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Sensitivity Optimization of Microwave Biosensors
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ScienceDirect Procedia Engineering 168 (2016) 634 – 637
30th Eurosensors Conference, EUROSENSORS 2016
Sensitivity Optimization of Microwave Biosensors T. Voglhuber-Brunnmaiera,b, , L. Wagnera , C.G. Diskusb , B. Jakobyb , M. Brandla a Center b Institute
for Integrated Sensor Systems, Danube University, Krems, Austria for Microelectronics and Microsensors, Johannes Kepler University, Linz, Austria
Abstract A microwave biosensor, suitable for the detection of dielectric overlays, formed by bonding of bio-molecules to a functionalized substrate, is investigated. The sensor consists of a resonant coupled split-ring configuration in microstrip technology. An analytical model for the sensor structure is developed and compared to measurement results. The complexity of the model is further reduced and equations for resonance frequency shift and Q-factor change are determined from which the sensitivity and the detection limit can be estimated. It is found that higher operating frequencies facilitate higher sensitivity and that the electrical conductivity of the sample dominates the Q-factors and therefore the achievable accuracy. © by Elsevier Ltd. This is an openLtd. access article under the CC BY-NC-ND license © 2016 2016Published The Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference. Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference Keywords: Type your keywords here, separated by semicolons ;
1. Introduction Figure 1a shows a photograph of the split-ring biosensor in microstrip technology. Basic properties of an earlier design can be found in [1]. The split-ring resonator (SRR) is coupled to a parallel transmission (TML) line segment which is attached to a network analyzer (NWA) via SMA connectors. The active sensing area is at the gap of the SRR, where changes of the electrical properties have the greatest impact on the resonance characteristics. However the guided waves on the TML segments are not strictly confined to the substrate, such that the phase velocity and thus the resonance characteristics are also affected by the electrical properties on top of the structure. Therefore the resonance frequency is also significantly detuned when a dielectric medium (e.g. a drop of liquid) is placed on the TML by introducing a wave impedance change. The resonance condition of the SRR is when the half wavelength, or its odd multiples, equals the length of the SRR. For the given structure the resonance frequency is approx. 2GHz. The use of microwave frequencies for biosensing feature the benefit of higher sensitivity as will be shown below. However frequency shifts may be very small such that using an accurate resonance frequency estimation method is crucial. In this paper we use the RBEfit from [2] which is a minimum variance estimator with known error propagation. It is therefore possible to estimate the detection limits of the setup which can surprisingly low, given the Q-factor is moderate. The paper is structured as follows: A model of the sensor is developed using basic network analysis, and it is verified with measurements. Subsequently, a reduced model is derived which yields simple expressions for resonance frequency (f0) and Q-factor (Q) that approximate f0 and Q of the complex model well. Finally the
1877-7058 © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference
doi:10.1016/j.proeng.2016.11.232
635
T. Voglhuber-Brunnmaier et al. / Procedia Engineering 168 (2016) 634 – 637
sensitivity of the sensor is determined and measurement results for different samples are shown.
Fig. 1. a) Photograph of split-ring resonator (SRR) with geometric dimensions. The wave impedance of the transmission lines is Z0,T ¨ 66.25 + j0.088, the effective permittivity is İr ¨ 2.75 j0.0075 and the complex phase velocity is v = c¥İr = (0.6033 + j0.0008) c . b) Comparison between measured and calculated Yin. The coupler properties were determined using an Ansys HFSS simulation.
2. Modeling Multi-port networks in high frequency applications are mostly described by their S-parameters assembled in the Smatrix (scattering matrix), which can be directly measured using an NWA. However, for network calculations, expressions in terms of voltage and current are more suitable. The transformations between the S-matrix and Y-matrix (admittance matrix) are given by Y = Y0 (I+S)1Ã(IS) and S = (IZ0 Y) Ã (I+Z0 Y)1 with Ii = Yi j V j ,
(1)
where Vi , Ii denote voltage and current at terminal i, respectively. Z0 = 1/Y0 is the wave impedance of the reference system that measured the S-parameters (i.e. 50) and I is the identity matrix. The structure is segmented as shown
Fig. 2. a) Main constituents of sensor structure. The bevelled TML indicate that in principle the TML should be miltered at edges. However it can be shown that this is not required at 2 GHz [3]. b) Block diagram, where the coupler and the circuit between port 3 and 4 of the coupler are represented by their respective Y-parameters Y and YL. c) The composition of the AL by chain matrices of both transmission lines ATML and series capacitor AC . AL is transformed to YL and inserted in b).
in Fig. 2, such that the coupler can be represented by a 4 [4 Y-matrix Y. The load attached to the coupler ports 3 and 4 is composed by chain matrices of the transmission lines (TML3, TML4) and the gap capacitance C g.
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T. Voglhuber-Brunnmaier et al. / Procedia Engineering 168 (2016) 634 – 637
AL is transformed to YL and the two-port Y-matrix Y2p at port 1 and 2 of the coupler are calculated using Eq. 3, where Y11 ...Y22 denote the four 2 [ 2 block matrices of Y. For termination with the characteristic TML admittance Y0,T at port 2, the admittance at port 1 (Y1) and subsequently at the input (Yin) can be calculated using the following equations based on Fig. 2.
The agreement between simulated and measured Yin is shown in Fig. 1b.
2.1 Reduced Model The model shows a good match for amplitudes, phase, offset, Q-factor and resonance frequency, but the expressions are complex for non-zero reflection and isolation coefficients of the coupler as in our case. In practice, the frequency shift is of primary interest and is mainly determined by the SRR loop characteristics. The natural frequency of the
Fig. 3. a) Split ring resonator (SRR) consisting of a TML of length L with phase velocity v and equivalent gap capacitance C g and conductivity G g. b) Block diagram of SRR for calculation of frequency shift and Q-factor with Yg = jȦ C g + G g . c) Transcendental equation for resonance frequency shifts due to C g at the first two harmonics n = 0, 1. The linearization of the cot function is shown as red dashed lines.
SRR loop alone is determined according to Fig. 3, where also a finite gap conductivity G g is considered.
For Yg= 0 and loss-less TML, the resonance condition for the n-th harmonic is when the wavelength matches L / (1/2 + n) with n 0, 1,… . The associated natural frequency is denoted by f0,n. For Yg non-zero, but small compared to Y 0,T , Eq. 5 can be linearized and solved for Ȧ. For Gg = 0, the roots are real, but become complex in case of non-zero Gg. In this case, natural frequency and Q-factor are approximately given by
With Eq. 6 is shown that the sensor is more sensitive in terms of relative frequency shift at large frequencies. This is the main reason for operating at microwave frequencies. The Q-factor Qn of the n-th resonance depends on the the gap conductivity. Due to dielectric losses, also the unloaded structure features a finite Q-factor QTML which adds approximately inversely to Qn with 1/Q = 1/QTML + 1/Q n . To facilitate accurate frequency estimation, the total Q should be as high as possible as will be outlined in the following.
T. Voglhuber-Brunnmaier et al. / Procedia Engineering 168 (2016) 634 – 637
Fig. 4. a) Nyquist plot of input admittance Yin for three different conditions. b) The magnitude of Yin. The dashed lines show the fitting results.
2.2. Accuracy Considerations The accurate estimation of resonance parameters from complex data, is only possible with a correct underlying signal model. In [2] the signal model Y(f) in Eq. 7 was introduced which is appropriate for a variety of resonant sensors. In [4] the standard deviation (std (fn)) of the resonance frequency estimation process was derived which is used to define an accuracy factor ǻfn /std (fn) with
3. Results Fig. 4 shows three measured resonances when a 100µ m thick piece of cellulose of dimensions 2mm [ 2mm is placed on the gap. The S-matrix of the sensor was recorded with an Agilent E5061B NWA (calibrated using 8055E calibration kit). The measured S-matrix is transformed to the Y-matrix and port 2 is arithmetically terminated with Y0,T (see Eq. 4). The cellulose is wetted with silicone oil (APN26 viscosity standard) which has low permittivity and practically no conductivity. When the cellulose is wetted with DI water a significant frequency change results due to high permittivity accompanied by a strongly lowered Q-factor due to conductivity. The dashed lines in the figure are fitting results obtained with the RBEfit, showing excellent agreement. The estimated resonance parameters as well as standard deviations are shown in Tab. 1. Acknowledgments This work was supported by the Lower Austrian Forschungs- und Bildungsges.m.b.H. (NFB) through the Life Science grant LS13-023. Partial support was provided by the Austrian COMET program (Project "Process Analytical Chemistry", PAC) and the Austrian Funds for Scientific Research FWF (project L657-N16). References [1] M. Wellenzohn, M. Brandl, A theoretical design of a biosensor device based on split ring resonators for operation in the microwave regime, Procedia Engineering 120 (2015) 865-869. [2] A. O. Niedermayer, T. Voglhuber-Brunnmaier, J. Sell, B. Jakoby, Methods for the robust measurement of the resonant frequency and quality factor of significantly damped resonating devices, Meas. Sci. Technol. 23 (8) (2012) 085107. [3] T. C. Edwards, T. Edwards, M. Steer, Foundations for microstrip circuit design, John Wiley & Sons, 2016. [4] T. Voglhuber-Brunnmaier, A. Niedermayer, R. Beigelbeck, B. Jakoby, Resonance parameter estimation from spectral data: Crame´r-Rao lower bound and stable algorithms with application to liquid sensors, Meas. Sci. Technol. 25 (10) (2014) 105303-105313. [5] T. Voglhuber-Brunnmaier, A. Niedermayer, M. Heinisch, A. Abdallah, E. Reichel, B. Jakoby, V. Putz, R. Beigelbeck, Modeling-free evaluation of resonant liquid sensors for measuring viscosity and density, in: 2015 9th ICST, IEEE, 2015, pp. 300-305.
637
ScienceDirect Procedia Engineering 168 (2016) 634 – 637
30th Eurosensors Conference, EUROSENSORS 2016
Sensitivity Optimization of Microwave Biosensors T. Voglhuber-Brunnmaiera,b, , L. Wagnera , C.G. Diskusb , B. Jakobyb , M. Brandla a Center b Institute
for Integrated Sensor Systems, Danube University, Krems, Austria for Microelectronics and Microsensors, Johannes Kepler University, Linz, Austria
Abstract A microwave biosensor, suitable for the detection of dielectric overlays, formed by bonding of bio-molecules to a functionalized substrate, is investigated. The sensor consists of a resonant coupled split-ring configuration in microstrip technology. An analytical model for the sensor structure is developed and compared to measurement results. The complexity of the model is further reduced and equations for resonance frequency shift and Q-factor change are determined from which the sensitivity and the detection limit can be estimated. It is found that higher operating frequencies facilitate higher sensitivity and that the electrical conductivity of the sample dominates the Q-factors and therefore the achievable accuracy. © by Elsevier Ltd. This is an openLtd. access article under the CC BY-NC-ND license © 2016 2016Published The Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference. Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference Keywords: Type your keywords here, separated by semicolons ;
1. Introduction Figure 1a shows a photograph of the split-ring biosensor in microstrip technology. Basic properties of an earlier design can be found in [1]. The split-ring resonator (SRR) is coupled to a parallel transmission (TML) line segment which is attached to a network analyzer (NWA) via SMA connectors. The active sensing area is at the gap of the SRR, where changes of the electrical properties have the greatest impact on the resonance characteristics. However the guided waves on the TML segments are not strictly confined to the substrate, such that the phase velocity and thus the resonance characteristics are also affected by the electrical properties on top of the structure. Therefore the resonance frequency is also significantly detuned when a dielectric medium (e.g. a drop of liquid) is placed on the TML by introducing a wave impedance change. The resonance condition of the SRR is when the half wavelength, or its odd multiples, equals the length of the SRR. For the given structure the resonance frequency is approx. 2GHz. The use of microwave frequencies for biosensing feature the benefit of higher sensitivity as will be shown below. However frequency shifts may be very small such that using an accurate resonance frequency estimation method is crucial. In this paper we use the RBEfit from [2] which is a minimum variance estimator with known error propagation. It is therefore possible to estimate the detection limits of the setup which can surprisingly low, given the Q-factor is moderate. The paper is structured as follows: A model of the sensor is developed using basic network analysis, and it is verified with measurements. Subsequently, a reduced model is derived which yields simple expressions for resonance frequency (f0) and Q-factor (Q) that approximate f0 and Q of the complex model well. Finally the
1877-7058 © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 30th Eurosensors Conference
doi:10.1016/j.proeng.2016.11.232
635
T. Voglhuber-Brunnmaier et al. / Procedia Engineering 168 (2016) 634 – 637
sensitivity of the sensor is determined and measurement results for different samples are shown.
Fig. 1. a) Photograph of split-ring resonator (SRR) with geometric dimensions. The wave impedance of the transmission lines is Z0,T ¨ 66.25 + j0.088, the effective permittivity is İr ¨ 2.75 j0.0075 and the complex phase velocity is v = c¥İr = (0.6033 + j0.0008) c . b) Comparison between measured and calculated Yin. The coupler properties were determined using an Ansys HFSS simulation.
2. Modeling Multi-port networks in high frequency applications are mostly described by their S-parameters assembled in the Smatrix (scattering matrix), which can be directly measured using an NWA. However, for network calculations, expressions in terms of voltage and current are more suitable. The transformations between the S-matrix and Y-matrix (admittance matrix) are given by Y = Y0 (I+S)1Ã(IS) and S = (IZ0 Y) Ã (I+Z0 Y)1 with Ii = Yi j V j ,
(1)
where Vi , Ii denote voltage and current at terminal i, respectively. Z0 = 1/Y0 is the wave impedance of the reference system that measured the S-parameters (i.e. 50) and I is the identity matrix. The structure is segmented as shown
Fig. 2. a) Main constituents of sensor structure. The bevelled TML indicate that in principle the TML should be miltered at edges. However it can be shown that this is not required at 2 GHz [3]. b) Block diagram, where the coupler and the circuit between port 3 and 4 of the coupler are represented by their respective Y-parameters Y and YL. c) The composition of the AL by chain matrices of both transmission lines ATML and series capacitor AC . AL is transformed to YL and inserted in b).
in Fig. 2, such that the coupler can be represented by a 4 [4 Y-matrix Y. The load attached to the coupler ports 3 and 4 is composed by chain matrices of the transmission lines (TML3, TML4) and the gap capacitance C g.
636
T. Voglhuber-Brunnmaier et al. / Procedia Engineering 168 (2016) 634 – 637
AL is transformed to YL and the two-port Y-matrix Y2p at port 1 and 2 of the coupler are calculated using Eq. 3, where Y11 ...Y22 denote the four 2 [ 2 block matrices of Y. For termination with the characteristic TML admittance Y0,T at port 2, the admittance at port 1 (Y1) and subsequently at the input (Yin) can be calculated using the following equations based on Fig. 2.
The agreement between simulated and measured Yin is shown in Fig. 1b.
2.1 Reduced Model The model shows a good match for amplitudes, phase, offset, Q-factor and resonance frequency, but the expressions are complex for non-zero reflection and isolation coefficients of the coupler as in our case. In practice, the frequency shift is of primary interest and is mainly determined by the SRR loop characteristics. The natural frequency of the
Fig. 3. a) Split ring resonator (SRR) consisting of a TML of length L with phase velocity v and equivalent gap capacitance C g and conductivity G g. b) Block diagram of SRR for calculation of frequency shift and Q-factor with Yg = jȦ C g + G g . c) Transcendental equation for resonance frequency shifts due to C g at the first two harmonics n = 0, 1. The linearization of the cot function is shown as red dashed lines.
SRR loop alone is determined according to Fig. 3, where also a finite gap conductivity G g is considered.
For Yg= 0 and loss-less TML, the resonance condition for the n-th harmonic is when the wavelength matches L / (1/2 + n) with n 0, 1,… . The associated natural frequency is denoted by f0,n. For Yg non-zero, but small compared to Y 0,T , Eq. 5 can be linearized and solved for Ȧ. For Gg = 0, the roots are real, but become complex in case of non-zero Gg. In this case, natural frequency and Q-factor are approximately given by
With Eq. 6 is shown that the sensor is more sensitive in terms of relative frequency shift at large frequencies. This is the main reason for operating at microwave frequencies. The Q-factor Qn of the n-th resonance depends on the the gap conductivity. Due to dielectric losses, also the unloaded structure features a finite Q-factor QTML which adds approximately inversely to Qn with 1/Q = 1/QTML + 1/Q n . To facilitate accurate frequency estimation, the total Q should be as high as possible as will be outlined in the following.
T. Voglhuber-Brunnmaier et al. / Procedia Engineering 168 (2016) 634 – 637
Fig. 4. a) Nyquist plot of input admittance Yin for three different conditions. b) The magnitude of Yin. The dashed lines show the fitting results.
2.2. Accuracy Considerations The accurate estimation of resonance parameters from complex data, is only possible with a correct underlying signal model. In [2] the signal model Y(f) in Eq. 7 was introduced which is appropriate for a variety of resonant sensors. In [4] the standard deviation (std (fn)) of the resonance frequency estimation process was derived which is used to define an accuracy factor ǻfn /std (fn) with
3. Results Fig. 4 shows three measured resonances when a 100µ m thick piece of cellulose of dimensions 2mm [ 2mm is placed on the gap. The S-matrix of the sensor was recorded with an Agilent E5061B NWA (calibrated using 8055E calibration kit). The measured S-matrix is transformed to the Y-matrix and port 2 is arithmetically terminated with Y0,T (see Eq. 4). The cellulose is wetted with silicone oil (APN26 viscosity standard) which has low permittivity and practically no conductivity. When the cellulose is wetted with DI water a significant frequency change results due to high permittivity accompanied by a strongly lowered Q-factor due to conductivity. The dashed lines in the figure are fitting results obtained with the RBEfit, showing excellent agreement. The estimated resonance parameters as well as standard deviations are shown in Tab. 1. Acknowledgments This work was supported by the Lower Austrian Forschungs- und Bildungsges.m.b.H. (NFB) through the Life Science grant LS13-023. Partial support was provided by the Austrian COMET program (Project "Process Analytical Chemistry", PAC) and the Austrian Funds for Scientific Research FWF (project L657-N16). References [1] M. Wellenzohn, M. Brandl, A theoretical design of a biosensor device based on split ring resonators for operation in the microwave regime, Procedia Engineering 120 (2015) 865-869. [2] A. O. Niedermayer, T. Voglhuber-Brunnmaier, J. Sell, B. Jakoby, Methods for the robust measurement of the resonant frequency and quality factor of significantly damped resonating devices, Meas. Sci. Technol. 23 (8) (2012) 085107. [3] T. C. Edwards, T. Edwards, M. Steer, Foundations for microstrip circuit design, John Wiley & Sons, 2016. [4] T. Voglhuber-Brunnmaier, A. Niedermayer, R. Beigelbeck, B. Jakoby, Resonance parameter estimation from spectral data: Crame´r-Rao lower bound and stable algorithms with application to liquid sensors, Meas. Sci. Technol. 25 (10) (2014) 105303-105313. [5] T. Voglhuber-Brunnmaier, A. Niedermayer, M. Heinisch, A. Abdallah, E. Reichel, B. Jakoby, V. Putz, R. Beigelbeck, Modeling-free evaluation of resonant liquid sensors for measuring viscosity and density, in: 2015 9th ICST, IEEE, 2015, pp. 300-305.
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