Optimum design of microstrip parallel coupled-line band-pass filters for multi-spurious pass-band suppression M. Moradian and H. Oraizi Abstract: A modified configuration for the parallel coupled-line band-pass filters is presented which allows it to largely suppress the spurious pass-bands. The proposed filter configuration is composed of two attached open-circuit stubs at the open-end of each section of the convention- al coupled-line filter. A least-square-based algorithm is developed for the design and optimisation of the proposed filter. First, the two-port impedance matrix of a coupled line is determined from its four-port matrix. Then, the transmission matrix of a coupled line and subsequently that of the multi-section filter are obtained, which lead to its scattering parameters. Finally, an error function is constructed by the specified insertion and return losses of the filter. To demonstrate the charac- teristics of the proposed filter, a third-order band-pass filter centred at the operating frequency of 1.7 GHz with 5% fractional bandwidth is designed, optimised, fabricated and tested. Simulated and measured data show that for such a filter prototype, a rejection level exceeding 20 dB is obtained in the first four spurious pass-bands, while keeping the desired pass-band attenuation less than 2 dB. In addition, the filter circuitry size is reduced in comparison with the conventional parallel coupled-line filters, and an impedance matching function is also embedded in the filter configuration. 1 Introduction The parallel coupled-line (or edge-coupled) band-pass filter is widely used in microwave microstrip circuits because of its simple configuration and ease of fabrica- tion. Its analytical development and design procedures for Butterworth and Chebyshev models achieving less than 20% bandwidths are described in several references. [1–4]. However, despite its advantages, the conventional parallel coupled-line filter has several shortcomings. Its basic drawback is the appearance of repeated pass-bands approximately at integer multiples of the centre frequency. These spurious pass-bands produce poor harmonic sup- pression when used as output filters in oscillators and amplifiers. To overcome this problem, a low-pass filter is usually added to the output of the filter, but such a sol- ution increases filter dimensions, adds extra insertion loss and is not quite effective in suppressing all the unwanted spurious pass-bands. The even and odd spurious harmonics are generated by different mechanisms. The undesired odd spurious pass- bands are associated with the inhomogeneous nature of the dielectric medium surrounding the conductors, which cause the odd-mode wave to propagate faster than the even- mode wave in the coupled microstrip lines. The even spur- ious pass-bands are associated with the periodic nature of the distributed network [4]. Two basic methods have been proposed in the literature to suppress the first spurious pass-band located at twice the centre frequency (2f 0 ). These methods fall into two categories. The first one endeavours to provide different lengths for the even- and odd-mode waves by modifying the line shapes, and equalising the modal phase velocities. An over-coupled section is proposed to extend the odd-mode phase length of the microstrip to compensate for the difference in phase velocities [5, 6]. The capacitively compensated structures [7], meandered lines and coupling/ shielding lines are also effective in equalising the modal phase velocities [8, 9]. Other attempts such as ground-plane aperture [10–12] and substrate suspension have also been proposed to sup- press the first spurious pass-band [13]. However, all these methods are more or less difficult to realise, because the whole structure should be kept far from the other grounded conductors. Other approaches utilising both the above methods have also been introduced. These approaches try to modify and perturb the widths of the conventional lines in different forms, such as wiggly, corrugated, grooved or even fractal shapes [14–18]. These periodic structures can be used to create Bragg reflections so that the first spurious pass-band is rejected, whereas the desired pass-band response is main- tained virtually unaltered. All these methods are suitable for suppressing the second pass-band (2f 0 ), but have little effect on other spurious pass- bands. Few efforts have been directed for multi-spurious pass-band suppression in the microstrip coupled-line band- pass filters. In one approach, the spurious pass-bands were controlled or even suppressed by applying the stepped impedance resonator [19, 20]. Other efforts for eliminating the spurious pass-bands have introduced other methods such as tapped wiggly-coupled lines and wiggly-lines [21–23]. # The Institution of Engineering and Technology 2007 doi:10.1049/iet-map:20060207 Paper received 6th February 2006 The authors are with the Department of Electrical Engineering, Iran University of Science and Technology, Narmak Tehran 16844, Iran E-mail: m_moradian@ee.iust.ac.ir IET Microw. Antennas Propag., 2007, 1, (2), pp. 488–495 488