## 1. Introduction

[2] This paper is focused on the implementation of novel filtering microwave structures in planar technology. Because of the need of efficiently use the electromagnetic spectrum in modern communication systems, it is required the development of frequency selective components, exhibiting sharp cut-off slopes [see *Williams*, 1970]. This need of rejecting certain unwanted frequencies, leads to the development of microwave filters whose insertion loss response exhibits transmission zeros at finite frequencies [see *Kurzok*, 1966]. These filters, showing pseudo-elliptic responses, normally introduce very large group delay variations, therefore not being suitable in many digital transmissions systems. To solve this problem, several techniques for group delay reduction based on external equalization [*Lee et al.*, 2003], have been proposed in the past. Also, design techniques for phase equalization can directly be applied, as in the study of *Cameron and Rhodes* [1981].

[3] The method traditionally used for the implementation of transmission zeros at precise frequencies is the introduction of cross-couplings between nonadjacent resonators. An example composed of square open-loop resonators is presented by *Hong and Lancaster* [2000]. More recently, novel schemes for microwave filters were proposed by *Rosenberg and Amari* [2003]. In this case, different coupling topologies for microwave filters based on the transversal concept were investigated. The main difference with respect to traditional structures, is that in transversal filters the input signal is coupled at the same time to several resonators. In the original work, several structures of different orders were investigated. The study also included cross couplings between non-adjacent resonators, and couplings between the input port and internal resonators. An extension to in-line filters was presented by *Amari and Rosenberg* [2004a], where they introduced the concept of internal non-resonating nodes.

[4] In the last years, several practical examples of transversal filters implemented in different technologies have been presented. For instance, two simple structures were designed, fabricated and measured by *Rebenaque et al.* [2004]. Other interesting examples using planar or waveguide technology can be found by *Moktaari et al.* [2006].

[5] In this paper we will further explore transversal filters in microstrip technology, by implementing the topology known as Modified Doublet (MD) (shown in Figure 1). In this figure, solid line represents coupling between input/output ports and resonators, while dashed line represents coupling between the ports (*M*_{SL}). The coupling scheme is similar to the one introduced by *Rosenberg and Amari* [2003], but now a direct coupling between input and output ports is introduced, as shown by *Amari and Rosenberg* [2003]. The advantage of the structure proposed, is that the additional direct coupling introduces a new transmission zero in the insertion loss response of the filter. Therefore two transmission zeros can be obtained for maximum selectivity above and below the passband.

[6] First, it is presented a compact microstrip configuration that implements the coupling scheme shown in Figure 1. The resonators used in the practical implementation are the same as those introduced by *Rebenaque et al.* [2004]. They consist of an open-loop resonator and of a short-circuited T-shaped stub. We show that by changing the coupling signs appropriately, the positions of the transmission zeros can be conveniently controlled. In addition, we present a discussion on the influence of the position of these transmission zeros, both in the frequency response and in the phase equalization of transversal filters. Finally, a dual frequency response of the above filter can be obtained, just by changing the direct coupling sign (*M*_{SL}) between the ports. Following this idea, we present a novel structure that implements a band-stop response, using the same basic topology and coupling scheme as before (Figure 1). The resonator topologies employed in this second structure are the same open-loop and T-shaped stub used before. Only the original capacitive coupling between the ports is changed in sign, and it is transformed into an inductive type coupling. It is shown in this paper that the change in sign of this direct coupling (*M*_{SL}) transforms the band-pass frequency response into a dual stop-band frequency response.

[7] In addition to the novel implementation of band-stop filters using a transversal topology, an important novel aspect of the work is the practical demonstration of complex transmission zeros using these microstrip structures. Also, this is the first time that an explanation of these microstrip structures, following the transversal filter concept [*Cameron*, 2003] is presented, together with supporting coupling matrices. Finally, a rigorous study on the direct coupling term *M*_{SL}, that can be achieved by bending together the input/output ports, is for the first time presented. The introduction of this direct coupling element will allow the implementation of a maximum number of transmission zeros for increased selectivity.

[8] In addition to the theoretical discussion, several filter prototypes implementing different frequency responses are manufactured and tested. Measured results are found to be in good agreement with respect to predictions, therefore validating the new filtering structures.