In previous blog posts, we demonstrated conductivity and permittivity measurements of liquids using the MFIA Impedance Analyzer. To reach the best accuracy, the measurements were carried out using immersion probes or dielectric fixtures with a precisely defined electrode area and spacing. This step is important as any error in the specified sample dimension will result in an error in the derived material properties. In this post, we want to have a look at a low-cost alternative to a probe or fixture, namely an interdigitated electrode sensor patterned on a printed circuit board (PCB). Table 1 gives a quick overview: the sensor may have a few limitations, but using it properly with the MFIA can still lead to a reliable result. We begin with a noise analysis using the Scope module in LabOne® to identify the frequencies of interest, continue with an investigation on the sources of inaccuracy, and finally extract the dielectric properties with equivalent circuit modeling.
|Increased signal intensity||Increased noise||Measure at low-noise frequencies|
|Low cost without precise sample dimension control||Low accuracy||Use shorter cables|
|Customizable for different sample volumes||Lack a standard||Apply equivalent circuit models|
Table 1: Summary of advantages, disadvantages and workarounds of typical interdigitated electrode sensors in terms of electrical or electrochemical impedance spectroscopy (EIS).
In this blog post, we use an interdigitated electrode sensor kindly provided by Dr. Shlomo Gadelovits at the University of Sheffield. The sensor has 2 SMA connectors soldered onboard. As shown in Figure 2, to connect the sensor to the MFIA using BNC outputs we need to add BNC cables, breakouts, and BNC-SMA adaptors in between. This will result in a degraded measurement accuracy, which we will look at in detail later. The sensor can then be submerged into olive oil for measurements, as described in a previous blog post.
Figure 1: Sketch showing the MFIA impedance analyzer connected to a third-party interdigitated electrode sensor in a '4-terminal' configuration. The sensor uses 2 SMA connectors, so to have a 4-terminal connection to the MFIA, cables (black wires) with breakouts and adaptors are necessary.
Results and Discussion
Optimizing the measurement frequency range with noise analysis
Dielectrics commonly have a large impedance (low capacitance), making the low current measurement challenging with just one pair of electrodes. Naturally, with more pairs in interdigitation, a larger current will flow through. However, as the electrodes are also exposed to the environment, noises can be picked up at the same time. Therefore, the signal-to-noise ratio (SNR) will only increase when the sensing electrodes are used at low-noise frequencies.
The MFIA is a great tool to study the noise in this type of sensor. Figure 2 shows the voltage and current simultaneously measured on the sensor, using the LabOne Scope module (the MF-DIG option is required). A large power frequency (50 Hz) noise and its higher-order harmonics are present in the current signal. While it is possible to filter these noises by using a filter in a narrow bandwidth in the LabOne software, they still occupy part of the input range and may block low current measurements at low frequencies. Hence, it is advisable to walk away from this region. In the rest of the blog post, we will only measure the sensor at kHz or above.
Figure 2: LabOne Scope module showing the measured voltage (in blue) and current (in orange) from the interdigitated electrode sensor in FFT mode. The voltage trace contains only a signal at 1 kHz. In contrast, the current trace includes many additional noise peaks at 50 Hz and its higher-order harmonics. (Click to zoom)
Exploring the origin of measurement inaccuracies
The sensor used in this post is designed to be submerged into liquid samples. So cables are absolutely necessary to connect the sensor to the MFIA, preventing the MFIA from short circuit. In this specific case, the 4-terminal connection on the sensor composes of 2 cores and 2 shields (shields are used to flow currents, not as ground), which effectively puts the cable capacitance in parallel. The measured capacitance and dissipation factor (D) will be affected, and we will describe how to compensate for the capacitance in the next section. A true 4-terminal sensor with shorter cables can help to alleviate the problem.
In addition, the sensor may also work as a proximity sensor. Figure 3 shows the outcome when an object moves closer to and away. The measurement error for the impedance amplitude goes up to ~0.2%, which is beyond the basic accuracy (0.05%) of the MFIA. Therefore, to achieve high accuracy, one should stabilize the sensor during the measurements, avoiding mechanical movements in addition to electromagnetic perturbations.
Fig. 3 LabOne Plotter module showing the measured RMS current (in purple), impedance amplitude (in blue), and phase (in orange) from the interdigitated electrode sensor in real-time. Even a tiny perturbation around the sensor can create a change of ~0.2%. Click the figure to zoom.
Calculating dielectric properties with a proper ECM
Finally, let's compare the result with our previous result taken with a liquid dielectric fixture. Despite allowing customization for different volumes of samples, the form factor of interdigitated electrode sensors is unknown. Lacking a good standard, we need to use other measurements as our reference. If we choose the previous result on olive oil, as shown in Figure 4, we can get a scaling factor of ~338 pF/9 pF = 37.6. However, recall D is a material property, which should not vary with sample dimension. This suggests that the interdigitated electrode sensor may not be suitable for measuring D accurately.
Figure 4: LabOne Sweeper module showing the dissipation factor and the capacitance of the same olive oil sample measured with the dielectric fixture (in blue) and with the interdigitated electrode sensor (in red). (Click to zoom)
To confirm this point, we measure the capacitance of air reference with the same sensor. Figure 5 shows a nearly identical D in both measurements, indicating it is heavily influenced by the parasitic impedance (the cables, for instance). And the ratio of the capacitances from the two measurements gives just ~1.3, which is too low for the dielectric constant of the olive oil (typically >3).
Figure 5: LabOne Sweeper module showing the dissipation factor and the capacitance measured from the air (in blue) and from the olive oil sample (in red). (Click to zoom)
In order to get the correct dielectric constant, we can simply subtract the capacitance (216 pF, which can also be measured by the MFIA) of the cables as our baseline. In doing so, the ratio at 10 kHz becomes 3.27, which matches closely to the previous result at 3.23. However, at higher frequencies, this simple model fails, as the cable inductance is not taken into account.
Note that the ECM may also become complicated if the sample under test behaves differently. For instance, an additional Warburg diffusion element could appear if the liquid sample is ionized, creating an electrochemical double layer at the electrode interface. As such, extreme attention should be paid to the modeling. You can find more relevant information from an interdigitated electrode humidity sensor in an earlier blog post.
In this blog post, we demonstrate that the MFIA is a versatile instrument in characterizing interdigitated electrode sensors. We find them as useful devices to estimate the dielectric constant (permittivity) from liquid dielectrics. The derived permittivity at 3.27 matches well to our previous result at 3.23, but only in a narrow frequency region (around 10 kHz). On the other hand, if the goal is to measure accurately (particularly for D) over a wide frequency span, a fixture that has small noise and can precisely define the sample form factor is highly preferable. Interested in a demo? Please get in touch with us.
Acknowledgments: The author would like to thank Dr. Shlomo Gadelovits at the University of Sheffield for providing interdigitated electrode sensors for the measurements in this blog post.