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(1.2) Z 0 = 120 π ε e f f where r is the mean radius of the designed resonator, n is the mode number, f is the resonant frequency, c is the velocity of the light in the free space, ε eff is the effective permittivity of the substrate, W is the microstrip line width, d is the thickness of the substrate (which is equal to the distance between the microstrip line and the ground plane) and Z 0 is the characteristic impedance of the microstrip line. Numerical model 2.1 Preliminary calculationsĭimensions of the microstrip ring resonator were roughly approximated using the following equations ( Pozar, 2012) (for geometry): At the first stage, we started with numerical modelling of the ring resonator integrated with a microfluidic channel. On the basis of the obtained results, we decided to develop a microstrip ring resonator with an integrated microfluidic channel. Our studies have shown that the microwave parameters of the microstrip line deposited using the ink-jet printing are satisfactory for the rapid prototyping of microwave, conductive structures on LTCC substrates. As a part of our earlier work, we used the ink-jet printing method to fabricate microstrip transmission lines ( Szostak et al., 2019). In that case, similar to the glass-epoxy laminates, the microchannel was made of PDMS and then inserted under the paper layer with the antenna structure printed on it ( Su et al., 2014). It was successfully used to make a microfluidic device with a microwave antenna on a paper substrate. Ink-jet printing seems to be a promising solution. Therefore, it would be good to have an alternative to screen printing, especially in the field of rapid prototyping. However, it can be a very time consuming and demanding technique ( Drela et al., 2014 Słobodzian, 2015). In contrast to the previously mentioned methods, the low temperature co-fired ceramics (LTCC) technology (Low-Temperature Co-fired Ceramics) allows fabricating the monolithic microfluidic devices with integrated microwave components on the same substrate material ( Macioszczyk et al., 2017 Malecha et al., 2019).Ĭurrently, screen printing is the most popular method of depositing a mosaic of conductive paths on the LTCC substrates. Another approach is the use of polymeric substrates, such as PDMS (polydimethylsiloxane), onto which the conductive paths are deposited using various techniques ( Leroy et al., 2015 Shah et al., 2010). The next step is adding a microfluidic channel made from another (frequently polymer) material over the selected part of the microstrip circuit ( Abduljabar et al., 2014 Chretiennot et al., 2013 Ebrahimi et al., 2014 Zarifi and Daneshmand, 2016).
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One of the most common trends is creating a planar microwave circuit on a dedicated glass-epoxy laminate with dielectric parameters suitable for microwave applications. In the literature, various techniques for developing the microfluidic-microwave microsystems can be found. Within these types of systems, the biomedical applications such as a cancer cell detection ( Grenier et al., 2010, 2013), the concentration of glucose ( Kim et al., 2015 Schwerthoeffer et al., 2013), ethanol ( Sohrabi et al., 2014) or humidity measurements ( Bogner et al., 2017 Jones et al., 2017) can be mentioned.
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The second field of applications includes testing/sensing some changes in the fluid parameters by means of microwave signal reflection and transmission. The main advantage of this solution, in contrast to the resistance heating, is the precise heat delivery, almost exclusively, to the fluid located in a microchannel. The first type of application is commonly used to control heating of the substance placed inside the microchannel, which is frequently used in chips dedicated to the PCR (Polymerase Chain Reaction) process ( Marchiarullo et al., 2013 Morgan et al., 2013 Shah et al., 2010). A microwave circuit can act as a heating or sensing component. Such hybrid devices are relatively small and have many advantages, including fast response time, good resolution and real-time control over reaction parameters. Nowadays, many types of highly integrated microfluidic systems incorporate microwave circuits for rapid heating and dielectric parameters detection purposes.
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