution is equal to 0.0176. Similarly, the permittivity resolution based on r in intervals of sample = 1−2.1 and sample = 2.1−3 are fmin 0.0354 and 0.0264, respectively. Next, we study the accuracy of the extraction method presented in Section III-A. The data obtained by using air and Rogers RO3003 board is used as the calibration data to extract t )−2 . By employing linear relation between sample and (fmin this calibration method, the permittivity of the Teflon sample is calculated as 2.07, which lies within the expected range.
A new sensor structure is presented for material characterization based on electrically small resonators, namely, the SRR and CSRR. A rectangular CSRR structure, which is the sensing element in our system, is etched out on the ground plane of a microstrip line to realize a stopband filter. The sensor is based on the shift in the minimum reflection coefficient and the minimum transmission coefficient of the stopband filter as a function of the permittivity of the sample material. The CSRR-based sensor possesses the advantages of easy and inexpensive fabrication. The quasi-static nature of the CSRR sensor combines the accuracy of the resonator-based material characterization techniques with the subwavelength capabilities of near-field sensors. Therefore, extensive sample preparation procedures are eliminated, except for insuring smooth surface of the sample material for placement next to the sensor element. This feature allows for easy measurement of liquids as well. In addition, the CSRR-based sensor can be easily integrated in microwave circuitry since it is based on microstrip-line structures. Finally, we note that the sensing mechanism when using CSRR elements is fundamentally based on the high Q of the element. Placement of the CSRR element next to a medium with substantial loss can significantly lower the Q of the element, which can potentially result in significant reduction of the sensing accuracy. Therefore, the CSRR sensor presented in this paper is most effective when sensing material with very low loss. R EFERENCES [1] S. O. Nelson, W. C. Guo, S. Trabelsi, and S. J. Kays, “Dielectric spectroscopy of watermelons for quality sensing,” Meas. Sci. Technol., vol. 18, no. 7, pp. 1887–1892, Jul. 2007. [2] S. O. Nelson and S. Trabelsi, “Dielectric spectroscopy measurements on fruit, meat, and grain,” Trans. ASABE, vol. 51, no. 5, pp. 1829–1834, 2008. [3] W. C. Guo, S. O. Nelson, S. Trabelsi, and S. J. Kays, “10-1800-mhz dielectric properties of fresh apples during storage,” J. Food Eng., vol. 83, no. 4, pp. 562–569, Dec. 2007. [4] S. O. Nelson and S. Trabelsi, “Influence of water content on rf and microwave dielectric behavior of foods,” J. Microw. Power Electromagn. Energy, vol. 43, no. 2, pp. 13–23, 2009. [5] C. Dalmay, A. Pothier, P. Blondy, F. Lalloue, and M.-O. Jauberteau, “Label free biosensors for human cell characterization using radio and microwave frequencies,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., Jun. 15–20, 2008, pp. 911–914. [6] J. Kim, A. Babajanyan, A. Hovsepyan, K. Lee, and B. Friedman, “Microwave dielectric resonator biosensor for aqueous glucose solution,” Rev. Sci. Instrum., vol. 79, no. 8, pp. 086107-1–086107-3, Aug. 2008. [7] D. Ghodgaonkar, V. Varadan, and V. Varadan, “Free-space measurement of complex permittivity and complex permeability of magnetic materials at microwave frequencies,” IEEE Trans. Instrum. Meas., vol. 39, no. 2, pp. 387–394, Apr. 1990. [8] P. K. Kadaba, “Simultaneous measurement of complex permittivity and permeability in the millimeter region by a frequency-domain technique,” IEEE Trans. Instrum. Meas., vol. 33, no. 4, pp. 336–340, Dec. 1984. [9] A. Khosrowbeygi, H. Griffiths, and A. Cullen, “A new free-wave dielectric and magnetic properties measurement system at millimetre wavelengths,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., 1994, pp. 1461–1464. [10] M. Aris and D. Ghodgaonkar, “Nondestructive and noncontact dielectric measurement method for high-loss liquids using free space microwave measurement system in 8–12.5 GHz frequency range,” in Proc. RFM, Oct. 5/6, 2004, pp. 169–176. [11] A. Erentok, R. W. Ziolkowski, J. A. Nielsen, R. B. Greegor, C. G. Parazzoli, M. H. Tanielian, S. A. Cummer, B.-I. Popa, T. Hand, D. C. Vier, and S. Schultz, “Low frequency lumped element-based
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negative index metamaterial,” Appl. Phys. Lett., vol. 91, no. 18, pp. 184 104-1–184 104-3, Oct. 2007. M. Akhtar, L. Feher, and M. Thumm, “A waveguide-based two-step approach for measuring complex permittivity tensor of uniaxial composite materials,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 5, pp. 2011– 2022, May 2006. C. Jones, J. Grosvenor, and C. Weil, “Rf material characterization using a large-diameter (76.8 mm) coaxial air line,” in Proc. 13th Int. Conf. MIKON, 2000, vol. 2, pp. 417–420. W. Barry, “A broad-band, automated, stripline technique for the simultaneous measurement of complex permittivity and permeability,” IEEE Trans. Microw. Theory Tech., vol. 34, no. 1, pp. 80–84, Jan. 1986. H. Yue, K. Virga, and J. Prince, “Dielectric constant and loss tangent measurement using a stripline fixture,” IEEE Trans. Compon., Packag., Manuf. Technol. B, Adv. Packag., vol. 21, no. 4, pp. 441–446, Nov. 1998. P. Queffelec, P. Gelin, J. Gieraltowski, and J. Loaec, “A microstrip device for the broad band simultaneous measurement of complex permeability and permittivity,” IEEE Trans. Magn., vol. 30, no. 2, pp. 224–231, Mar. 1994. M. Tabib-Azar, N. S. Shoemaker, and S. Harris, “Non-desctrutive characterization of materials by evanescent microwaves,” Meas. Sci. Technol., vol. 4, no. 5, pp. 583–590, May 1993. S. Ganchev, N. Qaddoumi, S. Bakhtiari, and R. Zoughi, “Calibration and measurement of dielectric properties of finite thickness composite sheets with open-ended coaxial sensors,” IEEE Trans. Instrum. Meas., vol. 44, no. 6, pp. 1023–1029, Dec. 1995. M. Stuchly, T. Athey, G. Samaras, and G. Taylor, “Measurement of radio frequency permittivity of biological tissues with an open-ended coaxial line: Part II—Experimental results,” IEEE Trans. Microw. Theory Tech., vol. MTT-30, no. 1, pp. 87–92, Jan. 1982. T. Athey, M. Stuchly, and S. Stuchly, “Measurement of radio frequency permittivity of biological tissues with an open-ended coaxial line: Part I,” IEEE Trans. Microw. Theory Tech., vol. MTT-30, no. 1, pp. 82–86, Jan. 1982. D. Misra, “A quasi-static analysis of open-ended coaxial lines (short paper),” IEEE Trans. Microw. Theory Tech., vol. MTT-35, no. 10, pp. 925– 928, Oct. 1987. J. Baker-Jarvis, M. D. Janezic, P. D. Domich, and R. G. Geyer, “Analysis of an open-ended coaxial probe with lift-off for nondestructive testing,” IEEE Trans. Instrum. Meas., vol. 43, no. 5, pp. 711–718, Oct. 1994. S. Bakhtiari, S. I. Ganchev, and R. Zoughi, “Analysis of radiation from an open-ended coaxial line into stratified dielectrics,” IEEE Trans. Microw. Theory Tech., vol. 42, no. 7, pp. 1261–1267, Jul. 1994. T. C. Gabriel and E. H. Grant, “Admittance models for open ended coaxial probes and their place in dielectric spectroscopy,” Phys. Med. Biol., vol. 39, no. 12, pp. 2183–2200, Dec. 1994. J. Baker-Jarvis, R. Geyer, J. Grosvenor, J. H. , M. Janezic, C. Jones, B. Riddle, C. Weil, and J. Krupka, “Dielectric characterization of low-loss materials a comparison of techniques,” IEEE Trans. Elect. Insul., vol. 5, no. 4, pp. 571–577, Aug. 1998. B. Milovanovic, S. Ivkovic, and V. Tasic, “A simple method for permittivity measurement using microwave resonant cavity,” in Proc. 12th Int. Conf. MIKON, 1998, vol. 3, pp. 705–709. D. Shimin, “A new method for measuring dielectric constant using the resonant frequency of a patch antenna,” IEEE Trans. Microw. Theory Tech., vol. 34, no. 9, pp. 923–931, Sep. 1986. T. Itoh, “A new method for measuring properties of dielectric materials using a microstrip cavity (short papers),” IEEE Trans. Microw. Theory Tech., vol. MTT-22, no. 5, pp. 572–576, May 1974. P. Bernard and J. Gautray, “Measurement of dielectric constant using a microstrip ring resonator,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 3, pp. 592–595, Mar. 1991. D. M. Pozar, Microwave Engineering, 3rd ed. Hoboken, NJ: Wiley, 2005, p. 299. C. Gao, T. Wei, F. Duewer, Y. Lu, and X. D. Xiang, “High spatial resolution quantitative microwave impedance microscopy by a scanning tip microwave near-field microscope,” Appl. Phys. Lett., vol. 71, no. 13, pp. 1872–1874, Sep. 1997. C. Gao and X. D. Xiang, “Quantitative microwave near-field microscopy of dielectric properties,” Rev. Sci. Instrum., vol. 69, no. 11, pp. 3846– 3851, Nov. 1998. J. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 11, pp. 2075–2084, Nov. 1999. J. D. Baena, R. Marqués, F. Medina, and J. Martel, “Artificial magnetic metamaterial design by using spiral resonators,” Phys. Rev. B, vol. 69, no. 1, pp. 014402-1–014402-5, Jan. 2004.
[35] L. Yousefi and O. M. Ramahi, “New artificial magnetic materials based on fractal Hilbert curves,” in Proc. IWAT, Cambridge, U.K., Mar. 2007, pp. 237–240. [36] A. Kabiri and O. Ramahi, “Limitations of artificial magnetic materials with negative permeability,” in Proc. IEEE APSURSI, Jun. 1–5, 2009, pp. 1–4. [37] F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett., vol. 93, no. 19, pp. 197 401-1–197 401-4, Nov. 2004. [38] F. Falcone, T. Lopetegi, J. Baena, R. Marques, F. Martin, and M. Sorolla, “Effective negative- ϵ stopband microstrip lines based on complementary split ring resonators,” IEEE Microw. Wireless Compon. Lett., vol. 14, no. 6, pp. 280–282, Jun. 2004. [39] N. Suwan, “Investigation of Rf direct detection architecture circuits for metamaterial sensor applications,” M.S. thesis, Univ. Waterloo, West Waterloo, ON, Canada, 2011. [40] J. Bonache, M. Gil, I. Gil, J. García-García, and F. Martín, “On the electrical characteristics of complementary metamaterial resonators,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 10, pp. 543–545, Oct. 2006.
Muhammed Said Boybay (S’07–M’09) received the B.S. degree in electrical and electronics engineering from Bilkent University, Ankara, Turkey, in 2004 and the Ph.D. degree in electrical and computer engineering from the University of Waterloo, Waterloo, ON, Canada, in 2009. From 2004 to 2009, he was a Research and Teaching Assistant with the Department of Electrical and Computer Engineering and the Department of Mechanical and Mechatronics Engineering, University of Waterloo, where he was a Postdoctoral Fellow from 2009 to 2010 and from 2010 to 2012, respectively. Currently, he is an Assistant Professor with Antalya International University, Turkey. His research interests include double- and single-negative materials, near-field sensing, electrically small resonators, electromagnetic band-gap structures and microwave sensor, and component design for microfluidic platforms. Dr. Boybay held Mitacs Elevate Postdoctoral Fellowship from 2011 to 2012.
Omar M. Ramahi (F’09) was born in Jerusalem, Israel. He received the B.S. degrees in mathematics and electrical and computer engineering (summa cum laude) from Oregon State University, Corvallis, and the Ph.D. degree in electrical and computer engineering from the University of Illinois at UrbanaChampaign, Urbana, in 1990, under the supervision of Professor R. Mittra. He held postdoctoral and visiting fellowship positions with the University of Illinois at UrbanaChampaign under the supervision of Profs. Y. T. Lo and R. Mittra. He then worked with Digital Equipment Corporation (currently HP), where he was a member of the Alpha Server Product Development Group. In 2000, he joined the faculty of the James Clark School of Engineering, University of Maryland, College Park, as an Assistant Professor and later as a tenured Associate Professor. He was also a faculty member of the CALCE Electronic Products and Systems Center, University of Maryland. He is currently a Professor with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada. He holds cross appointments with the Department of Mechanical and Mechatronics Engineering and the Department of Physics and Astronomy. He served as a Consultant to several companies and was a cofounder of EMS-PLUS, LLC and Applied Electromagnetic Technology, LLC, and the Eastern Rugs and Gifts Company. He is the author or coauthor of over 250 journal and conference technical papers on topics related to the electromagnetic phenomena and computational techniques to understand the same. He is a coauthor of the book EMI/EMC Computational Modeling Handbook, (First Edition: Kluwer, 1998; Second Edition: Springer–Verlag, 2001. Japanese Edition published in 2005). Dr. Ramahi served as a Co-Guest Editor for the Journal of Applied Physics A Special Issue on Metamaterials and Photonics in 2009. He is currently serving as an Associate Editor for the IEEE T RANSACTIONS ON A DVANCED PACKAGING and as an IEEE EMC Society Distinguished Lecturer.
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Material Characterization Using Complementary Split-Ring Resonators Muhammed Said Boybay, Member, IEEE and Omar M. Ramahi, Fellow, IEEE
Abstract—A microwave method based on complementary split-ring resonators (CSRRs) is proposed for dielectric characterization of planar materials. The technique presents advantages such as high measurement sensitivity and eliminates the extensive sample preparation procedure needed in resonance-based methods. A sensor in the shape of CSRRs working at a 0.8– 1.3 GHz band is demonstrated. The sensor is etched in the ground plane of a microstrip line to effectively create a stopband filter. The frequencies at which minimum transmission and minimum reflection are observed depend on the permittivity of the sample under test. The minimum transmission frequency shifts from 1.3 to 0.8 GHz as the sample permittivity changes from 1 to 10. The structure is fabricated using printed circuit board technology. Numerical findings are experimentally verified. Index Terms—Complementary split-ring resonators (CSRRs), material characterization, near-field sensors.
I. I NTRODUCTION
P
ERMITTIVITY is an important material characteristic for electrical engineers. The response of a material to electrical signals depends on the permittivity of materials. Thus, precise determination of the permittivity is an important task for microwave/radio-frequency circuit design and antenna design, and for microwave engineering in general. In addition, characterization of materials or detecting changes in the electrical properties of materials has applications in areas such as quality control in food industry, biosensing, or subsurface detection [1]–[6]. For most of the applications, properties such as the material composition, moisture or water content, etc., of the sample under test carry valuable information. Since electrical properties of materials depend on these properties, quality control in materials science, in food industry, biosensing, or subsurface detection can be conducted based on sensing electrical properties of materials. Many methods have been proposed and used for material characterization. These methods can be classified as free-space methods, transmission-line methods, near-field sensors, and resonant cavity methods. In free-space methods, the classical bistatic measurement setup consists generally of a pair of spotManuscript received January 30, 2011; revised August 12, 2011; accepted August 29, 2011. Date of publication June 29, 2012; date of current version October 10, 2012. The Associate Editor coordinating the review process for this paper was Dr. S. Trabelsi. M. S. Boybay is with the Department of Computer Engineering, Antalya International University, Antalya, Turkey (e-mail: [email protected]). O. M. Ramahi is with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2012.2203450
focusing lens antennas connected to a vector network analyzer (VNA) [7]–[10]. In this configuration, the free-space reflection and transmission coefficients of the sample placed between the antennas are measured. This method has the advantage of being nondestructive and contactless; however, it calls for the use of expensive lenses and horn antennas, and the need of a large sample. Another method for characterization of materials is the transmission-line method. In this method, the sample under test is employed as a filling material for transmission lines. For example, a slab of material can be inserted to a waveguide [11], [12], or the insulating materials of a coaxial line can be replaced by the sample under test [13]. The transmission and reflection from the sample-filled region gives the information needed for extraction of material properties. The method is relatively cheaper than the free-space methods since the use of lenses are eliminated, but the sample preparation remains a challenging task. Microstrip-line and stripline structures are also employed for this method [14]–[16]. Near-field sensors are also used for material characterization [17]–[20]. The most common near-field sensor used for this purpose is open-ended coaxial lines. Since the response of an open-ended coaxial line structure can be analytically obtained, the material properties of the sample under test can be extracted by measuring the reflection coefficient from the open end when the sample under test is placed right at the opening [21]–[23]. Since the technique is not limited by the diffraction limit, the method can be used to extract local material properties. Although the near-field sensors provide an inexpensive method for characterization, irregularities on the sample surface deteriorate the accuracy of the extraction. Additionally, the modeling of the measured reflection coefficient as a function of the dielectric properties remains a difficult task [24]. Among the aforementioned characterization techniques, the most accurate method is the resonant cavity method [25], [26]. In this technique, a cavity resonator is filled with the sample under test, and the shift in the resonance frequency and the change in the quality factor are measured. In addition, partially filled resonators can be used for material characterization. Other than a conventional box resonator, microstrip-line resonators and circular resonators have been used for this purpose [27]– [29]. Although the resonant cavity method is applicable over a narrow band, it is the most precise characterization technique. This method also needs precise sample preparation. In this paper, we present a new method for sensing material properties. The use of electrically small resonators or quasistatic resonators as a near-field probe is introduced and demonstrated. More specifically, the behavior of a complementary
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split-ring resonator (CSRR) as a sensor for material characterization is numerically and experimentally analyzed. The technique combines the accuracy of resonant cavity methods with the ability of the near-field sensors for extracting local material properties with a subwavelength resolution. In addition, the sensor requires simple sample preparation. II. E LECTRICALLY S MALL R ESONATORS FOR D IELECTRIC C HARACTERIZATION A. Resonator Types At the resonance frequency of a resonating structure, the electric field energy and the magnetic field energy stored in the structure must be equal to each other. When a material interacts with the stored magnetic and/or electric field energy or when a material perturbs the field distribution, the resonance frequency changes. The change in the resonance frequency and the material properties of the sample is related to each other by the following formula [30]: (E1 · E0 + μH1 · H0 )dv fr (1) = v 2 2 fr v (0 |E0 | + μ0 |H0 | ) dv where fr is the shift in the resonance frequency fr , and μ are the change in the permittivity and permeability, respectively, and v is the perturbed volume. E0 and H0 are the field distributions without the perturbation and E1 and H1 are the field distributions with the perturbation. If the perturbation is small and the field distribution is assumed unchanged, then (1) reduces to |E0 |2 + μ|H0 |2 dv fr v = . (2) 2 2 fr v (0 |E0 | + μ0 |H0 | ) dv The perturbation approach is used in resonant cavity methods and near-field sensors to extract the properties of materials [31], [32]. In the case of conventional microwave resonators, the structure is not electrically small. The resonance condition is achieved by arranging phase propagation to obtain constructive interference of bouncing waves within the resonator. As an example, at 1.3 GHz, the dimensions of a resonator made of a WR-770 waveguide is 14.27 cm × 19.56 cm × 8.60 cm. Similarly, the length of a λ/2 resonator made of a 50-Ω microstrip line on a 1.56-mm-thick FR-4 substrate is 6.59 cm. (The frequency used in these examples is selected to provide a fair comparison with the sensor designed in this paper, which has a size of 1.2 cm and is analyzed in detail in the succeeding sections.) On the other hand, quasi-static resonators are not based on the proper phase propagations. Usually, a loop is designed to generate a path for current to flow. As shown in Fig. 1, the geometries are designed to generate inductance due to the circulating current and capacitance on the path. Therefore, the structure resonates due to the inductance and capacitance of the path. Most typical electrically small resonators (see Fig. 2) are SRRs [33], spiral resonators [34], Hilbert curves [35], sinusoidal closed loops [36], etc. Similarly, the complementary structures
Fig. 1. Sample quasi-static resonator. The current that circulates around the ring generates a magnetic field passing through the ring, which effectively behaves as an inductance. The gaps on the ring and the separation between the rings behave as capacitance.
Fig. 2. Some example structures for quasi-static resonator concept. (a) SRR. (b) CSRR. (c) Hilbert curves (d) Spiral. All structures are electrically small at their resonance frequencies.
of the same geometries also resonate [37]. The complementary structures are based on Babinet’s principle. For example, in the case of a split-ring resonator, instead of having two conductive concentric rings, two concentric rings are removed from a conductive surface to achieve a CSRR, as shown in Fig. 2(b). B. Sensor Design In this paper, we consider two types of electrically small resonators: the SRRs and CSRRs. In such resonators, the capacitance of the current path has direct dependence on the permittivity of the medium, and the inductance of the current path has direct dependence on the permeability of the medium. Since CSRRs are excited by an electric field polarized in the direction normal to the plane of the resonator, the CSRRs are more sensitive to the permittivity of the medium. Analogously, SRRs are more sensitive to the permeability of the medium. First, we analyze the sensors for their sensitivity to changes in the permittivity of the surrounding medium. For this purpose, SRR and CSRR structures are designed with identical dimensions, as depicted in Fig. 3. In order to have the sensor operating around 1 GHz and to reduce the electrical size of the sensor, the dimensions are selected as s = 0.2 mm, g = 0.2 mm, t = 0.2 mm, and d = 12 mm. Without loss of generality and for the purpose of validating the response of the sensors using
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Fig. 3. To compare SRR and CSRR structures, two resonators are designed. The structures have exact dimensions. Black regions correspond to conductive parts, and white regions correspond to etched-out parts. Dimensions are s = 0.2 mm, g = 0.2 mm, t = 0.2 mm, and d = 12 mm. In order to obtain a high Q resonator, a low loss Rogers substrate is used.
Fig. 5. (a) Sensor is placed on the ground plane of a microstrip line. The microstrip line generates a perpendicular electric field on the ground plane that excites the CSRR. (b) As the sample under test is placed below the ground plane of the microstrip line, the resonance frequency of the CSRR changes.
Fig. 4. Behavior of CSRR and SRR sensors for permittivity change in the surrounding medium. The relative resonance frequency shift is calculated with respect to the resonance frequency when the medium is vacuum. CSRR sensor experiences a higher resonance frequency shift as the permittivity changes.
measurements, the structures are assumed to be printed on a Rogers RO4350 substrate with a thickness of 0.75 mm, a permittivity value of 3.48, and a loss tangent of 0.0031. In the case of an SRR, the electric field is confined between the traces. Therefore, for characterization purposes, it is harder for sample material to interact with the electric field. On the other hand, the magnetic field is spread and can be easily affected by the sample material. In the case of a CSRR, the behavior of magnetic and electric fields are interchanged. As a result for permittivity characterization, a CSRR is expected to behave as a better sensor. In order to investigate this idea, the effect of the permittivity of the surrounding medium is numerically analyzed. The sensors in Fig. 3 are modeled using the full-wave simulator High Frequency Structure Simulator (HFSS). Fig. 4 shows the resonance frequency shift of the CSRR and SRR structures as a function of the permittivity of the medium. The simulation is conducted using the eigenmode solution of HFSS, where the sensor is placed in a box with perfect electric conductor boundaries. Determining the size of the simulation box is important in order not to affect the resonance frequency of the electrically small resonator. In order to prevent the interaction between the electrically small resonator and the boundaries of the box, the size of the box should be around two times (or larger) the size of the electrically small resonator. In addition, having a very large box can also affect the result by having cavity resonance in the frequency range of interest. When the resonator is surrounded by vacuum, the resonance frequency
is considered to be the base (reference) resonance frequency. As the permittivity of the medium is changed, the frequency shift with respect to the base resonance frequency is recorded. Note that, in this procedure, the permittivity of the entire box is changed, except for the substrate of the resonators and the conductive traces. From the simulation results presented in Fig. 4, we conclude that the CSRR is more sensitive to change in permittivity than the SRR structure. Therefore, the CSRR geometry is selected as the sensor to be analyzed further for the purpose of permittivity characterization. C. Excitation of the Sensor In order to excite a CSRR structure, an electric field (E) perpendicular to the CSRR plane is needed. This excitation can be accomplished by using a microstrip transmission line with the CSRR etched out on the ground plane. The structure is presented in Fig. 5(a). This structure resembles a well-known stopband filter [38]. Therefore, as the sample placed at the bottom of the board, as shown in Fig. 5(b), the resonance frequency of the CSRR changes, which results in a shift in the filtering characteristics. The width of the microstrip line is chosen to be 1.68 mm in order to have a 50-Ω characteristic impedance suitable for matching to the internal input impedance of a VNA that will be used later for measurements. This structure also has the advantage of easy integration in microwave circuits. Therefore, a readout circuit that will eliminate the use of bulky and expensive laboratory equipment, such as VNAs, can be designed within the same board that can lead to a compact hand-held sensor. Sample readout circuits that can be designed using commercial components for measuring transmission coefficient and the phase of the reflection coefficient are presented in [39]. However, the readout circuitry and integration with the sensor is beyond the scope of this paper and are the subject of future publication.
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Fig. 6. Magnitude of reflection and transmission coefficients as a function of frequency. The response is plotted for sample = 1 and sample = 3. The minimum transmission frequency is shifted by 14.95%, and the minimum reflection frequency is shifted by 10.23%.
t r t Fig. 7. fmin and fmin values as a function of sample permittivity. fmin r . As the permittivity changes experiences a larger shift compared with fmin t r shifts 37.5%, and fmin shifts 30.2%. from 1 to 10, fmin
III. A NALYSIS OF THE S ENSOR The structure is assumed to be excited by a coaxial panelmount SMA connector from the bottom of the board. The microstrip line is assumed to be 10 cm long, and the width of the ground plane is 5 cm. The reflection and transmission coefficients are computed using full-wave simulation for two values of sample permittivity sample = 1 and sample = 3 (throughout this paper, all full-wave simulations are performed using HFSS). The magnitude of the S-parameters are presented in Fig. 6. The transmission coefficient experiences a minimum value at 1.286 GHz when the sample = 1. In addition, the reflection coefficient experiences a minimum value at 1.052 GHz. These two minimum values change as a function of sample . When the sample = 3, minimum transmission (S21,min ) frequency shifts to 1.106 GHz, and the minimum reflection (S11,min ) frequency shifts to 0.956 GHz. We define the frequency at which the S21 is minimum and the frequency at which the S11 is minimum as t r and fmin , respectively. These frequencies are the measured fmin quantities that will be used to determine the permittivity of t r shifts 37.5% and fmin the sample. Fig. 7 shows that fmin shifts 30.2% when the permittivity of the sample changes from 1 to 10. In order to analyze the sensitivity of the new sensor proposed here, the following method is used to quantify the resolution of the system for determining permittivity. Since, in the meat r and fmin are used as surement procedure, the shift in fmin the data that are related to the permittivity of the sample, the resolution of the sensor depends on the derivative of sample t r with respect to fmin and fmin . In order to achieve expressions t r and fmin , the data for the dependence of sample on fmin presented in Fig. 7 are used. By using curve fitting tools, the polynomials presented in (3) and (4) are obtained as follows: t 3 t 2 + 98.94 fmin sample = − 23.44 fmin t − 147.09fmin + 76.32 r sample = 63.69 (fmin )3
−
(3)
r 124.98 (fmin )2
r + 40.26fmin + 22.88.
(4)
Fig. 8. Permittivity resolution as a function of sample permittivity. The resolution is determined by calculating the required permittivity change to r t . As the sample permittivity increases, generate a 1-MHz shift in fmin and fmin the resolution is reduced.
Using these equations, the derivative of sample with respect r t and fmin are calculated as to fmin t 2 ∂sample t = − 70.32 fmin + 196.48fmin − 147.09 t ∂fmin
(5)
∂sample r r = 191.07 (fmin )2 − 255.96fmin + 40.26. r ∂fmin
(6)
Next, we assume a value for the dynamic range of the system used for measurement. This assumption includes the signal-tonoise ratio and the accuracy of the equipment that is used for excitation of the sensor and the equipment used for measuring the transmission and reflection coefficients. For the purpose of illustration, let us assume that the accuracy of the equipment r t and fmin is or circuit that is being used to measure fmin 1 MHz. Using this assumption and (5) and (6), the change in the permittivity Δ that corresponds to a 1-MHz shift in r t and fmin is calculated. (Note that the assumed accuracy fmin of 1 MHz is a very conservative choice.) Fig. 8 presents the resolution of the sensor as a function of sample permittivity. As the sample permittivity increases, the resolution is reduced. t corresponds to a When sample = 1, a 1-MHz shift in fmin Δ = 0.011. At sample = 10, a 1-MHz shift corresponds to Δ = 0.035.
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Fig. 9. Linear relationship between sample and the minimum reflection/ transmission frequencies is used for the calibration of the sensor.
Fig. 10. Phase of reflection and transmission coefficients as a function of frequency. The response is plotted for sample = 1 and sample = 3. At the minimum transmission frequency, a phase jump of 101◦ is observed, and at the minimum reflection frequency, a phase jump of 138◦ is observed.
A. Extraction of the Sample Permittivity
B. Determination of Permittivity Using Phase Response
In order to extract the permittivity of the sample material, the relation between the permittivity and the S-parameters of the sensor is needed. In [40], a circuit model is presented for a very r t and fmin similar structure. According to the circuit model, fmin are given by
Another method for determining the permittivity of the sample material is based on the phase of the reflection and transmission coefficients. The resolution of the system can be further increased by analyzing the shift in the phase of the transmission r and and reflection coefficients. Fig. 10 shows that, at fmin t , the phase of the reflection and transmission coefficients fmin experiences a drastic shift. Therefore, at these frequencies, the phase of the reflection and transmission coefficients is very sensitive to changes in the permittivity of the sample material. r Compared with the previous method where the shift in fmin t and fmin were the measured quantities for characterization, in the case of the phase detection method, the reflection coefficient provides better sensitivity. Notice that the change in the phase r t and fmin are 138◦ and 101◦ , respectively. at fmin In the phase detection method, the frequency is fixed, and the phases of the reflection and transmission coefficients are monitored. In order to obtain high sensitivity, the operation frequency must be in the region where the phase has a very high slope. As the permittivity of the sample increases, the phase transition shifts to lower frequencies. Although this method provides higher precision compared with the previous method, it is confined to a small permittivity range. This is because if the permittivity change is large so that the operation frequency is no longer in the high slope region, the sensitivity reduces, and a nonlinear behavior is observed. Fig. 11 shows the phase shift as a function of the sample permittivity. The center permittivity is selected to be sample = 4, around the permittivity of an FR-4 laminate. The phase of the transmission coefficient provides an almost linear behavior from sample = 3.9 to sample = 4.1. Assuming that the minimum measurable phase shift is 1◦ , the resolution of the sensor corresponds to 0.005. Using the phase information of the reflection coefficient for the same permittivity interval, a resolution of 0.0042 is obtained. In addition, the phase of the reflection coefficient provides a linear region for wider permittivity range, from sample = 3.8 to sample = 4.2. On the other hand, the method based on the minimum reflection and transmission frequencies provide a resolution of Δ = 0.028
r = fmin
1 2π Lc (C + Cc )
(7)
t = fmin
1 √ 2π Lc Cc
(8)
where C is the capacitance between the microstrip line and the CSRR, and Cc and Lc are the capacitance and inductance of the CSRR, respectively. The sensor uses the change in the capacitance of the CSRR Cc in order to reflect the change in the permittivity of the sample material. We assume that the ground plane of the microstrip line divides the space in to two halfspaces. These two half-spaces provide two parallel capacitance values that form the total capacitance of the CSRR Cc . The first half-space is above the ground plane, which is composed of the substrate, the microstrip line, and the air above the microstrip line. The first half-space has constant capacitance Csubstrate . The second half-space is below the ground plane, which is filled by the sample. This region has a capacitance proportional to the permittivity of the sample, Csample . Since capacitance values Csample and Csubstrate are parallel to each other, the total capacitance can be written as Cc = Csample + Csubstrate . Therefore, the total capacitance and the permittivity of the sample have a linear relationship. Using (7) and (8), and the linear relationship between Cc and sample , it is found that t −2 r sample ∝ (fmin )−2 and fmin
(9)
r This relation is presented in Fig. 9, where (fmin )−2 and are plotted as a function of sample . Since there is a linear relationship, the sensor can be calibrated using two measurements, and permittivity values of unknown materials can be calculated using the relationship presented in (9).
t )−2 (fmin
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Fig. 11. Phase shift as a function of sample permittivity at fixed frequencies. The phase of the reflection coefficient provides a better resolution over a wider permittivity range. Fig. 13. S-parameters of the fabricated sensor without any sample material. As predicted by numerical simulations, the structure possesses a band-stop filter with distinct frequencies at which minimum reflection and minimum transmission are observed.
Fig. 12. Fabricated sensor. (a) Top view. (b) Bottom view. (c) Close-up picture of the CSRR.
for reflection coefficient and a resolution of Δ = 0.0175 for the transmission coefficient around sample = 4. IV. M EASUREMENTS The CSRR-based sensor is fabricated using printed circuit board technology. The fabricated sensor is shown in Fig. 12. All measurements were performed using an Agilent 8722ES VNA. The intermediate frequency bandwidth of the VNA is 3 kHz, the input power is −10 dBm, and the number of points used for the measurement is 1601. A 3.5-mm calibration kit was used. According to the data sheet of the equipment, at a −20-dB transmission, the uncertainty in the magnitude of the transmission coefficient is 0.1 dB, and the uncertainty in the phase of the transmission coefficient is 0.7◦ . The reflection coefficient around −40 dB, on the other hand, has higher uncertainties in both magnitude and phase. Therefore, for this equipment, the transmission coefficient measurement is more accurate. Fig. 13 presents the measured reflection and transmission coefficients of the unloaded sensor. As predicted by the numerical simulations, reflection and transmission coefficients experience minimum values at specific frequencies. The discrepancy be-
Fig. 14. S11 as a function of frequency for different sample materials. The frequency at which the reflection is minimized shifts to lower frequencies as the permittivity of the sample material is increased. The bandwidth of the S11 dip depends on the loss tangent of the sample material.
tween the measured data presented in Fig. 13 and the numerical data presented in Fig. 6 is due to errors in the fabrication process. Measured s and t for the fabricated structure (see Fig. 3) is equal to 0.161 and 0.2627 mm, respectively. As a consequence of this slight change in the design parameters, the minimum S21 frequency is shifted from 1.28 to 1.16 GHz. Three sample materials with permittivity values ranging from 2 to 4 were prepared for permittivity measurements. The copper layer on a Rogers RO3003 board was completely removed using ammonium persulfate solution. Six layers of the copperremoved board were stacked to realize a 4.5-mm-thick medium with a permittivity of 3. Similarly, FR-4 boards are used to realize a medium with a permittivity value around 4.3. Finally, a Teflon block is used to realize a medium with a permittivity value around 2.1. Based on empirical findings, the material thickness for the sensor considered here had to be at least 2–3 mm. In other words, the shift in the resonant frequency converges to a fixed value as the thickness of the sample reaches 2–3 mm. Beyond such thickness, the resonant frequency does not change.
BOYBAY AND RAMAHI: MATERIAL CHARACTERIZATION USING COMPLEMENTARY SPLIT-RING RESONATORS
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Fig. 15. S21 as a function of frequency for different sample materials. The frequency at which the transmission is minimized shifts to lower frequencies as the permittivity of the sample material is increased. The bandwidth of the S21 dip depends on the loss tangent of the sample material. TABLE I S UMMARY OF THE E XPERIMENTAL R ESULTS
Fig. 14 shows the change in the reflection coefficient when the permittivity of the sample material changes. As predicted using the numerical simulations, increasing the sample permittivity reduces the frequency at which the minimum reflection is observed. In addition, it is observed that when the sample material is FR-4, the dip of the S11 is smaller than when using other materials. This is a result of the high loss tangent of the FR-4 material. The effect of the permittivity of the sample material is more dominant on the behavior of S21 compared with the behavior of S11 . Fig. 15 shows that the minimum transmission frequency shifts by almost 18% when the sample material is FR-4. The experimental results and properties of the sample materials are summarized in Table I. The permittivity resolution of the sensor, which is based on an assumed 1-MHz measurement accuracy, is calculated. By assuming that the relation between the permittivity of the r t and fmin is linear between data points, the sample and the fmin permittivity resolution is calculated. The permittivity resolution t in the interval of sample = 1−2.1 is equal to based on fmin 0.0159, and in the interval of sample = 2.1−3, the resolution is equal to 0.0176. Similarly, the permittivity resolution based on r in intervals of sample = 1−2.1 and sample = 2.1−3 are fmin 0.0354 and 0.0264, respectively. Next, we study the accuracy of the extraction method presented in Section III-A. The data obtained by using air and Rogers RO3003 board is used as the calibration data to extract t )−2 . By employing linear relation between sample and (fmin this calibration method, the permittivity of the Teflon sample is calculated as 2.07, which lies within the expected range.
A new sensor structure is presented for material characterization based on electrically small resonators, namely, the SRR and CSRR. A rectangular CSRR structure, which is the sensing element in our system, is etched out on the ground plane of a microstrip line to realize a stopband filter. The sensor is based on the shift in the minimum reflection coefficient and the minimum transmission coefficient of the stopband filter as a function of the permittivity of the sample material. The CSRR-based sensor possesses the advantages of easy and inexpensive fabrication. The quasi-static nature of the CSRR sensor combines the accuracy of the resonator-based material characterization techniques with the subwavelength capabilities of near-field sensors. Therefore, extensive sample preparation procedures are eliminated, except for insuring smooth surface of the sample material for placement next to the sensor element. This feature allows for easy measurement of liquids as well. In addition, the CSRR-based sensor can be easily integrated in microwave circuitry since it is based on microstrip-line structures. Finally, we note that the sensing mechanism when using CSRR elements is fundamentally based on the high Q of the element. Placement of the CSRR element next to a medium with substantial loss can significantly lower the Q of the element, which can potentially result in significant reduction of the sensing accuracy. Therefore, the CSRR sensor presented in this paper is most effective when sensing material with very low loss. R EFERENCES [1] S. O. Nelson, W. C. Guo, S. Trabelsi, and S. J. Kays, “Dielectric spectroscopy of watermelons for quality sensing,” Meas. Sci. Technol., vol. 18, no. 7, pp. 1887–1892, Jul. 2007. [2] S. O. Nelson and S. Trabelsi, “Dielectric spectroscopy measurements on fruit, meat, and grain,” Trans. ASABE, vol. 51, no. 5, pp. 1829–1834, 2008. [3] W. C. Guo, S. O. Nelson, S. Trabelsi, and S. J. Kays, “10-1800-mhz dielectric properties of fresh apples during storage,” J. Food Eng., vol. 83, no. 4, pp. 562–569, Dec. 2007. [4] S. O. Nelson and S. Trabelsi, “Influence of water content on rf and microwave dielectric behavior of foods,” J. Microw. Power Electromagn. Energy, vol. 43, no. 2, pp. 13–23, 2009. [5] C. Dalmay, A. Pothier, P. Blondy, F. Lalloue, and M.-O. Jauberteau, “Label free biosensors for human cell characterization using radio and microwave frequencies,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., Jun. 15–20, 2008, pp. 911–914. [6] J. Kim, A. Babajanyan, A. Hovsepyan, K. Lee, and B. Friedman, “Microwave dielectric resonator biosensor for aqueous glucose solution,” Rev. Sci. Instrum., vol. 79, no. 8, pp. 086107-1–086107-3, Aug. 2008. [7] D. Ghodgaonkar, V. Varadan, and V. Varadan, “Free-space measurement of complex permittivity and complex permeability of magnetic materials at microwave frequencies,” IEEE Trans. Instrum. Meas., vol. 39, no. 2, pp. 387–394, Apr. 1990. [8] P. K. Kadaba, “Simultaneous measurement of complex permittivity and permeability in the millimeter region by a frequency-domain technique,” IEEE Trans. Instrum. Meas., vol. 33, no. 4, pp. 336–340, Dec. 1984. [9] A. Khosrowbeygi, H. Griffiths, and A. Cullen, “A new free-wave dielectric and magnetic properties measurement system at millimetre wavelengths,” in Proc. IEEE MTT-S Int. Microw. Symp. Dig., 1994, pp. 1461–1464. [10] M. Aris and D. Ghodgaonkar, “Nondestructive and noncontact dielectric measurement method for high-loss liquids using free space microwave measurement system in 8–12.5 GHz frequency range,” in Proc. RFM, Oct. 5/6, 2004, pp. 169–176. [11] A. Erentok, R. W. Ziolkowski, J. A. Nielsen, R. B. Greegor, C. G. Parazzoli, M. H. Tanielian, S. A. Cummer, B.-I. Popa, T. Hand, D. C. Vier, and S. Schultz, “Low frequency lumped element-based
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Muhammed Said Boybay (S’07–M’09) received the B.S. degree in electrical and electronics engineering from Bilkent University, Ankara, Turkey, in 2004 and the Ph.D. degree in electrical and computer engineering from the University of Waterloo, Waterloo, ON, Canada, in 2009. From 2004 to 2009, he was a Research and Teaching Assistant with the Department of Electrical and Computer Engineering and the Department of Mechanical and Mechatronics Engineering, University of Waterloo, where he was a Postdoctoral Fellow from 2009 to 2010 and from 2010 to 2012, respectively. Currently, he is an Assistant Professor with Antalya International University, Turkey. His research interests include double- and single-negative materials, near-field sensing, electrically small resonators, electromagnetic band-gap structures and microwave sensor, and component design for microfluidic platforms. Dr. Boybay held Mitacs Elevate Postdoctoral Fellowship from 2011 to 2012.
Omar M. Ramahi (F’09) was born in Jerusalem, Israel. He received the B.S. degrees in mathematics and electrical and computer engineering (summa cum laude) from Oregon State University, Corvallis, and the Ph.D. degree in electrical and computer engineering from the University of Illinois at UrbanaChampaign, Urbana, in 1990, under the supervision of Professor R. Mittra. He held postdoctoral and visiting fellowship positions with the University of Illinois at UrbanaChampaign under the supervision of Profs. Y. T. Lo and R. Mittra. He then worked with Digital Equipment Corporation (currently HP), where he was a member of the Alpha Server Product Development Group. In 2000, he joined the faculty of the James Clark School of Engineering, University of Maryland, College Park, as an Assistant Professor and later as a tenured Associate Professor. He was also a faculty member of the CALCE Electronic Products and Systems Center, University of Maryland. He is currently a Professor with the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada. He holds cross appointments with the Department of Mechanical and Mechatronics Engineering and the Department of Physics and Astronomy. He served as a Consultant to several companies and was a cofounder of EMS-PLUS, LLC and Applied Electromagnetic Technology, LLC, and the Eastern Rugs and Gifts Company. He is the author or coauthor of over 250 journal and conference technical papers on topics related to the electromagnetic phenomena and computational techniques to understand the same. He is a coauthor of the book EMI/EMC Computational Modeling Handbook, (First Edition: Kluwer, 1998; Second Edition: Springer–Verlag, 2001. Japanese Edition published in 2005). Dr. Ramahi served as a Co-Guest Editor for the Journal of Applied Physics A Special Issue on Metamaterials and Photonics in 2009. He is currently serving as an Associate Editor for the IEEE T RANSACTIONS ON A DVANCED PACKAGING and as an IEEE EMC Society Distinguished Lecturer.
