Asymmetrically-loaded interdigital coupled line for wideband microstrip bandpass filters with good out-of-band performance S. Sun and L. Zhu An asymmetrically-loaded interdigital coupled line is proposed for design of wideband microstrip bandpass filters with good out-ofband performance. This interdigital coupled line with three fingers is formed by stretching one of two outer arms with one two-stage open-ended stub. Its characteristics are analysed in terms of admittance matrix to exhibit simultaneous emergence of extra transmission zeros in lower and upper stopbands. A wideband filter with two half-wavelength resonators is then designed and fabricated. Measured results show low-loss wide passband in the range 2.95 –5.15 GHz and highly attenuated stopbands at DC to 2.2 GHz and 6.6 –10.0 GHz, respectively.

Introduction: Over the past decades, coupled three-line microstrip structures have been widely characterised for applications in planar couplers, filters and other components. Their characteristics were extensively analysed in terms of per-unit-length impedance and admittance matrices [1]. Using them, a spurline bandstop filter [2] and a bandpass filter [3] were successfully designed. For a traditional parallel coupled-line filter, the spacing between the end-stage resonators and feedlines definitely needs to be sufficiently small so as to obtain a tight coupling for wideband applications. However, this requirement is usually restricted by available etching processes. The above three-line structure has been demonstrated to have a capability in compensating for the coupling degree in exploring a microstrip bandpass filter with a fractional bandwidth of 40 – 50% [4]. In this regard, the spacing at the end-stage can be greatly released at least twice. Very recently, this three coupled-line structure in the format of an interdigital capacitor has been employed to constitute an ultra-wideband (UWB) bandpass filter [5]. Moreover, by extending one of its outer coupling arms, one transmission zero was excited to develop a notch-band UWB filter [6]. In this Letter, an asymmetrically-loaded interdigital coupled line is proposed and studied to produce one transmission zero in the lower stopband and two transmission zeros in the upper stopband. By using this proposed coupled line at the edge-end, a wideband filter with two physical resonators is then designed and fabricated. Measured results demonstrate a low-loss wide passband in the range 2.95– 5.15 GHz with a fractional bandwidth of 54% and highly attenuated stopbands at DC to 2.2 GHz and 6.6– 10.0 GHz, respectively.

Fig. 1 Frequency responses of asymmetrically-loaded interdigital coupled lines with varied impedance ratios (R ¼ Z1/Z2)

Asymmetrically-loaded interdigital coupled lines: The inset of Fig. 1 shows a diagram for the proposed asymmetrical three-line structure with a two-stage open-ended stub in one of two outer arms. The total length of this nonuniform stub is selected as about one half-wavelength such that transmission performance of the whole coupled line is almost unaffected at the central frequency f0. From the simulated results in Fig. 1, we can see that the desired passband of this coupled line gradually becomes narrow while one or two extra transmission zeros appear in the lower and upper stopbands as the two-stage stub is introduced and its stepped-impedance ratio (R ¼ Z1/Z2) varies from 5.0 to 0.2. Stemming from the analysis of an initial six-port three-line network, this coupled line with known loads at four ports can be modelled as a simple

two-port admittance matrix. Using normal modes of a coupled system [1 – 3], six sets of port voltages and currents of the three lines with six external ports, shown in Fig. 2a, can be derived. For the two-port coupled line in Fig. 2b, the terminal conditions among those ports must be valid: I2 ¼ I6 ¼ 0; I4 ¼ V4 Yx ; I1 þ I3 ¼ Ii ; V1 ¼ V3 ¼ Vi ; I5 ¼ Io ; V5 ¼ Vo

ð1Þ

where Yx denotes the input admittance of the two-stage open-ended stub, i.e. Yx ¼ jY1

R tan u2 þ tan u1 1
R tan u1 tan u2

ð2Þ

Consequently, a two-port network of the proposed structure can be obtained in terms of two sets of port voltages and currents. Fig. 3 shows the derived mutual admittance as a function of frequency, thus implying the condition that excites transmission zeros under zero mutual admittance. Four intersection points are observed in the plotted frequency range (excluding the point at DC). One transmission zero is generated below 2.0 GHz and three transmission zeros appear in the frequency range 6.0– 10.0 GHz. Compared with the traditional case without stub (dashed line), one can find that one and two extra zeros have been properly produced below and above the desired passband. In this way, the stopband performance can be greatly improved, as can be seen from Fig. 1. On the other hand, the 3 dB fractional bandwidth of the upper stopband has been increased from 39.2 to 60.6% as the stepped-impedance ratio R of the two-stage open-ended stub varies from 5.0 to 0.2.

Fig. 2 Generalised six-port three-line structure, and resulting two-port coupled line a Generalised six-port three-line structure b Resulting two-port coupled line

Fig. 3 Frequency responses of mutual admittance for coupled lines without stub (dashed line) and with stub (solid line)

Experimental results: To provide verification of the proposed structure, a prototype filter with two half-wavelength resonators is designed and optimised using EM simulator [7]. The filter is implemented on the RT/Duroid 6010 with a substrate thickness of 0.635 mm and dielectric constant of 10.8. Fig. 4a shows the layout of the designed bandpass filter with two half-wavelength resonators and Fig. 4b shows the frequency responses of the designed bandpass filter. A good agreement is achieved between the simulated and measured results. Measured results show a wide passband in the frequency range 2.95– 5.15 GHz with the insertion loss of 1.4 dB at 4.05 GHz. As predicted, the out-of-band rejection achieves 38 dB at DC to 2.2 GHz, and 26 dB at 6.6 – 10.0 GHz. Fig. 4b also shows that the spurious frequency response around twice that of the central frequency (4.05 GHz) has been fully suppressed.

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properly allocated in the lower and upper stopbands, thus constituting a bandpass filter with adjustable dominant passband and improved out-of-band performance in both the lower and upper stopbands. # The Institution of Engineering and Technology 2008 23 January 2008 Electronics Letters online no: 20080206 doi: 10.1049/el:20080206 S. Sun and L. Zhu (School of Electrical and Electronics Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798 Singapore) E-mail: [email protected] References

Fig. 4 Physical layout, and simulated and measured results of a wideband microstrip bandpass filter a Physical layout (R ¼ 0.2) b Simulated and measured results

Conclusions: An asymmetrically-loaded interdigital coupled line is presented and utilised to construct a compact wideband bandpass filter. The installed two-stage open-ended stub in one of the two outer arms has brought out three extra useful transmission zeros. These zeros are

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