# Planar Microwave Resonant Sensors: A Review and Recent Developments
## 4 Prototype Examples
### Differential-Mode Sensors
#### 4.4.1 Measuring Electrolyte Concentration  
Electrolytes are ions, such as sodium (Na\({}^{+}\)), potassium (K\({}^{+}\)), calcium (Ca\({}^{2+}\)), chloride (CI\({}^{-}\)), and bicarbonate (HCO\({}_{3}\)\({}^{-}\)), among others, present in the blood and urine. Electrolytes play a key role in several vital functions, such as blood pH and pressure control, body hydration, nerve and muscle functions, etc. [95]. There are electrochemical methods to determine selectively the concentration of electrolytes in blood and urine, mainly based on the so-called ion-selective electrodes (ISE), but such methods are expensive. Measuring the total concentration of ions does not provide complete information, but it may be indicative of certain pathologies, or it can be useful as a prescreening diagnosis tool. Moreover, monitoring the real-time variations of the total electrolyte content in urine or blood samples, as compared to a reference (REF), is also of interest from a medical viewpoint. These functionalities can be achieved by means of the differential sensors reported in this section, where the main advantageous aspect is sensor cost (e.g., as compared to electrochemical sensors), and real-time functionality. Within this context, the development of low-cost microwave methods able to provide the electrolyte concentration in samples of blood and urine is of high interest. Nevertheless, to avoid using biosamples, and for the sake of easy comparisons, it is usual to estimate sensor performance by considering electrolyte solutions of standard liquid, typically DI water. The reported differential sensor aimed to the measurement of electrolyte concentration in DI water is the one reported in [66], as it provides (to the best of our knowledge) the finest achieved resolution (0.125 g/L). Such a sensor is based on a pair of CSRR-loaded microstrip lines. The topology and a perspective view, including the fluidic channels, are depicted in Figure 26, whereas Figure 27 shows a photograph of the fabricated device. The output variable in these sensors is the cross-mode transmission coefficient, proportional to the difference between the transmission coefficient of both lines (the REF and the MUT line), namely,  
\[S_{21}^{DC}\ =\ \frac{1}{2}(S_{21}-S_{43}) \tag{4}\]  
This proportionality is valid provided the lines are uncoupled (otherwise, the cross-mode transmission coefficient is given by \(S_{21}^{DC}\) = (1/2) \(\cdot\) (\(S_{21}+S_{23}-S_{41}-S_{43}\)). The input variable is the electrolyte concentration of the MUT sample (provided pure DI water is the REF sample). The cross-mode transmission coefficient obtained after subsequently injecting solutions with different electrolyte content (with DI water in the REF channel) is depicted in Figure 28a. The considered electrolyte precursor is NaCl (which dissociates into anions and cations when dissolved in water). As the electrolyte concentration increases, the magnitude of the cross mode transmission coefficient shifts up. As it can be seen, a concentration as small as 0.125 g/L can be discriminated, as far as the corresponding curve is perfectly differentiated form the one of the REF sample (with 0 g/L of electrolyte concentration, i.e., pure DI water). Figure 28b depicts the dependence of the maximum cross-mode transmission coefficient with the electrolyte concentration. The maximum sensitivity (achieved for small electrolyte concentrations) is 0.034 (g/L)\({}^{-1}\), whereas the input dynamic range is at least 60 g/L. From the data points of Figure 28, the following calibration curve, with correlation coefficient of R\({}^{2}\) = 0.9996, results  
\[NaCl\Big{(}\frac{g}{L}\Big{)}\ =\ 0.41e^{(\frac{\Delta S_{21}^{DC}}{42})}+4.91 \cdot 10^{-8}e^{(\frac{\Delta S_{21}^{DC}}{0.68})}-0.59 \tag{5}\]  
This calibration curve can be used to determine unknown concentrations of NaCl in DI water, from the measured cross mode transmission coefficient. Note that other similar sensors for the measurement of electrolyte concentration have been reported [62; 63; 64; 65].