II. ANTENNA DESIGN

The layout of the proposed LPDA antenna is shown in Fig. 1. A standard LPDA antenna consists of a series of dipole elements arranged along the antenna axis on the center feed-line. The length of the dipoles and their relative spacing dictate the resonance frequencies within the operating bandwidth of the LPDA. The proposed inkjet-printed LPDA antenna follows the same configuration as log-periodic wire antennas. Therefore, the standard design procedure for LPDAs proposed by Carrel [Reference Carrel9] is adopted. The design goals for the LPDA are directivity and operating bandwidth, while the design parameters are the scaling factor τ and the spacing factor σ.

Fig. 1.

Layout of the proposed paper-based LPDA antenna, L _F  = 130, W _a  = 60 mm.

An average directivity of 10 dBi and a bandwidth of 2–11 GHz are targeted. By applying Carrel design curves, the calculated values of τ and σ are 0.865 and 0.17, respectively. The number of elements of the proposed LPDA antenna is then calculated by,

(1) $$N = 1 + \displaystyle{{{\rm ln}(B.\; \; B_{AR} )} \over {\ln \left( {1/\tau} \right)}},$$

where “B” is the operating bandwidth and B _AR is the bandwidth of the active region. The value of B for the proposed design is

$$B = \displaystyle{{f_{max}} \over {f_{min}}} = \displaystyle{{11} \over 2} = 5.5,$$

$$\alpha = \arctan \left( {\displaystyle{{1 - \tau} \over {4\sigma}}} \right) = \arctan \left( {\displaystyle{{1 - 0.865} \over {4 \times 0.17}}} \right) = 11.22,$$

$$B_{AR} = 1.1 + 7.7.\left( {1 - \tau} \right)^2. {\rm cot}\alpha = 1.80,$$

where “α” is the log-periodic antenna aperture angle (see Fig. 1). Using the above values in equation (1), the number of dipole elements is N = 16.84. Since the value of N must be an integer therefore 16 elements are utilized in the design. The optimized values of all the design parameters are summarized in Table 2.

Table 2.

Optimized values of the design parameters.

The paper substrate used for inkjet-printing has relative permittivity ε _r  = 3 and loss tangent tan δ = 0.02. The optimized dipole length L _n and width W _n is 25 and 4.82 mm, respectively, and are determined for the lower frequency of 2 GHz through full-wave simulation in CST Microwave Studio. The lengths, widths and spacing for the other dipoles are computed by:

(2) $$\tau = \displaystyle{{L_{n + 1}} \over {L_n}} = \displaystyle{{W_{n + 1}} \over {W_n}} = \displaystyle{{S_{n + 1}} \over {S_n}}. $$

Table 3 shows the dimensions of all the dipole elements. The spacings between the dipoles are computed using aperture angle α.

Table 3.

Dimensions of the 16 dipole elements of the LPDA antenna.

The current distribution gives an insight into the physical behavior of the antenna at various frequencies as shown in Fig. 2. It is seen that the current at 3 GHz is concentrated along the feed line. As the frequency is increased from 5 to 7 GHz, the current starts to concentrate in the smaller dipole elements thus making the antenna highly directional. At 10 GHz, majority of the surface currents are accumulated along the narrow end of the LPDA making it more directional at higher frequencies.

Fig. 2.

Surface current density: (a) 3 GHz, (b) 5 GHz, (c) 7 GHz, (d) 10 GHz.

III. FABRICATION AND MEASURED RESULTS

The fabricated antenna is displayed in Fig. 3. This LPDA is inkjet-printed using a Diamatix DMP-2831 printer and UT Dots silver nano-particle ink [Reference Aboutarboush and Shamim10–Reference Khan, Tahir, Farooqui, Shamim and Cheema12]. The inkjet printing technology has become quite mature over the last 6–8 years providing better printing resolutions as well as repeatable structures [Reference Shaker, Safavi-Naeini, Sangary and Tentzeris4, Reference Cook and Shamim5, Reference Aboutarboush and Shamim10–Reference Khan, Tahir, Farooqui, Shamim and Cheema12]. In addition, the nano-particle inks offer suitable conductivities and viscosity for accurate jetting through the printer cartridges and nozzles. A typical antenna fabrication involves selection of the right droplet size, drop spacing, and number of layers. It is important to note that few calibration structures (straight lines, etc.) are printed before printing of the actual antenna. Once the calibration is achieved, repeatable printing is easily achieved. A final step after inkjet printing is called sintering which can be done through conventional heating or laser heating. This is done to evaporate the solvent mixed in the nano-particle ink hence improving the conductivity of the traces. The sintering process is also found to be repeatable offering same conductivity each time. In our design, we used commercial photo paper as a dielectric substrate. However, various other flexible polymers such as Kapton and polyethylene terephtalate (PET) have also been used to demonstrate flexible antennas, sensors, and electronics [Reference Shaker, Safavi-Naeini, Sangary and Tentzeris4, Reference Cook and Shamim5, Reference Aboutarboush and Shamim10–Reference Khan, Tahir, Farooqui, Shamim and Cheema12]. However, paper substrate is better than the others due to its lowest cost and porous nature. The latter property is critical because the nano-particle ink tends to flow on smooth plastic substrates and it is very challenging to obtain accurate dimensions of the required structures.

Fig. 3.

Fabricated prototype (130 × 60 mm²) of LPDA with infinite balun feed.

In order to obtain accurate on-paper dimensions for our design, an optimized drop diameter of 25 µm and a drop spacing of 30 µm are chosen. Each side of the LPDA is printed on a separate 0.25 mm-thick photo paper and then glued together to achieve a total substrate thickness of 0.5 mm. The printed antenna is heat-sintered at 80 °C for 15 min achieving a subsequent ink conductivity of 6 × 10⁶ S/m [Reference Aboutarboush and Shamim10–Reference Khan, Tahir, Farooqui, Shamim and Cheema12]. The antenna is fed using a coaxial cable; the outer conductor of the coaxial cable is connected to the bottom layer of the line while the inner conductor is connected to the top side via a through-hole in the paper substrate using conductive epoxy. The overall size of the LPDA is 130 × 60 mm².

Antenna measurements in both straight and bended forms is performed in an 18 GHz Satimo-Star-Lab anechoic chamber, as shown in Fig. 4. The simulated and measured reflection coefficient and gain are shown in Figs 5 and 6, respectively. The measured return loss is in general agreement within the complete UWB band. The slight deviation is attributed to the manual gluing process which has two consequences. Firstly, the two dipole arms are minutely misaligned and secondly the discontinuity in the dielectric due to air gaps occurs between the two layers of paper. The gain is measured using a broadband Horn as a reference antenna. The proposed antenna has a peak gain of 9.5 dBi with slight degradation at the lower-frequency band.

Fig. 4.

Antenna measurement setup.

Fig. 5.

Measured and simulated S ₁₁ for the LPDA.

Fig. 6.

Measured and simulated gain (IEEE) for the fabricated LPDA.

The simulated radiation efficiency is given in Fig. 7. It is about 80% for the whole UWB band. The radiation efficiency does not include the reflection losses that are represented by the reflection efficiency in terms of S ₁₁. In Fig. 8, the measured radiation patterns in both E and H planes at frequencies of 3, 6, and 9 GHz are shown. The end-fire radiation patterns with side lobe levels (SLLs) well below −21 dB are achieved.

Fig. 7.

Simulated radiation efficiency of the LPDA.

Fig. 8.

Simulated (-------) and measured (_____) radiation patterns at different frequencies.

IV. BENDING ANALYSIS

As the antenna is intended for flexible wireless devices, its performance under bent conditions is also validated. For this purpose, the antenna is placed on a cylindrical surface with a diameter “D” of 65 mm as shown in Fig. 9. The bending analysis is only done in horizontal direction; in vertical direction the bending analysis is not possible due to non-flexible coaxial feed.

Fig. 9.

LPDA in bent configuration.

Figure 10 depicts the antenna reflection coefficient in bent and unbent forms. Other than a slight mismatch at 11 GHz, no major shift is observed and can be attributed to change in the antenna electrical length in the bent stage. To show the antenna ability to perform in extreme bending conditions, simulated S ₁₁ with 48 mm diameter cylinder is also given in Fig. 10. The choice of the radii was made due to the cylinders available in the laboratory on which the antenna could be mounted. However, these values also indicate the limit at which the antenna can be bent. At the upper limit of 65 mm, slight changes in the return loss and radiation pattern begins to occur, as shown in Figs 10 and 12. While 48 mm is the lowest limit after which further bending results in distortion and deviation in radiation properties taking the performance below the required acceptable level.

Fig. 10.

Measured and simulated S ₁₁ in bending state.

The simulated gain for bent and unbent conditions is also compared in Fig. 11 showing a good match. The radiation patterns of the antenna are also measured in bent configuration and then compared with the unbent patterns as shown in Fig. 12. No significant change is observed in the radiation patterns and the antenna maintains its radiation characteristics after repeated testing, making it suitable for highly directive UWB antennas in flexible wireless devices.

Fig. 11.

Simulated gain in unbent and bent (R = 68 mm) condition.

Fig. 12.

Measured radiation patterns in bent (-------) and unbent (_____) configurations.