20

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 semi-

lumped 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

21

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

22

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].

23

211

PLR (2.1)

where is the input reflection coefficient for a lossless network terminating in a

resistive load impedance ZL = RL. The insertion loss, measured in decibel is

PLRIL log10 (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:

)()(1 2

2

NMPLR (2.3)

where M (ω2) and N (ω2) 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:

24

Order of filter N = 5

RS = RL = 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.

g0 = 1 g1 = 0.7563 g2 = 1.3049 g3 = 1.5773

g4 = 1.3049 g5 = 0.7563 g6 = 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 :

gZLc

c0

; g representing the inductance (2.4a)

0Z

gCc

c

; g representing the capacitance (2.4b)

Where Ωc is cut off frequency of LPP, ωc desired cut off frequency, and Z0 is

load and source impedance. The transformed filter network with its elemental

values has been shown in figure (2.1).

25

Fig.2.1 Schematic of the Low Pass Filter after scaling.

Rs = 50Ω C1 = 1.1041 pf L2 = 4.7624 nh C3 = 2.3026 pf

L4 = 4.7624 nh C5 = 1.1041 pf RL = 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

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 (ZH/ZL) should be as high

as possible (where ZH and ZL 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 ZH=100 to 150 and ZL=15 to

25. In this design we have selected ZL =24Ω and ZH = 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

82 A

A

ee

hW for W/h < 2

rr

r BBBh

W

61.039.01ln2

112ln12 For W/h >2

(2.5)

Where

rr

rr0 11.023.011

21

60ZA

r0Z2377B

27

wh

rrre 121

12

12

1 (2.6)

reg

0 (2.7)

Where εr relative dielectric constant, εre, effective dielectric constant, λ0

wavelength in free space and λg 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 ZL = 24Ω For ZH = 100Ω

w = 6.3525 mm w = 0.4801 mm

εre = 2.8042 εre = 2.3456

λgL = 71.6599 mm λgH = 78.3527 mm

Also for Z0 = 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].

28

L

Lkck

ZCl

where k=1,3,5 (2.8a)

HH

kck Z

Ll 1

1 (2.8b)

Where lk and lk+1 are the lengths of resonators, ωc is the cut-off frequency, Ck

and Lk+1 are the corresponding transformed values of capacitances and

inductances, βL and βH 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.

l1= 3.95 mm, l2= 9.33 mm, l3= 8.25 mm, l4 = 9.33 mm,

l5= 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).

29

-70

-60

-50

-40

-30

-20

-10

0

0 2 4 6 8 10

Frequency in GHz

S-pa

ram

eter

s in

dB

S11 parameters S21 parameters

Fig. 2.3 Simulated values of S11 and S21 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, 900 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

30

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 l2 and l4 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

of the filter has been reduced from 54321 lllll to

5

43

21 22

lllll .

31

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

S11 and S21 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.

-70

-60

-50

-40

-30

-20

-10

0

0 1 2 3 4 5 6

Frequency in GHz

S11

in d

B

Without fractal structure With fractal structure

Fig.2.6. S11 parameters of lowpass filter with and without fractal structure.

32

-25

-20

-15

-10

-5

0

0 1 2 3 4 5 6

Frequency in GHz

S21

in d

B

Without fractal structure With fractal structure

Fig. 2.7. S21 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 S11 and S21 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.

33

-30

-25

-20

-15

-10

-5

0

0 1 2 3 4 5 6

Frequency in GHz

S21

in d

B

Simulated S21 Measured S21

Fig.2.9 Measured and simulated S21 parameters of the filter with fractal lines.

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

0 1 2 3 4 5 6

Frequency in GHz

S11

in d

B

Simulated S11 Measured S11

Fig.2.10 Measure and simulated S11 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).

34

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 (Cp) in high impedance line.

2tan1 gC

Hcp Z

C

(2.9a)

Fig.2.12 Stray inductance (Ls) in low impedance line.

2tan gL

c

Ls

ZL

(2.9b)

35

Where Cp and Ls are the stray capacitances and inductances. β is the phase constant,

ωc is the cutoff frequency and λgC and λgL 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 S11 and

S21 values are shown for every iteration in figures (2.13) and (2.14).

-60-55-50-45-40-35-30-25-20-15-10

-50

0 1 2 3 4 5 6

Frequency in GHz

S11

in d

B

Without Iteration With first iteration

With second Iteration With third Iteration

Fig. 2.13 Comparison of S11 parameters of conventionally designed filter with considering end and T-junction effect.

-25

-20

-15

-10

-5

0

0 1 2 3 4 5 6

Frequency in GHz

S21

in d

B

Without Iteration With first Iteration With second Iteration With third Iteration

Fig. 2.14 Comparison of S21 parameters of conventionally designed filter with considering end and T-junction effect.

36

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

37

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 roll-

off 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).

22

0

5)(c

cp

ff

fpFinC

(2.10)

)(250)(

0fCnHinL

pp

(2.11)

38

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:

L1=10.04mm, L2 =7.77mm, L3 =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.

39

2.5

3

3.5

4

4.5

2.6 2.7 2.8 2.9 3 3.1 3.2

frequency in GHz

Slot

wid

th in

mm

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.

40

Fig.2.19. Top view of the fabricated filter.

The structure shown in the figure (2.16) is simulated and the S11 and S21 parameters

are compared with the measured values of S11 and S21 parameters and shown in

figures (2.20) and (2.21).

-35.00

-30.00

-25.00

-20.00

-15.00

-10.00

-5.00

0.00

0 1 2 3 4 5 6 7 8 9 10

Frequency in GHz

S11

in d

B

Measured S11 Simulated S11

Fig. 2.20 Simulated and Measured S11 Parameters.

41

-30

-25

-20

-15

-10

-5

00 1 2 3 4 5 6 7 8 9 10

Frequency In GHz

S21

in d

B

Measured S21 Simulated

Fig. 2.21. Simulated and Measured S21 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

Frequency 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

42

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 L1 (mm) L2 (mm)

L3 (mm)

Conventional (without DGS)

Structure

10.0486 7.7734 4.359

Proposed structure

7.5 4.25 3.5

Fig. 2.22 S21 parameters of both LPFs (elliptical and square DGS) structures.

43

Fig. 2.23 S11 parameters of both the proposed.

To compare the rectangular and elliptical shape slots the S11 and S21

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 L1, L2, 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].

44

The design specifications of LPF are as follows:

Cutoff frequency 4GHz

Order of the filter N= 7

Pass band ripple= 0.1dB.

To determine w1 and w2 , 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:

gL

kgLL

121

37.0 (2.14)

gC

kgcba48.0

(2.15)

Where the L1, L2 and a, b and c are the lengths of slots as shown in figure

(2.24) and the values of gk and gk+1 have already been defined as in [1] . The

values for εr 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.

45

Fig. 2.24 Basic structure of the ground defect with dimensions of slots on ground L1 = L2= 4mm, W1=5mm, W2=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.

46

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 S11 and S21 are compared with the

corresponding experimental values and shown in figures (2.28) and (2.29)

respectively.

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

0 2 4 6 8 10

Frequency in GHz

S21

in d

B

S21Measured S21 Simulated

Fig.2.28 Measured and simulated values of S21 parameter.

47

-40

-35

-30

-25

-20

-15

-10

-5

0

0 2 4 6 8 10

Frequency in GHz

S11

in d

B

S11 Measured S11 Simulated

Fig.2.29 Measured and simulated values of S11 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 L1 and L3 and given

by equation (2.17) and for the length L2 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

48

width of the resonators w2 and w3 are calculated from equations (2.5-2.7), where

the Zc equal to 165 ohm for a narrow section and 11ohm for the wider section.

37.7339.5443.3739.9 234 xxxxxf (2.16)

kce

Lk g

ZεxπfZl

0

150

(2..17)

10

1150

k

Hlek g

ZεxπfZl

(2.18)

Where lk+1 and lk are the physical lengths and εle and εce 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 L1 = 1.41mm, L3 =

2.44mm, L2 = 2.64mm, W2 = 0.1mm and W3 = 20mm and the width of the 50

ohm line is W1 = 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.

49

Fig.2.31 Fabricated structure of the proposed LPF.

Fig.2.32 Measured and Simulated S11 parameter of designed structure.

50

Fig.2.33. Measured and Simulated S21 parameter.

The measured and simulated S11 and S21 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.

51

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.

52

The simulated values of the scattering parameters S11 and S21 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.

9.5

10.5

11.5

12.5

13.5

14.5

15.5

3 3.5 4 4.5 5

Height of triangualr patch in mm

Freq

uenc

y in

GH

z

Fig. 2.35 Graph between height and frequency.

53

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.

54

-70

-60

-50

-40

-30

-20

-10

0

0 2 4 6 8 10 12 14

Frequency in GHz

S11

par

amet

ers

in d

B

Measured S11 parametersSimulated S11 parameters

Fig. 2.39 Measured and simulated values of the S11 parameters Triangular LPF.

-40

-30

-20

-10

0

0 5 10

Frequency in GHz

S21

par

amet

ers

in d

B

Measured S21 parametersSimulated S21 parameters

Fig. 2.40 Measured and simulated values of the S21 parameters of Triangular LPF.

55

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).