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Filters are an integral part of any communication system and they can adapt to various topologies depending upon the requirements. Filters are mainly classified based on their transmission characteristics such as low-pass, high-pass, band-pass, band-stop and all-pass filters. One of the least-explored types of filter is the band-stop filter, which sometimes is needed more than anything else in the system to remove some of the unwanted CW signals (notches) or a specific band of frequencies.

This article presents theory and design of coupled-line spur line band-stop filters, which are quite compact structures, with significantly lower radiation loss than conventional shunt stub and coupled-line filters. Coupled-line spur line band-stop filters can be used to advantage in high-frequency communications systems. They offer compact size and reasonable insertion loss, which can be a problem in high-frequency systems.

Two coupled-line microstrip filters are more common and were first introduced by Schiffman and Matthaei.^[1] The conventional spur line filters have a wider bandwidth, and designs using parallel-coupled resonator filters have narrow stop bands. However, the asymmetric topology and layout and via hole requirements make it difficult to use at higher frequencies. Here, we compare the design of symmetrical and asymmetrical three-coupled line section topologies used in spur line band-stop configurations.

The asymmetric, three-coupled line topology can be designed to have wider stop bandwidth compared to a symmetrical section by choosing appropriate line dimensions. Nguyen and others have published a mathematical formulation of asymmetric two-coupled line filters but they have not compared them to the three-line symmetrical filter.^[4]

The three-section asymmetrical and symmetrical structures are shown in Figures 1a and 1b. The structure of three symmetric-coupled lossless lines in an inhomogeneous medium includes three quasi-TEM propogation modes, referred to as a, b, c. The elements of the impedance matrix of a three-symmetrical coupled line considering a lossless case is given as:

z11=z22=z33=z44=-j½[Z_oecotθe + Z_oocotθo]

z12=z21=z34=z43=-j½[Z_oecotθe - Z_oocotθo]

z13=z31=z24=z42=-j½[Z_oecscθe - Z_oocscθo]

z14=z41=z23=z32=-j½[Z_oecscθe + Z_oocotθo]

where, Z_oe and Z_oo are the even and odd mode characteristics impedance respectively; θe and θo are electrical lengths of even and odd modes, respectively. The terminal equations are given by

Va = V1 = V2 = V3

Vb = V4 = V6

Ia = I1+I2+I3

Ib = I4+I6

This transformation changes the matrix into a two-port network. With the appropriate termination condition applied to the coupled-line six-port network, the chain matrix can be written as

|V_A
V_B| = 1
E |L
M M
N| |I_A
I_B

Reflection and transmission coefficients of the filter can be obtained using these chain matrices^[4]. From the schematic shown in Figures 1a and 1b, shorting points 1, 2, 3 make one end, shorting points 4 and 6 make the other end of the filter, while port 5 is kept open-ended. Due to a notch at the other side, the open-ended discontinuity can be abbreviated as a combination of series and shunt capacitance. The electrical lengths of the coupled lines are kept as one-quarter wavelength.

The asymmetric uniform coupled lines in an inhomogeneous medium can be analyzed in terms of the line properties for two independent modes of excitation.^[3] The mode characteristics are derived in terms of the series impedances, the shunt admittances and the mutual impedance and admittance per unit length of the lines. The 6 × 6 matrices are then obtained in terms of the mode parameters. Appropriate terminal conditions are introduced to convert it into 4 × 4 matrix. The four-port circuit matrix is much easier and more convenient to use in formulating design procedures for various circuitry.

The three-section symmetric and asymmetric spur line filters are shown in Figures 2a-c. They were designed on a 10-mil alumina substrate (ε _r= 9.8). The width and gap of the symmetrical-coupled lines was kept at 3 mils and in asymmetrical case w1 = 3 mils and w2 = 4.8 mils, with a gap equal to 2.4 mils. A notch is incorporated, as shown in Figure 2b. There is no drift in frequency by incorporating the notch. The lines are connected to input and output lines having 50 Ω impedance. The coupled lines were one-quarter wavelength at the center frequency and the gap was optimized for minimal insertion loss. The filters were analyzed using Agilent's Advanced Design System software and its integrated Momentum electromagnetic software.

Figures 2a and 2b show the asymmetrical spur line filters with and without the notch, respectively. Figure 2c represents the symmetrical spur line filter topology as implemented in ADS software for simulation comparison.

Simulation results obtained after performing a Momentum simulation are shown in Figure 3 to demonstrate that the asymmetrical topology offers a wider stop bandwidth as compared with symmetrical topology.

The same approach is further applied and validated by designing coupled-line asymmetric spur line band-stop filter at Ka band at the frequency of 18.5 GHz. Figure 4a depicts the designed spur line filter and Figure 4b shows the close agreement between the measured and simulated results.

Three-section symmetric line filters demonstrate improved Q due to reduction in bandwidth, which can be useful in many applications, such as the series feedback oscillator. Further investigation and optimization is needed to determine the notch's effect on phase velocity equalization.

1. Schiffman and Matthaei, “Exact Design of Bandstop Microwave Filters,” IEEE Trans Microwave Theory and Technique, vol. MTT-12, pp. 6-15, January 1964.

2. V.K Tripathi, “On the Analysis of Symmetrical Three-Line Microstrip Circuits,” IEEE Trans Microwave Theory and Technique, vol. MTT-25, pp. 726-729, September 1977.

3. V.K Tripathi, “Asymmetric Coupled Transmission Lines In an Inhomogeneous Medium,” IEEE Trans Microwave Theory and Technique, vol. MTT-23, pp. 734-739, September 1975.

4. Nguyen and Chang, “On the Analysis and Design of Spur Line Bandstop Filters,” IEEE Trans Microwave Theory and Technique, vol. MTT-33, pp. 71416-1421, December 1985.

5. Nguyen, Hseih and Ball, “Millimeter Wave Printed Circuit Spur Line Filters,” IEEE TMTT-S, pp. 98-101, 1983.

Anurag Bhargava is an applications engineer with EEsof EDA, Agilent Technologies, India.

Kamaljeet Singh is scientist/engineer-SD, ISRO Satellite Centre, ISRO, Bangalore, India.

Surendra Pal is a deputy director of ISRO, Bangalore, India.