DIELECTRIC PROPERTIES CHARACTERIZATION

The second method, referred here as the two-transmission lines (2- TL) method, has the advantage of obtaining the dielectric characteristics in a wide range of frequencies, compared to the previous method in which just the information was only available at the resonance (or odd multiples) frequency. Moreover, its differential measurement facilitates the measurement setup because it dispenses with complex calibrations procedures. Both the permittivity and loss factor can be found from the following equations [147]:

εef f = ∆θ

2πf∆L, (C.6)

αt=−ln(|S21l|/|S21s|)

∆L (C.7)

whereα_tis the total loss factor, ∆θis the difference of phase of both lines in rads, ∆Lis the difference of length, and|S21l(s)|is the magnitude of the transmission coefficient of the long (short) line.

C.2.0.1 Experimental results

The methods described previously were used to characterize photo-quality paper from Multilaser. Even though, this paper was not suitable for printing structures, it is cheap and also sensitive to humidity of the environment, so it can be used for some sensing applications without requiring any extra materials. The methods were validated though the design of a patch antenna and compared simulation results using the dielectric parameters extracted. Since Epson paper is the paper selected for printing, their dielectric properties are also presented, however, an specialized probe kit for dielectric characterization was used in combination with a VNA.

After several tests, it was decided to fabricate the conductive traces of the microstrip structures with adhesive copper foil tape from 3M, since it was simpler, cheaper and faster than jetting or evaporating some metal over the paper. The prototypes for both extraction methods were build using 6 layers of photo-paper from Multilaser (180 g/m2) glued at the borders and at some points near the middle, avoiding to be right below of the conductive traces. The measurements were carried on a ROHDE&SCHWARZ ZVB VNA.

In the case of the T-resonator, noThru-Reflect-Line(TRL) cal- ibration kit was performed for this prototype because no important

differences were detected when measuring a previous prototype in FR4 substrate, therefore usual SOLT calibration was done. A photograph of the resonator is seen in Figure C.12. The measurements were done at a VNA, with previous Short-Open-Load-Thru (SOLT) calibration.

Measurement setup and transmission coefficient are shown in Fig. C.12.

Figure C.12: T-resonator prototype, transmission coefficient (S21) measure- ment setup and plot.

Source: The author.

For the second method, three transmission lines were build with 4, 6 and 8 cm of length. For the measurement, SOLT calibration was also previously applied. The transmission coefficient magnitude and phase were measured for each line, as shown in Figure C.13. Plots of the processed measurements are also shown, obtained from calculations in ADS software from Keysight ©. Since the dimensions of the structures are less than 10 cm long, too much noisy results were obtained at low frequencies (< 1 GHz). Also, not trusty results were obtained at frequencies higher than 3 GHz, since SMA connectors and connector- to-substrate transition EM response begin to show up. The extracted parameters from both methods are summarized in Table C.5.

An experimental validation of the extracted values was done through the design of a patch antenna Multilaser paper substrate and copper tape, as shown in Fig. C.14. It was designed to resonate around

Figure C.13: Two-transmission-lines structures, transmission coefficient (S21) measurement setup and plots obtained from ADS.

Source: The author.

2.4 GHz. The antenna was simulated in ADS with the Finite-Element Method (FEM) simulator, assuming an uniform substrate thickness of t = 220µm and a relative dielectric constant εr = 2.636 at 2.4 GHz.

The simulated vs measured results of the reflection coefficient are also shown in Fig. C.14. There values of resonance frequencies obtained from simulation and measurement are well correlated, indicating a good dielectric constant extraction. Differences, on the absolute value of the S11 are possibly due to calibration errors during measurement, the SMA connector and the effect of the adhesive layer of the cooper tape, which is somehow significant compared to the thickness of the paper substrate [102].

The Epson paper was also characterized, since it is suitable for printing electronics, differently from Multilaser paper. Dielectric properties of Epson A6-size paper were extracted by using the dielectric

Table C.5: Extracted dielectric parameters of Multilaser paper from T- resonator and 2-TL methods

Method T-res 2-TL

Eval. freq. [GHz] 1.09 2.4

ε 2.4 2.64

tanδ 0.77 0.66

Figure C.14: Patch antenna on paper for validating the dielectric parame- ters extracted from Multilaser paper. Simulated vs measured results of the normalized magnitude of the reflection coefficient to compare the resonance frequency. Dimensions of patch areL= 40.3 mm, W = 48 mm, of feed line are l= 21.7 mm, w= 2 mm, and of total antenna areLg = 80 mm, Wg= 90 mm.

Source: The author.

kit probe N1501A from Keysight Technologies. This kit contains several open-coaxial probes of different sizes and shapes, which can estimate the dielectric permittivity and loss factor from reflection coefficient measurement with the aid of a VNA. The high-temperature probe has been used, from which its relation of dielectric properties and measured reflection coefficient depends on its specific physical dimensions [148].

For the measurement of the Epson paper, a handheld VNA Fieldfox from Keysight was used together with a commercial software from the same company which performs the reflection coefficient to dielectric parameters conversion. Measurement setup and results are depicted in Fig. C.15.

Figure C.15: Dielectric probe kit measurement setup and dielectric properties results of Epson A6-size paper.

Source: The author.