A CPW T-resonator technique for electrical characterization of microwave substrates

A Stretchable Radio-Frequency Strain Sensor Using Screen Printing Technology

“…Its dielectric constant ( ε r ) and loss tangent were determined using a T-resonator method [19,20]. The resonant frequency of the rectangular patch can be calculated as follows [21,22]: $f_0=\frac{c}{2\sqrt{{\epsilon }_{\mathrm{eff}}}\left\{L_p+0.824H_s\left[\frac{\left({\epsilon }_{\mathrm{eff}}+0.3\right)\left(\frac{W_p}{H_s}+0.264\right)}{\left({\epsilon }_{\mathrm{eff}}-0.258\right)\left(\frac{W_p}{H_s}+0.8\right)}\right]\right\}}$ ${\epsilon }_{\mathrm{eff}}=\frac{{\epsilon }_r+1}{2}+\frac{{\epsilon }_r-1}{2}\left[\frac{1}{\sqrt{1+12\left(\frac{h_s}{W_p}\right)}}\right]$ where ε eff is the effective dielectric constant resulting from the fringe fields and H s is the thickness of the substrate.…”

“…The values of ε r and loss tangent of the PDMS were determined to be 3 and 0.02, respectively. In order to characterize dielectric constants and loss tangent of the PDMS, we used T-resonator technique, as introduced in [19,20]. The width ( W p ) and length ( L p ) of the rectangular patch were therefore set at 17 mm and 23 mm, respectively, to allow the device to resonate at 3.7 GHz.…”

Characteristics of coplanar waveguide on sapphire for high temperature applications (25 to 400° C)

“…Omitting the parasitic reactances of the structure, the stub has a transmission minimum when the stub length is an odd multiple of g/4, or when the open circuit termination is translated to a shunt short circuit at the tee junction. Therefore, the effective permittivity may be determined from (1) [16]. Wirebonds are used at the T-junction to minimize the excitation of the slotline parasitic mode.…”

Low cost characterization of the electrical properties of thin film and mold compound for embedded wafer level packaging (EMWLP)

“…From literature, the T-resonator [4][5] and TL technique [6] are among some of the common methods used for dielectric property characterization, since these methods do not require special test fixtures and are low cost (printed using lithography). For the T-resonator technique, the effective dielectric constant and attenuation can be obtained from the equations provided in [5].…”

“…For the T-resonator technique, the effective dielectric constant and attenuation can be obtained from the equations provided in [5]. Nevertheless, it is of great interest to vendors to obtain the relative dielectric constant and loss tangent values of their material.…”