Chapter-2 LOW PASS FILTER DESIGN 2.1 INTRODUCTION

Chapter-2 LOW PASS FILTER DESIGN 2.1 INTRODUCTION Low pass filters (LPF) are indispensable components in modern wireless communication systems especially in the microwave and satellite communication systems. Due to the advancement in satellite and mobile communications and miniaturization of the system and component effort has been made to develop a variety of compact lowpass filters. In the design of low pass microwave filters, the compact size and suppression of unwanted frequency components with excellent pass band characteristics are the major concerns. The highly desirable performances are a sharp cut off characteristic and a wide stop band. Conventional design of microstrip low pass filters basically involves either the use of shunt stubs or the stepped impedance network, which is a high-low impedance transmission line [1-3]. For lower microwave frequencies the size of the conventionally designed filter is large. Moreover, the microstrip LPF design using conventional methods requires even larger size to achieve a sharp cut-off. Several research works have been reported in the literature to reduce the size of microstrip lowpass filters [119-125]. Such as a microstrip lowpass filter using the slow-wave resonator has been realized by C. Jianxin et. al. [119], where both, size reduction and spurious band suppression have been achieved. In [120] a compact semilumped lowpass filter was designed, which has the capability of harmonics and spurious suppression. However, the use of lumped elements raises fabrication difficulties. In [121] a lowpass filter using a single microstrip stepped impedance hairpin resonator has been proposed, which has the advantage of extending the stop band between the first and second resonant frequency due to 20

capacitance loading. In [122] a lowpass filter using coupled lines was proposed, having two attenuation poles in the stop band. The utilization of microstrip open-loop resonators allows various filter configurations including those of elliptic or quasi-elliptic function response to be realized by J.S. Hong et al. [123]. In another approach the compact filter has been achieved using the defective ground structure (DGS) and/or Electromagnetic band gap structures [45], [54],[126]-[128]. An effective and commonly used method is to introduce the slow wave structure either on the main lines or on the ground plane of the substrate. In [124] a spiral resonator is used to replace the stepped impedance ladder network of the conventional filter design technique. The unsymmetrical stubs have also been used in [125] to design a compact filter. These techniques improve the stop band characteristics. The primary disadvantage of this configuration is the relatively lower stop band suppression. The slow wave structure on the ground plane can be introduced by using the defective ground structures (DGS). The value of inductance and capacitance of the resonators can be changed and thus the compact circuit size can be achieved. Simple equivalent circuit model of DGS can be made which gives a low-pass property with a wide stop band characteristic [45], [54], [126]- [128]. The dumb-bell DGS may be regarded as a parallel L-C resonant circuit and although it can provide attenuation in a wide stop band range however it can not provide a steep roll-off [126]. The structures suggested in [45], [54], [126]- [128] have rectangular slots connected with slot having small width. The increased inductance due to DGS was compensated by increasing the distance between two rectangular slots. The microstrip LPF designed in this thesis may be categorized mainly in two parts, the first type of LPFs is based on the solid ground plane and the other one is based on the defective ground structure. The lowpass filter synthesis and design using the microstrip is elaborated in a concise manner and a conventional lowpass microstrip filter is designed in the first section of this chapter. And this conventionally designed LPF is modified by applying the fractal curve. The fractal curve applied in this work is based on the Kotch curve [129]. The LPF with fractal structure is compared with stepped impedance microstrip low pass filter by reducing the end-effects and T-junction effects. A 21

compact microstrip LPF has been designed using non-periodic defective ground structure (DGS). The filter designed using this method is compact and shows wide stop band characteristics. The design technique is explained in detail the filter is fabricated and tested [130]. Another DGS has been studied which is used to design a microstrip LPF. In this design slots are etched on the ground plane of a microstrip line. The slots dimensions are based on the Chebyshev functions [131]. An effective modification has been suggested to design compact microstrip low pass filter for lower microwave frequencies [132]. The lengths of the high and low impedance lines in the filter can be directly calculated by the proposed formula. From the simulated and measured results it can be seen that the roll-off characteristics of the filter are sharper and it gives wide range of stop-band characteristics in comparison with the conventionally designed filter. A wide band LPF is also designed where a cascade structure of triangular patch resonators is used. 2.2 COMPACT DESIGN OF LOW PASS FILTER In this section a microstrip low pass filter is first designed using the step impedance technique, then Kotch fractal curve is applied on the filter which results a compact structure. The design procedure of step impedance microstrip structure is based on the insertion loss (IL) method. The IL method allows a high degree of control over the passband and stopband amplitude and phase characteristics, with a systematic way to synthesize a desired filter response [1]-[3]. In IL method power loss ratio is determined in terms of reflection coefficient. The power loss ratio of a network is defined as the ratio of available or the incident power to the actual power delivered to the load. Thus the power loss ratio (PLR) of a network is defined as the available or the incident power divided by the actual power delivered to the load [3]. 22

1 PLR (2.1) 1 2 where is the input reflection coefficient for a lossless network terminating in a resistive load impedance Z L = R L. The insertion loss, measured in decibel is IL 10 log PLR (2.2) In general insertion loss is defined as the ratio of the power delivered to load when connected directly to the generator to the power delivered when the filter is inserted. It has been seen that a realizable filter has a power loss ratio of the form given by: 2 M ( ) PLR 1 2 (2.3) N( ) where M (ω 2 ) and N (ω 2 ) are polynomials in the frequency domain.. There are many different types of polynomials that result in good filter response and each type has its own set of characteristics. In this work Chebyshev response has been considered to demonstrate the different design technique. Design of a filter using the Insertion-Loss approach usually begins by designing a normalized low-pass prototype (LPP). The LPP is a low-pass filter with source and load resistance of 1Ω and cut-off frequency of 1 rad/sec. Impedance transformation and frequency scaling are then applied to renormalize the LPP and synthesized. To demonstrate the conventional technique the following technical specifications are considered: 23

Order of filter N = 5 R S = R L = 50 Cut-off frequency = 2.5 GHz Pass band ripple = 0.01dB The element values for Chebyshev filters for desired pass band ripple for LPP circuit has been be taken from [1] and given as below. g 0 = 1 g 1 = 0.7563 g 2 = 1.3049 g 3 = 1.5773 g 4 = 1.3049 g 5 = 0.7563 g 6 = 1. By applying the frequency transformation along with the impedance transformation, the desired L-C ladder network is obtained. The transformed values from the prototype of corresponding inductance L and capacitance C can be calculated for the desired filter from following expressions given in [2] as below : c L Z0g ; g representing the inductance (2.4a) c c g C ; g representing the capacitance (2.4b) c Z 0 Where Ω c is cut off frequency of LPP, ω c desired cut off frequency, and Z 0 is load and source impedance. The transformed filter network with its elemental values has been shown in figure (2.1). 24

Fig.2.1 Schematic of the Low Pass Filter after scaling. R s = 50Ω C 1 = 1.1041 pf L 2 = 4.7624 nh C 3 = 2.3026 pf L 4 = 4.7624 nh C 5 = 1.1041 pf R L = 50Ω The above results represent the lumped parameters which have to be transformed into a distributed network through transformation methods. Microstrip stub filters implemented through Richards transformation [136] is one of the ways of designing low pass microwave filters. The more common and simple technique for microstrip filter design is using stepped impedance technique where the requirement of mapping as in the Richards transformation is not required and hence the frequency response is not periodic. Also in the stepped impedance technique the transmission lines are not needed to be proportionate [3]. In the design of stepped impedance filter it should be ensured that the transmission lines are electrically short that is their lengths should be less than one eighth of the wavelength. The filters designed using this technique is constructed by a cascade connection of low and high impedances of electrically short transmission lines. A short low impedance transmission line is approximated by a shunt capacitor to the ground and the short high impedance line is approximated by a series inductor. The design philosophy of the stepped impedance filter is based on the lumped approximation of the short transmission line. Since a typical low-pass filter consists of alternating series inductors and shunt capacitors in a ladder configuration as shown in figure 25

26 (2.1), one can implement the filter on a printed circuit board by using alternating high and low characteristic impedance sections of transmission lines, where the high and low impedances are used to get the effects of inductive and capacitive reactance from the distributive structure. In a microstrip the impedance of the line is inversely proportional to the width of the line for fixed substrate height. To get the appropriate values of the inductances and capacitances in microstrip the ratio of higher to lower impedance value of lines (Z H /Z L ) should be as high as possible (where Z H and Z L are the higher and lower impedances of the microstrip lines), but limited by the practical values that can be fabricated on a printed circuit board. The typical values are Z H =100 to 150 and Z L =15 to 25. In this design we have selected Z L =24Ω and Z H = 100Ω. The width (w) and height (h) of the microstrip lines for different impedances values have been calculated by using the equations given by [2]. 2 8 2 A A e e h W for W/h < 2 r r r B B B h W 0.61 0.39 1 ln 2 1 1 2 ln 1 2 For W/h >2 (2.5) Where r r r r 0 11 0. 0.23 1 1 2 1 60 Z A r 2Z 0 377 B

r 1 r 1 1 (2.6) re 2 2 12h 1 w (2.7) 0 g re Where ε r relative dielectric constant, ε re, effective dielectric constant, λ 0 wavelength in free space and λ g is the wave length in the corresponding lines. Using the above equations the different parameters such as widths, effective dielectric constants and wave lengths are listed in Table-2.1 for the low and high impedance lines. Table-2.1: The widths, effective dielectric constants and corresponding wavelengths of low and high impedance microstrip lines. For low impedance line For high impedance line For Z L = 24Ω For Z H = 100Ω w = 6.3525 mm w = 0.4801 mm ε re = 2.8042 ε re = 2.3456 λ gl = 71.6599 mm λ gh = 78.3527 mm Also for Z 0 = 50Ω, from above equations the width of the transmission line obtained is w = 1.836 mm. The relationship of inductance and capacitance to the transmission line length at the cut-off frequency c are given by [3]. 27

l k cckz L L where k=1,3,5 (2.8a) l k clk 1 (2.8b) 1 H Z H Where l k and l k+1 are the lengths of resonators, ω c is the cut-off frequency, C k and L k+1 are the corresponding transformed values of capacitances and inductances, β L and β H are the phase constant for capacitive and inductive lines. Using these design equations (2.8a) and (2.8b) and the lumped parameter values obtained above, the lengths of the inductive and capacitive lines have been determined. l 1 = 3.95 mm, l 2 = 9.33 mm, l 3 = 8.25 mm, l 4 = 9.33 mm, l 5 = 3.95 mm Fig. 2.2 Layout of Chebyshev LPF using stepped impedance technique. Thus using stepped impedance technique we have obtained a low pass filter structure. The simulated values of scattering parameters are depicted in the in figure (2.3). 28

S11 parameters S21 parameters 0 S-parameters in db -10-20 -30-40 -50-60 -70 0 2 4 6 8 10 Frequency in GHz Fig. 2.3 Simulated values of S 11 and S 21 parameters of stepped impedance structure. The total length of this filter is 34.81mm. Efforts have been made to reduce the size of this filter in the preceding section using the fractal technique without altering the basic characteristics of the filter. 2.3 FRACTAL STRUCTURE FOR SIZE REDUCTION The structure of Kotch fractal curve [129] has been utilized to reduce the size of the microstrip low pass filter. The lengths of inductive lines of the step impedance microstrip lowpass filter have been reduced by applying the proposed technique. The original physical lengths of the inductive lines are maintained where as the over all circuit length has been reduced. The basic structure of 1-D, 90 0 angles Kotch curve [129] taken into consideration for the proposed design. This fractal curve shown in figure is up to two iterations. The first iteration is shown in figure (2.4b) and the second iteration is shown in figure (2.4c). The length of the line that is the distance between the two end points p and q is considered as d which is shown in figure (2.4a). For first iteration the length of the unit section line becomes d/8 which makes the 29

distance between p and q shorter by half that is d/2 where as the total physical length of the line is unchanged. In similar fashion the distance between p and q becomes d/4 for the second iteration as the length of the unit section line becomes d/64 as shown in figure (2.4c). The structures shown in figure (2.4) may be utilized to reduce the lengths of the microstrip filters where long thin microstrip lines are used. This technique has been applied to the sections l 2 and l 4 of figure (2.2). (a) (b) (c) Fig.2.4. Basic structure of the Kotch curve (a) Zero Iteration (b) First iteration (c) Second Iteration. The LPF shown in figure (2.2) has been modified to figure (2.5) after the application of Kotch fractal curve with first iteration. In this process total length l2 l4 of the filter has been reduced from l1 l2 l3 l4 l5 to l 1 l3 l5. 2 2 30

Fig. 2.5 LPF with fractal shape inductive lines. The simulated values of S-parameters for the stepped impedance LPF with and without fractal change are given in the figures (2.6) and (2.7). From the S 11 and S 21 parameters shown in figures (2.6) and (2.7) it is clear that by the application of fractal without any appreciable change in the scattering parameters the length has been reduced. Without fractal structure With fractal structure 0-10 -20 S11 in db -30-40 -50-60 -70 0 1 2 3 4 5 6 Frequency in GHz Fig.2.6. S 11 parameters of lowpass filter with and without fractal structure. 31

Without fractal structure With fractal structure 0-5 S21 in db -10-15 -20-25 0 1 2 3 4 5 6 Frequency in GHz Fig. 2.7. S 21 parameters of lowpass filter with and without fractal structure. Fig. 2.8. Fabricated Structure of LPF using Fractal Structure. The LPF shown in figure (2.5) has been fabricated for the specifications mentioned earlier is designed and fabricated for the specifications mentioned earlier and shown in figure (2.8). The measured results are very much similar to the simulated values. The measured and simulated S 11 and S 21 parameters are shown in figures (2.9) and (2.10). The length for the filter with conventional technique is 34.81mm where as the total length of the filter with fractal shape is 25.48mm. Thus the total reduction in size takes place is more than 26%. The measured results are also in good agreement with the simulated results. 32

Simulated S21 Measured S21 0-5 -10 S21 in db -15-20 -25-30 0 1 2 3 4 5 6 Frequency in GHz Fig.2.9 Measured and simulated S 21 parameters of the filter with fractal lines. Simulated S11 Measured S11 S11 in db 0-5 -10-15 -20-25 -30-35 -40-45 -50 0 1 2 3 4 5 6 Frequency in GHz Fig.2.10 Measure and simulated S 11 parameters of the filter with fractal shaped lines. For the structure shown in figures (2.2) and (2.5) the effect of stray capacitance and inductance have not been considered. In the following section the same will be considered in the structure shown in figure (2.2) and the performance will be compared with the performance of structure shown in figure (2.5). 33

2.3.1 LENGTH CORRECTIONS DUE TO END AND T-JUNCTION EFFECTS Since the inductive lines produce some capacitance and capacitive lines produces stray inductance in stepped impedance ladder network. These are known as end effect and T-junction effects. Due to these stray inductances and capacitances, the overall inductance and capacitance of the structure change. The figures (2.11) and (2.12) depict this phenomenon. The values of Ls and Cp can be obtained from [2] which given below for convenience. Fig.2.11 Stray capacitance (C p ) in high impedance line. C p cz tan 2 1 gc H (2.9a) Fig.2.12 Stray inductance (Ls) in low impedance line. L s Z L tan c 2 gl (2.9b) 34

Where C p and L s are the stray capacitances and inductances. β is the phase constant, ω c is the cutoff frequency and λ gc and λ gl are the wave length of the capacitive and inductive lines. After solving the equations (2.9a) and (2.9b) for three iterations the circuit size get reduced. But as the number of iteration increases the cut-off frequency shifted towards higher side. To compensate the decreased length of lines are needed to be optimized using the simulation software, which leads a lengthy process to design a compact microstrip low pass filter using stepped impedance technique. The S 11 and S 21 values are shown for every iteration in figures (2.13) and (2.14). Without Iteration With second Iteration With first iteration With third Iteration S11 in db 0-5 -10-15 -20-25 -30-35 -40-45 -50-55 -60 0 1 2 3 4 5 6 Frequency in GHz Fig. 2.13 Comparison of S 11 parameters of conventionally designed filter with considering end and T-junction effect. 0 Without Iteration With first Iteration With second Iteration With third Iteration -5 S21 in db -10-15 -20-25 0 1 2 3 4 5 6 Frequency in GHz Fig. 2.14 Comparison of S 21 parameters of conventionally designed filter with considering end and T-junction effect. 35

It is evident from the figures (2.13) and (2.14) that the length reduction by minimizing the stray capacitance and inductance for the three iterations the cut off frequency has been increased from the desired value of 2.5 GHz to 3.2 GHz. By considering T-junction and end effect up to third iteration about 23% size reduction has been achieved at the cost of cutoff frequency but using the fractal technique a lot of lengthy calculation can be avoided and the size reduction of more than 26% can be achieved without any shift in the cut off frequency. At the same time there is no shift in the cutoff frequency. The above proposed design technique using the fractal curve suggests that to get the compact low pass filter structure Kotch curve can be used. This technique does not require any lengthy calculation. The size reduction using this technique is compared with size reduction by minimizing the effects of stray capacitances and inductances from the stepped impedance structures. 2.4 LOW PASS MICROSTRIP FILTER WITH SUPPRESSED HARMONICS Since the conventional stepped impedance filter suffers from spurious harmonics which makes the stop band limited. In section 2.3 the compact stepped impedance LPF has been achieved by using the fractal structure but it suffers from spurious modes. In this section efforts have been made to suppress the spurious harmonics along with the compactness by using the defective ground plane. First an LPF is designed for the desired specification using the stepped impedance technique as discussed in section (2.2). Then the slots are made on the ground plane. Due to these slots the inductance is increased. The increased inductive impedance due to slot has been compensated by reducing the length of high and low impedance lines thus the compact structure is achieved. After using the slots just below the high 36

impedance line, the ratio of high to low impedance of the stepped impedance structure has been increased without any reduction in the width of high impedance line. The complexity of the proposed circuit design is considerably lesser than the circuit suggested in [127-128]. Five poles Chebyshev function with 0.1dB pass band ripple has been considered to design the proposed stepped impedance microstrip low pass filter. The filter is conventionally designed using high-low impedance technique for the desired cut-off frequency of 2.5GHz as discussed in previous section. After the design of microstrip LPF the elliptical slots as shown in the figure (2.16) have been etched on the ground plane. The minor axis of the elliptical slot is equal to the length of the high impedance line and the major axis is equal to twice of the width of the low impedance line. Due to these slots the inductance of the line has been increased and thus the cut off frequency of the resultant filter reduces by 0.684 times the desired cut-off frequency. To compensate these increased inductive effects the size of resonators must be reduced further. By repeating this process the optimized dimensions of the resonators have been obtained using the full wave simulation software CST microwave studio [134]. The effect of width of the slot on the cut-off frequency has been shown in figure (2.17). The sharper rolloff response can be achieved by increasing the length of slot at the expense of pass band performance. Parallel capacitance values for the proposed DGS elliptical unit may also be extracted from the attenuation pole location which exists at the resonance frequency of the parallel L-C circuit [126] and prototype low pass characteristics by using the following equations (2.10) and (2.11). C ( in p 5 fc pf) 2 f0 f 2 c (2.10) L p 250 ( in nh ) (2.11) C ( ) p f 0 37

By changing the length of the slot the values of capacitance and inductance can be controlled effectively. Fig.2.15. Top view of stepped impedance LPF without DGS. Using the above design method the different dimensions are as follows: L 1 =10.04mm, L 2 =7.77mm, L 3 =4.35mm, width of 50Ω line=1.82, w1=5.05mm, w2=0.46mm. Fig.2.16. Top view of the proposed structure with two elliptical slots. 38

4.5 Slot width in mm 4 3.5 3 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 frequency in GHz Fig.2.17. Relation between the width of the slot (minor axis of the ellipse) and cutoff frequency. With the above dimensions the LPF has been fabricated and shown in figures (2.18) and (2.19). It has been critically observed that by applying the elliptical slots on the ground plane, the cut-off frequency shifts towards the lower side and by reducing the size of resonators the cut off frequency increases thus there has been a drastic decrease in the overall size of the proposed filter. Fig. 2.18. Bottom view of fabricated filter. 39

Fig.2.19. Top view of the fabricated filter. The structure shown in the figure (2.16) is simulated and the S 11 and S 21 parameters are compared with the measured values of S 11 and S 21 parameters and shown in figures (2.20) and (2.21). Measured S11 Simulated S11 0.00 0-5.00 1 2 3 4 5 6 7 8 9 10-10.00 S11 in db -15.00-20.00-25.00-30.00-35.00 Frequency in GHz Fig. 2.20 Simulated and Measured S 11 Parameters. 40

Measured S21 Simulated 0 0 1 2 3 4 5 6 7 8 9 10-5 S21 in db -10-15 -20-25 -30 Frequency In GHz Fig. 2.21. Simulated and Measured S 21 parameters. From these figures a close matching between the measured and simulated values has been observed. It is clear that along with a better pass band characteristic, a wider stop band characteristic also has been obtained. The insertion loss at 3.9GHz has been observed as 19dB. The design technique is simple. The transition band is quite sharp and transmission parameter reduces from 0.216dB to 19dB within 1.4 GHz. TABLE-2.2: Comparative results of three filter structure structures Structure type Max. Pass band ripple in db Frequen cy at the harmonic in GHz Max value S21 in db at harmonics Without DGS 0.705 8.1 6 Elliptical DGS 0.2159 No harmonics present Rectangular DGS 0.323 No harmonics present 41

From Table-2.2 it can be observed that with the solid ground the LPF shows a spurious response at about 8.1 GHz, it reaches about 6dB which is undesirable. When the slots are made on the ground plane, the undesired harmonics disappear. The lengths of the resonators of the proposed structure are compared in Table-2.3. There is about 33% reduction using the proposed technique. The length of conventional LPF is 34.28mm and the length of the proposed structure is 23mm. From the simulated results shown in figures (2.22) and (2.23) the performance of LPF with and without DGS can be observed. TABLE 2.3: Comparison of size of conventional and proposed structures Structures L 1 (mm) L 2 (mm) L 3 (mm) Conventional (without DGS) Structure Proposed structure 10.0486 7.7734 4.359 7.5 4.25 3.5 Fig. 2.22 S 21 parameters of both LPFs (elliptical and square DGS) structures. 42

Fig. 2.23 S 11 parameters of both the proposed. To compare the rectangular and elliptical shape slots the S 11 and S 21 parameters are shown in figures (2.22) and (2.23). From these results the better pass band and wide stop band characteristics is observed due to the slots at the ground with elliptical shape. The proposed LPF in this section is compact and give wide band characteristics. In the next section another work is proposed where the ladder network of DGS structure is used. 2.5 LOW PASS FILTER DESIGN USING THE DGS LADDER Here on the ground plane of the microstrip line of characteristic impedance 50Ω a series of slots have been cut. The lengths of the slots L 1, L 2, a, b, c as shown in figure (2.24) have been initially calculated and optimized using FDTD based electromagnetic simulation software CST microwave studio [134]. 43

The design specifications of LPF are as follows: Cutoff frequency 4GHz Order of the filter N= 7 Pass band ripple= 0.1dB. To determine w 1 and w 2, a series of simulations have been performed and it has been seen that the optimum values can be obtained through the following equations with d= 0.2mm. w2/d =75 (2.12) w1/d=25 (2.13) The lengths of the slots are calculated using the following equations: 0.37g k 1 L1 L2 (2.14) gl 0.48g a b c k (2.15) gc Where the L 1, L 2 and a, b and c are the lengths of slots as shown in figure (2.24) and the values of g k and g k+1 have already been defined as in [1]. The values for ε r and the height of the substrate h are taken as 3.2 and 0.762mm. The dimensions are shown in figure (2.24). This DGS proposed in this work is symmetrically placed on the ground plane of the microstrip line. 44

Fig. 2.24 Basic structure of the ground defect with dimensions of slots on ground L 1 = L 2 = 4mm, W 1 =5mm, W 2 =15mm, a=b=c=4mm and d=0.2mm. Fig.2.25 Top view of structure from the top. Fig. 2.26 Bottom view of the proposed structure. 45

Fig.2.27 Top view of the fabricated structure. The structure shown in figure (2.24) has been fabricated and shown in figures (2.26) and (2.27). The structure shown in figure (2.24) has been simulated and the scattering parameters S 11 and S 21 are compared with the corresponding experimental values and shown in figures (2.28) and (2.29) respectively. S21Measured S21 Simulated S21 in db 0-5 -10-15 -20-25 -30-35 -40-45 0 2 4 6 8 10 Frequency in GHz Fig.2.28 Measured and simulated values of S 21 parameter. 46

S11 Measured S11 Simulated 0-5 -10 S11 in db -15-20 -25-30 -35-40 0 2 4 6 8 10 Frequency in GHz Fig.2.29 Measured and simulated values of S 11 parameter. It is evident from figures (2.28 and (2.29) that both the simulated and experimental values of the scattering parameters are matching satisfactorily. There are some small mismatches in the stop band characteristics between the simulated and measured results and these are due to the manufacturing defects. 2.6 COMPACT LOW PASS FILTER FOR L-BAND APPLICATION This section presents a compact microstrip low pass filter with sharp roll-off characteristics. The structure of the proposed filter is shown in figure (2.30). The filter has also been fabricated and shown in figure (2.31). The proposed filter consists of three inter connected rectangular resonators. Eempirical expressions have been derived to calculate the lengths of the resonators L 1 and L 3 and given by equation (2.17) and for the length L 2 given by equation (2.18). The function f(x) used in equations (2.17) and (2.18) also derived empirically using large number of simulated data and curve fitting. This function is given in equation (2.16). The 47

width of the resonators w 2 and w 3 are calculated from equations (2.5-2.7), where the Z c equal to 165 ohm for a narrow section and 11ohm for the wider section. 4 3 2 x 9.39x 37.43x 54.9x 33x 7. 37 f (2.16) l k 150Z πf x ε L ce Z 0 g k (2..17) 150Z 0 l k 1 g k 1 (2.18) πf x εle ZH Where l k+1 and l k are the physical lengths and ε le and ε ce effective dielectric constant of inductive (smaller width) and capacitive lines (wider width). Other terms are defined as in section-2. The cut off frequency has been considered as 1.7 GHz for the proposed design. The filter has been fabricated using the substrate FR4 with dielectric constant 4.5 and height 1.5mm. By using the design equations (2.17 and 2.18) the lengths have been calculated for the frequency x = 1.7 GHz. The dimensions are calculated as L 1 = 1.41mm, L 3 = 2.44mm, L 2 = 2.64mm, W 2 = 0.1mm and W 3 = 20mm and the width of the 50 ohm line is W 1 = 2.81mm. The designed structure has been simulated using MoM based full wave electromagnetic simulation software IE3D [133] and fabricated using photolithographic technique. Fig.2.30 Lay out of the proposed design. 48

Fig.2.31 Fabricated structure of the proposed LPF. Fig.2.32 Measured and Simulated S 11 parameter of designed structure. 49

Fig.2.33. Measured and Simulated S 21 parameter. The measured and simulated S 11 and S 21 parameters are shown in the figures (2.32) and (2.33) respectively. There are good agreements between the simulated and measured results and are evident from figures (2.32) and (2.33). From the physical dimensions it is observed that by using proposed technique about 57% size reduction can be achieved with respect to the physical length of filter with this specification designed by conventional stepped impedance technique. From the results shown in figures (2.33) it is observed that there is more than 22dB change within a range of 0.5 GHz while in transition from pass band to stop band. We can conclude that this proposed filter configuration gives high roll off. The two basic limitation of this technique are (i) It is limited only for the low microwave frequency range. (ii) It does not provide wide stop band characteristic. The following section is dedicated to get the wide stop band in a stepped impedance low pass structure. 50

2.7 LOW PASS FILTER DESIGN TRIANGULAR PATCH RESONATOR In this section triangular patch resonators are used to design LPF for wide band applications. Patch resonators are more advantageous as compared with the line based resonator filters in terms of compact size, simpler structure, lesser design complexity and fabrication uncertainty, lower conducting loss, higher power handling features and easier miniaturization. The geometry of the proposed structure is shown in figure (2.34) where an isosceles triangular patch resonator has been used in with input and out put feed lines on the base of the triangle with distance b between them. The resonant frequency of the triangular patch resonator has been assumed to be 10.2 GHz. The dimensions of the patch resonators can be obtained by conventional design techniques as given in [135]. The widths of the input and output feed lines have been calculated using equations (2.5-2.7) for characteristic impedance 50 ohm and the dielectric constant 3.2, height of the substrate 0.762mm. The calculated values of the dimensions are shown in figure (2.34). Fig. 2.34 Unit triangular patch with 50ohm lines. 51

The simulated values of the scattering parameters S 11 and S 21 are shown in the figure (2.36) it evident from the simulated results that the cut off frequency is 10.57 GHz against the theoretical cut off of 10.2GHz. The stop band attenuation is more than 14dB and the pass band attenuation is approximately zero db. This structure gives quite broad pass band characteristics. The height of the triangular patch d is varied and the simulated results of variation of cut off frequency and the height of the triangular patch is shown in fig(2.35). It is observed that keeping all other parameters constant the cut off frequency of the LPF decreases almost linearly with the increase of d. For height d more than 3mm it gives band width more than 9.5GHz. Three such triangular patch resonators discussed above has been cascaded to obtained more attenuation in the stop band. This cascaded structure is shown in figure (2.39) and the corresponding fabricated structure is shown in figure (2.40). The experimental and the simulated results for S-parameters are shown in figures (2.41) and (2.42) and they show a good agreement with the simulated and measured values. And it has been observed that the stop band attenuation is more than 20dB. 15.5 Frequency in GHz 14.5 13.5 12.5 11.5 10.5 9.5 3 3.5 4 4.5 5 Height of triangualr patch in mm Fig. 2.35 Graph between height and frequency. 52

Fig. 2.36 Simulated response of the single triangular patch resonator. Fig. 2.37 Triangular patches for low pass structure. Fig. 2.38 Fabricated structure of proposed LPF. 53

Measured S11 parameters Simulated S11 parameters 0 S11 parameters in db -10-20 -30-40 -50-60 -70 0 2 4 6 8 10 12 14 Frequency in GHz Fig. 2.39 Measured and simulated values of the S 11 parameters Triangular LPF. Measured S21 parameters Simulated S21 parameters S21 parameters in db 0-10 -20-30 -40 0 5 10 Frequency in GHz Fig. 2.40 Measured and simulated values of the S 21 parameters of Triangular LPF. 54

2.8 CONCLUSIONS This chapter presents five different LPF structures. All the structures are fabricated and the measured results are compared with results obtained using simulation software. Using fractals the size of the low pass filter has been reduced by applying the fractal shape on the stepped impedance resonators. The designed structure is shown in figure (2.5). In another work the spurious frequency bands in the stop band has been suppressed using the defective ground plane. The wide stop band is achieved more than 10GHz. The maximum value of insertion loss in stop band is more than 15dB. The results are shown in figures (2.20) and (2.21). A pattern of ladder network of slots is etched on the ground plane of 50 ohm microstrip line. A LPF response is achieved through this. The design equations are derived using the simulation software. A low pass filter is designed using the open stub lines as shown in figure (2.30). This filter can be used for L-band application. The triangular patch resonator is used to design a low pass filter. A periodic arrangement of these patches is arranged. Excellent agreements between the measured and simulated results are obtained. These are evident from the figures (2.39) and (2.40). 55