диафрагмированные волноводные фильтры / ea612446-7a5e-485b-89bd-6837c708d506

9th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics - Metamaterials 2015

Oxford, United Kingdom, 7-12 September 2015

Tunable Second-Order Bandpass Filter Based on Dual ENZ Waveguide

N. Vojnovic1, B. Jokanovic1, M. Radovanovic1, F. Mesa2

1University of Belgrade, Institute of Physics, Pregrevica 118, 11080, Belgrade, Serbia

2Universidad de Sevilla, Department of Applied Physics 1, Reina Mercedes S/N, 41012, Sevilla, Spain nebojsav@ipb.ac.rs

Abstract – A novel tunable filter based on ENZ waveguide technology is presented and discussed. This kind of filter utilizes the possibility of independent tuning of two types of resonances that occur in ENZ waveguides using short slot cuts in the ENZ channels. By forming a dual-channel configuration, a second-order bandpass filter can be obtained using zero- order-resonance (ZOR) from one channel and Fabry-Perot (FP) resonance from the other one (whose frequency is slightly different from ZOR). Both resonances can be simultaneously and equally tuned by changing the respective slots’ lengths. The maximum observed passband shift is 900 MHz or 8.3%. During filter tuning, 3 dB-bandwidth varies between 330 MHz (3.4%) and 470 MHz (4.4%) as the length of the tuning slots decreases. Maximum insertion loss observed is 1.8 dB.

I. INTRODUCTION

Dispersion characteristics of a rectangular waveguide operating near the fundamental mode cutoff frequency can be utilized to realize ε-near-zero metamaterial [1]. One of the most prominent characteristics of the ENZ metamaterials is their inherent ability to squeeze or ”tunnel” electromagnetic energy through very tight waveguide channels. Theoretical basis for this phenomenon can be found in [2] while the experimental verification is given in [3].

Waveguide ENZ metamaterials are often used in the design of filters. Since a number of resonances occur in these structures, firstand higher-order filters can be obtained if a proper geometry is employed. An interesting second-order filter was described in [4], which takes advantage of a dual ENZ channel geometry. ENZ property was achieved in each of the channels by using conductive wires of different radii positioned perpendicular to the wave propagation direction. On the other hand, in [5] and [6] it was shown that both types or resonances occurring in ENZ waveguides can be effectively and independently tuned using appropriate longitudinal or inclined slots in the channel region. The main goal of this paper is to demonstrate a design of a continuously tunable second-order filter using a dual-channel ENZ waveguide. Filter tuning is achieved by means of two different nonresonant slots in the channel region.

II. TUNABLE SECOND-ORDER BANDPASS FILTER

The filter structure examined in this paper is depicted in Fig. 1a (metallization is omitted). It consists of two input waveguides which are connected to each other by means of two narrow ENZ channels. Dielectrics filling the input waveguides and the channels have constants εrw = εrch1 = 6.15, tanδ1 = 0.002 (Rogers RO3006) and εrch2 = 3, tanδ2 = 0.001 (Rogers RO3003). Conductors are made of copper with σ = 58 MS/m and RMS surface roughness of 0.5μm. Waveguide ports are placed at the leftand rightmost sides of the structure.

The equivalent circuit representing the structure from Fig. 1a is shown in Fig. 1b. All the waveguide sections are modelled using transmission-lines with appropriate characteristic impedances, propagation constants and lengths. Abrupt E-plane steps are accounted for by shunt capacitances C1 and C2 in accordance with [7]. Because slots are positioned in each of the channel’s centers, each of the transmission-lines modelling the channels had to be split into two equal parts. Since the longitudinal slot intercepts the transversal component of the surface current along the channel, it is represented with a shunt capacitor, Cslot2. On the other hand, the inclined slot intercepts the axial

9th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics - Metamaterials 2015

Oxford, United Kingdom, 7-12 September 2015

component of the surface current, so it is represented using a series inductor, Lslot1. A more detailed analysis and discussion about the equivalent circuit can be found in [5] and [6].

(a)

(b)

Fig. 1: a) A 3D model of the second-order filter (metallization omitted). Width of all the waveguides is a = 7.62 mm, heights of the input waveguides and both channels are bw = 4.064 mm and bch = 0.254 mm, respectively. Lengths of input waveguides and channels are Lw = Lch = 7 mm. Offset of the longitudinal slot is d = 2.1 mm and the angle of the inclined slot is ϕ = 40o. Lengths of both slots are varied in order to tune the position of the passband. Width of both slots is 0.2 mm.; b) Filter equivalent circuit.

Fig. 2a shows the manner in which the second-order bandpass filter is created. When only the lower channel is present, the resonance at 10.59 GHz can be observed and, bearing in mind that the fundamental mode cutoff in that channel is at 11.36 GHz, it is the zero-order resonance. When only the upper channel is present, another resonance can be seen at 11.03 GHz, and this is in fact a classic Fabry-Perot resonance since the fundamental mode cutoff in the upper channel is around 8 GHz (same as for the input waveguides). When both channels are present a superposition of these resonances can be observed (green curves in Fig. 2a), hence forming a secondorder bandpass filter. It can also be seen that this superposition is not perfect in the sense that the upper channel influences the resonance in the lower channel and vice versa. This imperfection results in a slight frequency shift of about 1% as observed in Fig. 2a. It should be noted that a second-order filter can be formed by combining resonances that are different in nature (one ZOR and another FP, or two FP resonances of different orders) since combining two resonances of the same nature results in a transmission zero at a certain frequency between the resonances.

After the passband is completed, technique described in [6] can be utilized to simultaneously tune both resonances by the same amount, thus tuning the whole passband while keeping its shape relatively intact.

In order to tune the ZOR, a longitudinal offset slot needs to be placed along the lower channel. An inclined slot is placed along the upper channel to tune the FP resonance. Slots are placed on the outward-facing conductive surfaces to facilitate the adjustment of the slots’ lengths. The position of ZOR can be manipulated either by changing the offset or the length of the longitudinal slot. Similarly, the position of the FP resonance can be tuned by changing the inclined slot’s angle or length. From a practical point of view, it is more convenient to alter the lengths of both slots. Longitudinal slot’s offset is fixed at 2.1 mm, while the inclined slot angle is equal to 400. Certainly there are many more geometries and dielectrics that can be employed to form a second-order pass band. Slots’ lengths could eventually be manipulated by means of trimming, varactor diodes or by using liquid metal as described in [8].

Fig. 2b demonstrates the passband tuning possibility as a consequence of changing the slots’ lengths (needed slot lengths are given in the caption). It can be observed that the 3 dB-bandwidth is around 400 MHz and shows a decrease from 470 MHz to 330 MHz (or from 4.4% to 3.4% in terms of fractional bandwidth), as the passband shift is increased. It should be noted that a narrower passband could be achieved by reducing the heights of the channels, bch. The maximum level of the S11-parameter between the resonances is kept lower than -15 dB and the insertion loss is less than 1.8 dB. The maximum observed passband shift is 900 MHz or 8.3% compared to the starting case (blue curves in Fig. 2b).

9th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics - Metamaterials 2015

Oxford, United Kingdom, 7-12 September 2015

Fig. 2: a) Forming of the second-order bandpass filter in the structure from Fig. 1a. Red curves show the case when only ZOR channel is present (lower channel). Blue curves show the case when FP channel is present (upper channel). Green curves show the case when both channels are present (ZOR and FP); b) Tuning capability of the proposed structure. i) S21-parameter along= 2.1 mm, ainc= 1 mm, ii) S21-parameter along= 3.29 mm, ainc= 2.93 mm, iii) S21-parameter along= 4.14 mm, ainc= 3.79 mm, iv) S21-parameter along= 4.87 mm, ainc= 4.46 mm, v)-viii) respective S11-parameters.

III. CONCLUSION

We have presented a novel method for tuning a second-order bandpass filter in dual-ENZ waveguide using longitudinal and inclined slots. The achieved tuning range is 900 MHz (8.3%) while keeping the bandwidth of the filter around 400 MHz (around 4% fractional bandwidth). Maximum insertion loss observed was 1.8 dB. The proposed technique for continuous filter tuning is very simple to implement and hence can be effectively used in the design of input filters for microwave front-ends.

ACKNOWLEDGEMENTS

This work was financed by the Serbian Ministry of Education, Science and Technological Development through the project TR-32024 and through the project of bilateral cooperation between Spain and Republic of Serbia PRI- AIBSE-2011-1119.

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[6]N. Vojnovic, B. Jokanovic, M. Radovanovic, F. Medina, F. Mesa, ”Modelling of nonresonant longitudinal and inclined slots for resonance tuning in ENZ,” IEEE Transactions on Antenna and Propagation, submitted.

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