# Compact and Broadband Microstrip Band-Stop Filters with Single Rectangular Stubs
## 1 Introduction  
With the development of RF technology, RF products and services spreading in modern society have been advanced and diversified. In addition, the amount of expert knowledge and technical ability required by engineers is increasing, and the fundamental things listed in standard textbooks are not enough for practical use [1, 2]. In order to foster technicians who can respond to the needs of modern society, sophisticated educational research programs to use the knowledge of pioneers to understand advanced expertise are essential to meet the demands of this era [3, 4]. RF components like filters are important components supporting the above system.  
In this study, we focus on a microstrip line (MSL) band-stop filter (BSF) by using a quarter-wavelength open circuited stub. The basic structure, in which the stub line width is equal to the signal line width, is simple and easy, but it is a narrow bandwidth and has poor practicality for BSF. As a general trend for MSL filters, compact and broadband characteristics are desirable, in addition to easy fabrication. To construct a band-stop filter, the following two methods are conceivable in a two-terminal network. One is to shunt a series resonance circuit to the transmission line, and the other is to insert a parallel resonance circuit in series in the transmission line. In any case, the transmission zeros are obtained at quarter-wavelength resonance. For example, corrugation or periodic structure like a photonic band gap (PBG) can obtain the highest attenuation in a wide band [5, 6, 7]. Cascading or multistage by filter synthesis is effective to achieve the desired stop bandwidth [8, 9]. The butterfly structure using symmetry is effective for broadening the bandwidth, compared with the singlestructure [10; 11; 12; 13]. However, in these examples, there is a feature that the circuit pattern becomes large. To overcome this problem, some methods for compatibility between compactness and broadband by a combination of existing structures, such as spureline, interdigital, and the quarter-wavelength open circuited stub, have been reported [14; 15; 16; 17; 18; 19; 20; 21; 22; 23]. However, the bandwidth becomes narrower because of the trade-off relationship between the size reduction and broadband. In addition, it is inevitable that the manufacturing process becomes troublesome because of the miniaturized structure.  
As another technique to increase the compatibility between compactness and broadband, we propose to increase the stop bandwidth as much as possible, for a simple single rectangular stub with frequency adjustment by inserting a reactance element at the attachment point of the stub. The method of widening the stop bandwidth by using a low impedance line for the stub is well known, but there are few quantitative reports on the case where the line widths of the main transmission line and the stub are different. In addition, we propose a method to adjust the resonant frequency by inserting an inductive window at the stub attachment point, not changing the resonator size. As a similar structure, radial stubs are widely used, because of their compactness and broadband, but the theoretical analysis is somewhat complicated, and the principle is not simple, except that the effective attachment point of the stub is identified [24].  
In this research, firstly we study a rectangular quarter-wavelength open stub from the viewpoint of the characteristic impedance ratio between the main transmission line and the stub line. Secondly, we investigate the possibility for miniaturization by series-connecting reactance to the attachment point of the stub. Furthermore, we compare the results with the well-known radial line stub, to confirm the validity we propose. Section 2 describes the principle of broadband and miniaturization. Section 3 describes the measurement sample, and Section 4 discusses the measurement results. Finally, we summarize in Section 5.