диафрагмированные волноводные фильтры / cc8cd8d7-aeb5-4ffc-999a-5172ed4f59e5

Figure 7 Comparison measured (boxed line) and reconstructed (solid line) of reflection coefficients for the critically-coupled regime of a quasioptical resonator

avoid this effect. A final checking of the behavior of S11 near the resonance frequency is also recommended.

5. CONCLUSION

A consistent approach for determination of Q factors was presented, applicable to mm-wave quasi-optical FEM resonators with high values of Q and proper coupling elements. The model is based on an inductively coupled shorted-line section substituting the FEM resonator. To reconstruct the value of the actual Q factors, a system of two nonlinear equations is solved for preliminarily determined values of attenuation constant and coupling inductance. Only two measurements of reflection coefficient amplitude near the resonance are needed. The examples have demonstrated a validity of this technique in different coupling regimes of the FEM waveguide resonator.

REFERENCES

1.M.E. Hill, W.R. Fowlex, X.E. Lin, and D.H. Whittum, Beam-cavity interaction circuit at W-band, IEEE Trans MTT 49 (2001), 998 –1000.

2.Y.M. Yakover, Y. Pinhasi, and A. Glover, Resonator design and characterization for the Israeli electrostatic FEL Project, Nuclear Instr Methods Phys Research A.358 (1995), 323–326.

3.T. Nakahara and N. Kurauchi, Guided beam waves between parallel

concave reflectors, IEEE Trans MTT 15 (1967), 66 –71.

4. M.A. Shapiro and S.N. Vlasov, Study of a combined millimeter-wave resonator, IEEE Trans MTT 45 (1997), 1000 –1002.

5.E.-Y. Sun and S.-H. Chao, Unloaded Q measurement the criticalpoints methods, IEEE Trans MTT 41 (1995), 1983–1986.

6.R.S. Kwok and J.-F. Liang, Characteristics of high-Q resonators for microwave filter applications, IEEE Trans MTT 47 (1999), 111–114.

7.H. Heuermann, Calibration procedures with series impedance and unknown lines simplifies on-wafer measurements, IEEE Trans MTT 47 (1999), 1–5.

8.D. Kajfez, S. Chebolu, M.R. Abdul-Gaffoor, and A.A. Kishk, Uncertainty analysis of the transmission-type measurement of Q-factor, IEEE Trans MTT 47 (2001), 998 –1000.

9.A.J. Lord, Comparing on-wafer cal techniques to 100 GHz, Microwaves RF 39 (2000), 114 –118.

10.B. Kapilevich, A. Faingersh, and A. Gover, Accurate measurements of unloaded and loaded Q-factors of quasi-optical resonators for mmwave FEL applications, Proc 5th Israeli Conf Plasma Science and Applications, Weizmann Inst Science, Rehovot, Israel, 2002, p 37.

11.P.A. Rizzi, Microwave engineering, Prentice Hall, 1988, p 445.

© 2003 Wiley Periodicals, Inc.

A TRANSMISSION LINE MODEL APPLIED TO SHAPED SLOT DIELECTRIC-FILLED WAVEGUIDE ANTENNAS

S. Chainon and M. Himdi

Institute of Electronics and Telecommunications of Rennes

UMR CNRS 6164

University of Rennes I

35042 Rennes Cedex, France

Received 8 August 2002

ABSTRACT: This paper presents an extension of the so-called transmission line model method (TLMM) applied to shaped slot dielectricfilled waveguide antennas (SDFWAs), especially the L-shaped slot. This radiating longitudinal slot is fed by a transversal slot used as a coupling element; their association is shaped like the letter L. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 306 –310, 2003; Published online in Wiley InterScience (www.interscience.wiley. com). DOI 10.1002/mop.10750

Key words: antenna; shaped slot; dielectric-filled waveguide

INTRODUCTION

Waveguide-fed slot arrays have numerous applications in microwave communications and radar systems, especially when narrowbeam and shaped-beam radiation patterns are required. This variety of applications can be explained by the resonant arrays’ very low losses and low crossed-polarization characteristics, typically in millimeter waves. Given these features, the radiation characteristics of longitudinal antennas in the broad face of a rectangular waveguide are determined by the slot’s length and its displacement from the center of the waveguide. Slots used in waveguide array are spaced one-half-guide wavelength at the design frequency, which requires them to alternate in order to compensate for the current phase. Weights are obtained by controlling the slot’s displacement. One consequence of the design is an increase in cross polarization and the half-power aperture in E-plane increments. The L-shaped slot can reduce these problems. Indeed, the longitudinal part, used as a radiating element, is centered on the broad face of the waveguide and fed by the transversal part. The power intensity is then controlled by the transversal slot’s length. Before using this kind of slot in array, its characteristics must be determined.

This paper presents a method which has already been used to compute longitudinal SDFWA [1, 2] and various printed slot antenna shapes [3]. The slot impedance in the slot’s plane, found via the TLMM, is computed in the waveguide by using a transformation ratio that corresponds to the voltage discontinuity introduced by the transversal slot.

To validate this method, first the computed results are compared with those of the CST Microwave software [4], in the millimeter-wave band, for several transversal slots’ length. Second, a comparison with measurements in the X band, for one transversal length, is done with a metallized foam waveguide [5].

Figure 1 (a) Dielectric L-shaped slot waveguide antenna; (b) L-shaped slot

ANALYSIS

The radiating slot analysis has been developed using a lossy transmission line model, whose constant propagation j and characteristic impedance Zc correspond to those of the fundamental mode TE10. and Zc are obtained thanks to the so-called Cohn’s method [6]. The attenuation of the field in the slot is the solution of the numerical equation Pi( ) Pr( ), where Pi( ) is the power delivered to the lossy line and Pr( ) is the radiated power from the slotted waveguide antenna.

Determination of the Slot’s Electrical Field

The L-shaped slot has a longitudinal and a transversal part, shown in Figure 1(a). The first step will be the introduction of in the electric field slot’s expression of the two slots’ parts. For this, we shall consider that the transversal slot is exited on its center by a generator (1 V, 50 ), and charged on its ends by a short circuit and

a stub, respectively, corresponding to the coupled slot, shown in Figure 1(b). Then the expression of the electric field on the transversal slot part is given by [7]:

(1)

To find the expression of the electrical field in the longitudinal slot, we shall consider the potential continuity at the L-shaped slot’s part junction. The potential expression at the end of the transversal slot is given by:

where the factor 1 corresponds to the incident wave and 2 to the reflected wave. So the transmitted wave voltage is:

Considering the short circuit at its end, one can express the electrical field in the longitudinal slot part:

Computation of the Power Radiated by the Slot

to radiate into free space and the radiated power Pr( ) may be computed by the following formula:

Figure 2 Radiated power ratio (PLs/PLa)dB versus Ls

Figure 3 Equivalent circuit for an L-shaped slot feed by 50 generator;

(b) equivalent circuit of the slot, including the transition waveguide/slot line

/ 2

Pr r2sin E 2 E 2 d d , (5)

00

where the radiating impedance is 120 .

For a longitudinal waveguide, the slot is placed on the broad face of the waveguide, then the size of the substrate is limited by the upper-face dimension. Consequently, some fringing fields and backward radiations appear. All these perturbations influence the upper-half-space radiated power, which is the reason why a corrective empirical coefficient is introduced: 3/ 2 r .

The upper-half-space power radiated is due to both the longitudinal slot’s part and the transversal slot’s part. This feeding process aims to decrease cross-polarization in slot waveguide arrays. Therefore, it can be interesting to plot the radiated power ratio (PLs/PLa) in order to see the influence of the transversal slot’s power radiated versus Ls (Fig. 2). As we can attest, the ratio

Figure 4 (a) Slot resistance and (b) reactance, according to the transmission line model. Wa 0.5 mm; a 7.112 mm; b 3.556 mm; t 0.02 mm; r 1.15 [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 6 (a) Transmission parameter modulus and phase; (b) comparison theory and experiments. Wa 1.0 mm; a 19.74 mm; b 9.38 mm; t 0.02 mm; r 1.15; Ls 4.85 mm; La 7.62 mm

RESULTS

The theory presented in the previous section was programmed via the Fortran language to analyze various L-shaped coupled slots, where both lengths are adjusted to keep the same resonance frequency. Aperture reflection and transmission coefficients were computed in order to find slot resistance and reactance.

As a first step, we considered a WR28 metallized-foam slotted waveguide, with a permittivity close to that of the air, r 1.15 in the millimeter-wave band (35.0 GHz). This technology has been developed at the laboratory and is a stamp for 2D and 3D structures realization [8], especially for low-cost industrial applications. Computed resistance and reactance versus frequency are shown in Figure 4 and compared with the CST software in Figure 5 for several slot lengths. The power intensity is controlled by the transversal slot lengths. Indeed, the more Ls, the more the radiated power. A consequence of this Ls increment is the resonance frequency decrement. For this reason, to keep the same resonance frequency, when Ls increases, La decreases, and vice-versa. Both methods are in a good agreement. Indeed, the slot’s couples are resonant at 34.5 GHz with TLMM and at 35.0 GHz with the CST Microwave method. The normalized resistanceand reactancecomputed levels via both methods are in a good agreement too.

As a second step, a measurement is presented, in the X band (11.5 GHz for the same frequency band of [1]), with the same realization technology ( r 1.15) for one L-shaped slot. It can be noticed, that in this case the longitudinal slot’s length is lower than the one given in [1], due to the transversal slot’s presence. In any case, the total L-shaped slot length is nearly the same than the one given in [1]. A comparison between theory and measurements is shown in Figure 6, and we can also see a good agreement between both curves. Indeed, only a small shift in resistance and reactance levels is observed, due to the difficulties of measuring this kind of level (S21 0.8 dB) at the resonant frequency with good precision.

CONCLUSION

This analytical method continues to be a useful tool for designing slotted dielectric-filled waveguides in the millimeter-wave band, taking into account the material’s permittivity, and present the advantages of high speed, small CPU time, and low memory capacity. Moreover, this method is easy to implement via CAD software or optimizing tools. We see a good agreement between the transmission line method and the CST Microwave software in terms of frequency and resistance and reactance values. Furthermore, the permittivity of the waveguide is taken into account. Several extensions could be done for other shaped slots. However, our main interest concerns the L-shaped slot, especially for array applications. Indeed, this shape provides low cross-polarization, and excitation weights can be easily obtained by the transversal slot’s length. Some realizations, in the millimeter-wave band, are in progress and will be presented in future papers.

REFERENCES

1. S. Chainon and M. Himdi, Extension of transmission line model for longitudinal slot dielectric-filled waveguide, MOTL (2002), 180 –183.

2.S. Chainon and M. Himdi, Transmission line model for longitudinal slot dielectric-filled waveguide, IEEE AP-S Proc, San Antonio, Texas, 2002.

3.M. Himdi, J.P. Daniel, and M. El Yazidi, Transmission line model of various printed slot antenna shapes, ISAP’92 Proc, Sapporo, Japan, 1992.

4.CST Microwave studio, version 3.

5.B. Jecko, F. Jecko, M. Himdi, and J.P. Daniel, Design and technologies of 2D and 3D from L band to V band, ISAP’00 Proc, Fukuoka, Japan, 2000.

6.S.B. Cohn, Slot-line on a dielectric substrat, IEEE MTT 10 (1969), 768 –778.

7.D.G. Kurup, A. Rydberg, and M. Himdi, Transmission line model for field distribution in microstrip line fed H-slots, Electron Lett 37 (2001), 873– 874.

8.M. Himdi, S. Chainon, and J.P. Daniel, Technologie de mousses me´t- allise´es au service des antennes 2D et 3D, (in French), OHD, Le Mans, France, 2001, pp. 205–208.

© 2003 Wiley Periodicals, Inc.

DUAL-MODE DOUBLE-RING RESONATOR FOR MICROSTRIP BAND-PASS FILTER DESIGN

Ji-Chyun Liu,1 Chin-Shen Cheng,1 and Leo Yao2

1 Dept. of Electrical Engineering

Chung Cheng Institute of Technology

Ta-hsi, Tao-yuan, Taiwan

2 Atech Totalsolution

Taipei, Taiwan

Received 6 August 2002

ABSTRACT: A novel design of a dual-mode resonator with doublering structure for a band-pass filter is presented in this paper. Voltage/ current couplings between the two rings are proposed based on a mode chart. Because each ring exhibits dual-mode responses, they determine the range of operation; that is, the inner/outer rings depict the upper/ lower frequencies of the pass band, respectively. This is an alternative approach to improve the bandwidth of the conventional dual-mode ring resonator. Experimental results are presented and discussed. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 310 –314, 2003; Published online in Wiley InterScience (www.interscience.wiley. com). DOI 10.1002/mop.10751

Key words: double ring; dual-mode; microstrip filter

1. INTRODUCTION

Attractive features of the microstrip ring resonator are its compact size, low cost, high Q, and low radiation loss. In applications, the ring resonator has been used to design filters, mixers, oscillators, and antennas [1]. It is well known that the dual mode first introduced by Wolff [2] can be excited on a microstrip ring resonator. This characteristic is usually applied to realize band-pass filters in microstrip circuits. These filters have wide applications in satellite and mobile communications, wireless telecommunication, and broadband microwave, and millimeter-wave communication systems [3–11].

The basic structure of the dual-mode ring resonator is presented in Figure 1. Input and output ports are spatially separated 90° from each other and perturbations, such as a stub, are located 135° degrees offset from input and output ports. The dual-mode effects can be observed in the frequency responses, thus this structure can be applied to the design of band-pass filters.

A dual-mode resonator with double-ring structure for bandpass filter design is proposed in this paper. Based on the dual-mode ring resonator, double-ring configuration, and voltage/current coupling techniques, an alternative dual-mode double-ring resonator is constructed experimentally. This is an alternative approach to improve the bandwidth of conventional dual-mode ring resonators.

In practice, the double ring structure is used to obtain the response of the desired pass-band. Basically, each ring exhibits the dual-mode responses respectively, and the inner/outer rings depict