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    Analysis and Modelling of Novel Band Stop and Band Pass Millimeter Wave Filters Using Defected Microstrip Structure (DMS)  Abstract: This paper presents novel millimeter wave  filter structures by creation of some slots on the strip. These slots perform a serious LC resonance property in certain frequency and suppress the spurious signals. In high frequencies and high density applications, the board area is seriously limited, so using these filters; the circuit area is minimized. The proposed filters are compact and very suitable for high density MMIC circuits. Keywords: Defected Microstrip Structure (DMS), bandstop filter, bandpass filter, millimetre wave, circuit modelling. 1 Introduction Frequency band between 30-300 GHz is called millimeter wave band. In atmospheric propagation at 22.2 and 183.3GHz, resonance peaks occur due to water vapour resonances, while resonances of molecular oxygen cause peaks at 60 and 120 GHz. Thus there are windows in the millimeter wave  band near 35, 94, and 135 GHz where radar and communication systems can operate with minimum loss [1]. In many applications reduction of size and weight of fi lters is very important. Thus, planar fi lters utilizing printed circuit technology seems very suitable [2]. Slot on the strip that is called defected microstrip structure (DMS) makes a defect on the circuit which can be used in designing fi lters,  power dividers, ampli fi ers, etc. This defect creates resonance characteristics in the frequency response. This kind of structure is constructed by removing pattern etched from the top conductor of microstrip and can be used as a band reject fi lter [3]. The DMS is advantageous in high frequency designs and millimeter wave applications. DMS circuits are more immune than defected ground structure (DGS) from crosstalk and ground plane interference. In this paper, a new approach for making three types fi lters using DMS has been presented and their equivalent circuits have been extracted. 2 BANDSTOP FILTER STRUCTURE AND EXTRACTION OF CIRCUIT MODEL The dimensional parameters of dumbbell shaped DMS fi lter which results in a resonance characteristic is sketched in Fig. 1. The resonance effect is due to the abrupt change of the current  path. In Fig. 1; A, D and G are 1.137 mm, 0.047 mm and 0.01 mm, respectively. For this microstrip fi lter the substrate is Rogers RT/duroid 5870 with the dielectric constant of ε r   =2.33 and thickness of 0.566 mm. The width of substrate is 1.6 mm to obtain 50 ohm characteristic impedance. The simulations are done with HFSS software. The mentioned structure is a bandstop fi lter whose frequency speci fi cation is shown in Fig. 2. The  phase response of the proposed structure is shown in Fig. 3. Figure 1: Millimeter wave bandstop filter M. Kazerooni*, M. A. Salari*, A. Cheldavi* and M. Kamarei** *College of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran **Faculty of Electrical and Computer, University of Tehran, Tehran, Iran Email: ,,,    Figure 4:Circuit model for DMS introduced in Fig. 1 Figure 2: Amplitude frequency response of millimeter wave bandstop filter Figure 3: Phase frequency response of millimeter wave  bandstop filter In full wave method the analysis of this fi lter will take very long time, in addition, full wave analysis cannot provide sufficient physical insight into operation of DMS filter. So, for solving these  problems, using the circuit model is very suitable. So the circuit model can be obtained by tracking the path of the current. There is a capacitive effect due to G slot and an inductive effect due to current rotation around dumbbell shaped section. The  proposed circuit model is shown in Fig. 4. The circuit parameters for the derived equivalent circuit can be extracted from the simulation result which can be fit for the one-pole Butterworth-type low-pass response [4-6]. In the following equations f  0  and f  c  are resonance frequency and cut-off frequency respectively: )f f (200 f C 2c20c −π=  (1)   Cf 41L 202 π=  (2) The effect of A, D, G variations on frequency response has been investigated and results are shown in Fig. 5. In these variations, other dimensions of the structure have not changed and are similar to Fig. 1. S21   S11   (a) S21   S11   (b) S21   S11   (c) Figure 5: Effect of a) A, b) D and c) G variations on frequency response of filter By referring to Fig .5a and 5b it can be observed the advantage of proposed filter which operates in one of the millimeter wave windows; for example near 35 GHz. Moreover the filter can be tuned by adjusting Critical dimensions A, D and G of  proposed filter. In table 1 the circuit parameters for different values of A, D and G has been calculated. It is evident that from this table with the changes of A and D, the inductance of equivalent circuit changes while with the change of G, capacitance of it alters.    Table 1. Circuit parameters for variations of A, D and G DMS dimensions(mm) A=1.097 A=1.057 D=0.057 D=0.062 G=0.012 G=0.014 A=1.137 D=0.047 G=0.010 Inductance(nH) 0.019 0.017 0.019 0.021 0.018 0.019 0.016 Capacitance(pF) 1.05 1.05 1.05 1.05 0.78 0.78 1.05 3 BANDSTOP FILTER WITH T-SHAPED PATTERN   The proposed filter has been shown in Fig. 6. It is also designed for 50 Ω  characteristic impedance. Figure 6: Millimeter wave bandstop filter The frequency response of the proposed filter is shown in Fig. 7. Equivalent circuit of this structure is same as Fig. 4 with capacitance of 0.144pF and inductance of 0.195 nH. Figure 7: Frequency response of millimeter wave  bandstop filter 4 BANDPASS FILTER FOR MILLIMETER WAVE BAND APPLICATION In some cases the specific frequency components are needed for applications in millimeter wave communications systems. So it is better to use  bandpass counterpart of previously proposed filters. This filter is shown in Fig. 8. It can be seen from this plan the bandpass filter has been  performed by introducing small gaps in both sides of a T-shaped slot. The frequency responses are shown in Figs. 9-10. Figure 8: Millimeter wave bandstop filter Figure 9: Amplitude frequency response of bandpass millimeter wave filter 2000510152025303540-200-150-100-50050100150Frequency(GHz)    P   h  a  s  e  o   f   S  -  p  a  r  a  m  e   t  e  r  s   (   d  e  g   ) Phase of bandpass DMS filter  S21S11   Figure 10: Amplitude frequency response of bandpass millimeter wave filter By referring to Fig. 9, it can be observed two resonances shown by f  s  and f   p . The first resonance is due to slots placed at two sides of T-shaped  pattern (L  p .C g ) and second resonance is due to T-shaped pattern (L  p .C  p ). For extracting the equivalent circuit, the inductance and capacitance of equivalent circuit of T-shaped slot can be calculated from previously discussion, then by using the previously calculated inductance and frequency of f  s , the capacitance C g  can be obtained easily. In Fig. 11 the obtained values for equivalent circuit parameters have been presented. Gap Gap Figure 11: Equivalent circuit for proposed bandpass filter     References [1]   D.M. Pozar Microwave Engineering John- Wiley,p. 668, 1998. [2]   Jia-Sheng Hong and Michael J. Lancaster, “Theory and Experiment of Novel Microstrip Slow-Wave Open-Loop Resonator Filters”, IEEE Transactions on Microwave Theory and Techniques, Vol. 45, No. 12, December 1997. [3]   Jun Seok Park and Jun-Sik Yun, “A Design of the Novel Coupled-Line Bandpass Filter Using Defected Ground Structure With Wide Stopband Performance”, IEEE Transactions On Microwave Theory And Techniques, VOL. 50, NO. 9, September 2002. Figure 12: Comparison between full wave analysis and equivalent circuit From Fig. 12, there is a reasonable conformity  between full wave analysis and the extracted equivalent circuit. [4]   M. Kazerooni, G. Rezai Rad, and A. Cheldavi Behavior Study of Simultaneously Defected Microstrip and Ground Structure (DMGS) in planar circuits , Progress In Electromagnetics Research Symposium, Beijing, China, March 23-27, 2009. For tuning the operating frequency one can change the dimensions of the T-shaped cell toward desired frequency response. Dimensions of the slots placed at both sides of T-shaped cell have effect on frequency response. Broadening slots will result in signal attenuation while narrowing the slots will result lower resonance frequency as well as signal attenuation. [5]   M. Kazerooni, N. P. Gandji, A. Cheldavi, and M. Kamarei, “A New Microwave Bandstop Filter Using Defected Microstrip Structure (DMS)”, Progress In Electromagnetics Research Symposium Proceedings, Moscow, Russia, August 18- 21, 2009. 5  CONCLUSION In this paper was introduced some new bandstop and bandpass filters using DMS. The superior  performances such as high quality factor (Q), very low complexity and compactness can be obtained easily from DMS technique. [6]   M. Kazerooni,A. Cheldavi, and M. Kamarei, “A New Bandstop Cascaded Defected Microstrip Structure (CDMS) With 10 GHz Symmetrical Bandwidth”, Progress In Electromagnetics Research Symposium Proceedings, Moscow, Russia, August 18-21, 2009.

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