© Springer Science+Business Media New York 2016

Abstract This paper presents an investigation of various phenomena signiÞcant for the fabrication process of waveguide structures and their inßuence on the frequency response. We consider a bandpass waveguide Þlter implemented using printed-circuit inserts, placed in the transverse plane of a standard WR-90 rectangular waveguide. The Þlter response is investigated with respect to the implementation technology of the printed-circuit inserts, imperfections of the machine used for fabrication, and precise positioning of the inserts. WIPL-D software is used to accurately model the considered waveguide structures, including the aforementioned phenomena related to the fabrication process. Also, experimental veriÞcation is performed to validate the simulation results. The main result of this work is identiÞcation of crucial parameters affecting the Þlter performance. The analysis carried out in this research is important for robust, practical waveguide Þlter design and implementation.

Keywords Bandpass waveguide Þlter · Fabrication · Implementation technology · Machine tolerance · Precise positioning

B Milka M. Potrebi«c

milka_potrebic@etf.rs

Snežana Lj. Stefanovski Pajovi«c stefanovskisnezana@gmail.com

Dejan V. Toši«c tosic@etf.rs

Zlata Ž. Cvetkovi«c

Zlata.Cvetkovic@elfak.ni.ac.rs

1School of Electrical Engineering, University of Belgrade, PO Box 35-54, Belgrade 11120, Serbia

2Faculty of Electronic Engineering, University of Niš, Aleksandra Medvedeva 14, Niš 18000, Serbia

1 Introduction

Waveguide components are known to be robust microwave structures, intended for use in communication systems and radar systems where strict requirements regarding power and loss have to be met. Waveguide Þlters are important components which can be designed in different ways. Herein, we consider Þlters realized by placing printed-circuit inserts in the transverse planes of a rectangular waveguide. The inserts operate as resonators, and the complete structure acts as a Þlter.

Recently, metamaterial-inspired Þlter designs have offered new implementations based on split-ring resonators (SRRs) and complementary split-ring resonators (CSRRs). Various solutions using such resonators and waveguides have been reported for the design of bandpass or bandstop Þlters.

In [1], CSRRs were used as key elements for miniaturization of microwave devices implemented in planar technology, such as Þlters and diplexers. Furthermore, bandpass Þlters have been designed using coupled rectangular split-ring resonators formed from conventional microstrip transmission lines, as proposed in [2]. Also, modeling of bandpass Þlters using a split-ring-type defected ground structure was presented in [3].

In the design of bandpass waveguide Þlters, CSRRs are also widely used, and corresponding design guidelines have been reported, e.g., in [4Ð7]. There are also multiband solutions, as in [8], and compact waveguide Þlters, as in [9Ð11]. Bandstop waveguide Þlters with multiple rejection bands have also been implemented using SRRs, as presented in [12Ð14]. Finally, an H-shaped metamaterial unit cell structure, with split-square resonators, placed between waveguide ports, provided multiple stop bands [15].

According to the well-known Þlter design procedure [16, 17], experimental veriÞcation of the designed Þlter assumes

measurement of the Þlter response on a fabricated prototype Þlter. Then, based on the obtained results, proposed simulation models are corrected and one more control fabrication of the optimized Þlter is performed, if needed. However, there are various phenomena related to the fabrication process itself that should be analyzed, since they can also affect the Þlter response.

Previously published papers have reported analyses of the frequency response of various microwave structures (including microwave Þlters) depending on the implementation technology [18Ð20], including the inßuence of substrate parameters [21]. The deviation of the frequency response and the performance of waveguide Þlters have been investigated as well. Some of the available results are published in [22Ð25]. The waveguide Þlter fabrication process was considered in [26,27], and some solutions intended to simplify the design procedure were proposed.

For waveguide Þlters employing printed-circuit inserts as discontinuities, the problem to be considered includes various effects in the fabrication process that can introduce deviation of the measured Þlter response compared with that obtained in simulations. Since the resonators are implemented with printed circuits, some of the parameters relevant for investigation are given in the substrate speciÞcation, namely the substrate thickness, dielectric permittivity, losses, and metallization thickness. On the other hand, the machine used for fabrication can also introduce imperfections and inaccuracy, caused by various effects during its operation. Finally, precise positioning of the inserts inside the rectangular waveguide is important for the desired operation of the considered structure; however, it is not always possible to keep the inserts stable, potentially jeopardizing the expected Þlter response.

The objective of this study is to investigate the waveguide Þlter frequency response, by making a precise model of the Þlter, taking into account various effects and phenomena by simulating their inßuence. This approach can signiÞcantly improve and shorten the design process, since it enables the majority of settings and analyses to be performed in software, without unnecessary fabrication.

In this paper, we consider the inßuence of various fabrication side effects, and implementation imperfections, on the frequency response of bandpass waveguide Þlters. The effects and phenomena considered can cause deviation of the measured frequency response, and herein we propose a method to investigate this problem. In fact, the main contribution of this paper is to point out relevant and real issues related to the fabrication process, using three-dimensional electromagnetic (3D EM) models and software simulation, conÞrmed by measurement results. The Þlters are designed to operate in the X frequency band. The frequency responses are investigated by taking into account actual values of the

substrate parameters and tolerances according to manufacturer speciÞcation. Furthermore, the parameters relevant for the operation of the machine used for fabrication, as well as its accuracy and deviation, are also taken into consideration. Finally, the positioning of the inserts in the transverse planes of the waveguide is considered critical for appropriate Þlter operation, being a potentially critical issue during the measurement procedure. Experimental veriÞcation conÞrmed the results obtained by modeling the structures and simulating the effects of interest in our investigation.

2 Technological speciÞcation

For the waveguide resonator and Þlter design, a standard rectangular WR-90 waveguide (width a = 22.86 mm, height b = 10.16 mm) was used. Waveguide structures were excited by quarter-wave monopoles, and the dominant mode of propagation is the transverse electric TE10 mode. CSRRs were implemented as printed-circuit inserts, placed in the transverse planes of the rectangular waveguide. For these printed circuits, copper-clad polytetraßuoroethylene (PTFE)/woven glass laminate (TLX-8) was used as substrate. According to the manufacturerÕs speciÞcation (http://www.taconic-add. com/), the nominal values of the substrate parameters and the tolerances are as follows: relative dielectric permittivityr = 2.55 ± 0.04, losses tan δ = 0.0019 ± 0.001, substrate thickness h = 1.143± 0.05715 mm, and metallization thickness t = 18 µm. The conductivity of the metal plates was set to σ = 20 MS/m, to take into account losses due to surface roughness and the skin effect. The metallization thickness and conductivity of the metal plates were not varied during the investigation of the frequency response. As a tool for modeling and simulation of the effects relevant for Þlter fabrication, WIPL-D software (http://www.wipl-d.com/) was used, representing a reliable solution when precise modeling of 3D objects is needed, as well as accurate analysis of metallic and dielectric structures [28]. Herein, we consider the frequency response of a waveguide resonator and a thirdorder waveguide Þlter, providing insight into the inßuence of various parameters on the considered structures and enabling estimation of which parameters can signiÞcantly affect their operation.

Printed-circuit inserts were fabricated using a MITS Electronics FP21-TP machine (http://www.mitspcb.com/). This machine can achieve a minimum microstrip line width of 50 µm and a minimum gap between microstrip lines of 50 µm, according to the manufacturerÕs speciÞcations. A milling process was used for Þlter implementation. Tool quality is important for the accuracy of the traces. An Agilent N5227A network analyzer was used for the measurements.

3 Study of imperfections affecting the frequency response of the bandpass waveguide Þlter using CSRR

The analysis of the frequency responses started with a model of a waveguide resonator with a single CSRR. This resonator was designed to operate at a center frequency of f0 = 11.1 GHz, having bandwidth of B3dB = 520 MHz. A 3D model of the resonator is shown in Fig. 1a.

The CSRR was implemented as a printed-circuit insert placed in the transverse plane of the rectangular waveguide. The dimensions of the CSRR are presented in Table 1.

A photograph of the fabricated insert is shown in Fig. 1b, whereas Fig. 1c shows a comparison of the simulated and measured amplitude responses, revealing good agreement between the obtained results.

Analysis of the frequency response was also performed for a third-order bandpass waveguide Þlter, representing a more complex structure than the previous one, since it uses three printed-circuit inserts as CSRRs (Fig. 2a). This Þlter

(a)

Table 1 Dimensions of CSRR in Fig. 1a

f [GHz]

(b)

Fig. 2 Third-order bandpass waveguide Þlter: a 3D model, b amplitude response (Color Þgure online)

Table 2 Dimensions of CSRRs in Fig. 2a

(b)

f [GHz]

(c)

Fig. 1 Waveguide resonator using single CSRR: a 3D model, b fabricated printed-circuit insert with the waveguide used for measurement, c comparison of amplitude responses obtained by simulation and measurement (Color Þgure online)

was designed to operate at f0 = 11 GHz, having bandwidth of B3 dB = 300 MHz. The dimensions of the resonators are presented in Table 2. These dimensions remained unchanged for each considered model, unless otherwise speciÞed. Since we are now considering a third-order Þlter, it is necessary to properly model the inverters between the resonators. The inverters were modeled as quarter-wave sections of the rectangular waveguide, of length λg11GHz/4 = 8.49 mm, according to previously reported design guidelines [9Ð11]. Figure 2b shows the amplitude response of the Þlter.

The inßuence of the considered phenomena on the waveguide Þlter was investigated by determining the deviation of the obtained frequency response. This deviation can

be qualiÞed as the difference between the nominal value of the observed parameter of the amplitude response and the value obtained when taking some of the aforementioned fabrication side effects into account. The relative change of the considered parameters of the amplitude response, in percent, is given as

where x denotes the obtained value, xref denotes the reference (nominal) value, and xrel is the relative change in percent. Herein, the nominal value is assumed to be that obtained when no possible inaccuracy is introduced. The absolute change can be determined as xabs = x − xref . The deviation of the waveguide Þlter frequency response was analyzed and veriÞed by means of 3D EM models and simulation, and measurements on a laboratory prototype.

From the practical standpoint, we can adopt criteria and measures for the performance degradation as follows: The Þlter performance is not signiÞcantly degraded if the relative change of the center frequency is less than 1 %, and if the relative change of the bandwidth is less than 2 %. In addition, we state that the absolute change of the passband attenuation should be less than 0.3 dB.

3.1 Inßuence of implementation technology

quency f0rel (%) and bandwidth B3dBrel (%), and the absolute change of the attenuation at the center frequency S21abs( f0) (dB). The results obtained for the waveguide resonator and Þlter are presented in Table 3.

As can be seen, variation of r introduced the most signiÞcant change in the frequency response, while changing the other two parameters (tan δ and h) had practically no inßuence. According to the numerical results, variation of r caused deviation of the resonant frequency of about 0.5 %, while the change in the 3-dB bandwidth was below 2 %, with respect to the reference values, for both the waveguide resonator and Þlter. These values are in accordance with the adopted criteria, so it can be concluded that changing the substrate parameters within the limits speciÞed by the manufacturer did not degrade the amplitude response signiÞcantly. A comparison of the amplitude responses for various values of r is shown in Fig. 3.

Since the relative dielectric permittivity has the most signiÞcant inßuence on the amplitude response, the change of the resonant frequency was investigated for each printedcircuit insert of the third-order Þlter. The amplitude response was analyzed for various values of r when only one CSRR insert was placed in the waveguide. For the Þrst/third insert, the second insert, and the third-order Þlter (according to Fig. 2), the resonant frequency can be expressed as a linear

To investigate the inßuence of the implementation technology on the waveguide resonator and Þlter response, the parameters were varied according to the substrate speciÞcation provided in Sect. 2. Since each of the three inserts employed for the Þlter design was made using the same substrate board, as is usual practice in the fabrication process, the same variation was applied to each insert. To measure the deviation, we used the relative change of the center fre-

where k = −1.43, while m varies. Figure 4 shows the change of the resonant frequency with the permittivity, for each insert and the third-order Þlter, with the best linear Þt to each set of experimental data. The formula above can be used to compensate for the uncertainty in the substrate permittivity r as speciÞed by the manufacturer. Practically, a single insert should be measured prior to Þlter design, and from