Performance Analysis of Probe-Fed Circularly-Polarized Moderately-Thick Microstrip Antennas Designed under the Null Reactance Condition

This work presents a performance analysis of probe-fed circularly-polarized moderately-thick microstrip patch antennas. Five typical geometries are designed according to the null reactance condition. A nonlinear regression, based on HFSS simulations, is implemented in order to identify the most robust geometry, regarding the manufacturing process. The analysis focus is on broadside axial ratio degradation and frequency deviation parameters. Experimental results validate the proposed approach and the nonlinear regression calculations.


I. INTRODUCTION
Microstrip antennas have been widely used in communication systems due to their many advantages, such as low profile, compatibility with integrated circuit technology, and conformability to a shaped surface.The conventional probe-fed linearly-polarized antenna, comprising a metallic patch printed on top of a thin grounded dielectric layer, is certainly the most popular radiator [1]- [5].However, this basic structure can only handle low power and operates over a narrow frequency range.A simple way to overcome these limitations would be the use of a thick substrate [6].Unfortunately, thick-substrate probe-fed antennas, designed according to the standard procedure (modes TM 01 and TM 10 excited at the same intensity and approximately equidistant from the operating frequency) [7], exhibit a highly inductive input impedance that cannot be properly matched to a 50- SMA connector [8].On the other hand, mobile devices require circularly polarized (CP) patches with good impedance matching, as well as broadside axial ratio, at the frequency of interest [9].Different approaches have been used to fulfill this requirement [1]- [4], [9]- [11].Based on [10], a new efficient and easy to implement approach, coined as the null reactance condition, is proposed.Thus, the antenna input impedance reactance can be compensated by acting simultaneously on the probe position and the patch dimensions with no additional matching circuit.In [12], this approach is applied for designing CP antennas with rectangular and truncated-corner rectangular (TCR) patches, with excellent results.
Using the strategy mentioned above, CP antennas with elliptical, elliptical with perturbation (EWP)    Moreover, differently from the standard procedure [7], the null reactance condition sets the frequency of the best broadside axial ratio on the mode controlled by the dimension W of the patch (W < L).Thus, it is intuitive to state that variations of this dimension can significantly affect the electrical characteristics of the antenna.In order to verify this statement, a performance analysis is carried out in Section 3.
To complete the comparative analysis, the directivity, radiation efficiency (RE), broadside axial ratio bandwidth (ARBW) and reflection coefficient bandwidth (RCBW) of the five antennas are also calculated.Results are given in Table II.As seen, the electrical characteristics of the antennas are similar, except for the triangular one -its operating bandwidth is slightly narrower than the others and the radiation patterns, in xz-plane, are asymmetrical, as shown in Figs.2(a

III. NONLINEAR REGRESSION ANALYSIS
In order to improve the comparison analysis, a nonlinear regression was carried out using the HFSS software.The purpose of this analysis was to determine which of the patches shown in Fig. 1 is the most robust in the manufacturing process.The results presented in Table II show that the return loss bandwidths are approximately four times larger than the broadside axial ratio ones.Consequently, small variations in the patch dimensions should not substantially affect the antenna return loss characteristic.Thus, only the broadside axial ratio was considered in the nonlinear regression analysis.
Two important effects were investigated: the frequency deviation (f), defined as the difference between the operating frequency (f o ) and the best broadside axial ratio deviated frequency (f d ), and the broadside axial ratio degradation, denoted by AR.These parameters are illustrated in Fig. 5.For the antennas under consideration, the quadratic regression coefficients were obtained from the HFSS Sensitivity analysis according to the following steps.The first one consists of the sensitivity analysis of the variables shown in Table I.This procedure is carried out in a local variable window, where the maximum and minimum values of these variables, as well as the initial displacement, are defined.For the present case, it was supposed that the antenna dimension and the probe position can move  0.05 mm around the nominal values.Next, an Optometrics Sensitivity simulation was carried out for each antenna.The maximum number of iterations was set as five, since that was sufficient to produce stable results in a satisfactory computing time.Additionally, using the Setup Calculations tab, the quadratic regression output (broadside axial ratio degradation and frequency deviation) was added by means of functions (min(…) and XAtYMin(…)).Finally, after extensive simulation, the regression coefficients were obtained.
According to [14], the expression for calculating the quadratic regression is given by (1), which can be rewritten as (2), now with respect to the nominal value of the independent variable.In (2),  1 and  2 are the regression coefficients.The relative value ∆x/x o = 0.001 is equivalent to 0.1% deviation (in absolute value) of the antenna dimension. (2) Introducing (2) in Mathematica [15], graphics of axial ratio degradation and axial ratio frequency deviation (with respect to the operation frequency) can be plotted.Figure 6(a) indicates the triangular patch is the most sensible to the dimension deviation -its axial ratio degrades sooner than the others.
Furthermore, antennas with TCR and EWP patches are more stable with respect to the dimension deviations.On the other hand, Fig. 6(b) shows that the frequency deviations behave similarly.A small error in the manufacturing process of the patch dimension W can produce a significant shift in the operating frequency.That is expected from the fact the frequency of best broadside axial ratio corresponds to the mode controlled by the dimension W (W < L), as previously mentioned.

IV. PROTOTYPES
In order to validate the proposed design criterion, antennas were prototyped at LAP's facility using the T-Tech 2500 [16] machine, all from the same Arlon CuClad 250 GX laminate plate.Input impedance and broadside axial ratio measurements were conducted inside the DCTA-IFI anechoic chamber.
Pictures of the prototypes are shown in Fig. 7, as well as the measured results compared with the simulated ones.Very good agreement is observed.Results for the frequency deviation and the broadside axial ratio degradation are compiled in Table III.As seen, the antennas with rectangular and TCR patches do not exhibit frequency deviation.
Rectangular patch.Comparison between experimental and simulated results.
Elliptical patch.In accordance with the regression analysis, it was noticed that the patches with geometrical perturbation suffer less axial ratio degradation than the others.Moreover, it can see from Fig. 7 that the triangular antenna exhibits the worst performance whereas the TCR microstrip radiator presents the best one.

V. FINAL COMMENTS
A comprehensive analysis of probe-fed, circularly-polarized microstrip antennas on moderately thick substrates, designed according to the null reactance condition, was carried out in this paper.
Typical patch geometries -i.e.rectangular, TCR, elliptical, EWP and triangular -were considered.A nonlinear regression was implemented in HFSS in order to identify, among the CP antennas, the most robust geometry in terms of the manufacturing process.Electrical characteristics, such as radiation pattern, directivity, radiation efficiency, input impedance, reflection coefficient magnitude, and broadside axial ratio, were calculated and discussed.All aforementioned CP antennas were prototyped

Fig. 7 .
Fig. 7. Pictures of the prototypes (left column) and graphics for input impedance and broadside axial ratio (right column).TABLE III.MEASURED RESULTS FOR F AND BROADSIDE AR Rectangular TCR Elliptical EWP Triangular f (MHz) 0.0 0.0 10.0 15.0 50.0 AR (dB) 1.0 0.0 0.8 0.3 1.4 , printed on moderately thick substrates, are designed here at 5.8 GHz to comply with the ISM band (5.725-5.875GHz).Results for radiation pattern, directivity, radiation efficiency, input impedance, reflection coefficient magnitude and broadside axial ratio are presented and discussed.A nonlinear regression analysis, based on HFSS [13] simulations, is carried out in order to identify the drawbacks of these radiators.Experimental results validate our calculations.

TABLE I .
PATCH DIMENSIONS (IN MM)