Corrected Report

7/31/2019 Corrected Report

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CHAPTER- ONE

INTRODUCTIONIn microwave communication systems, high performance and small size bandpass filters are

essentially required to enhance the system performance and to reduce the fabrication cost.

Parallel coupled microstrip filters, first proposed by Cohn in 1958 have been widely used in

the RF front end of microwave and wireless communication systems for decades. Major

advantages of this type of filter include its planar structure, insensitivity to fabrication

tolerances, reproducibility, wide range of filter fractional bandwidth (FBW) (20%) and an

easy design procedure . Although parallel-coupled microstrip filter with /2 resonators are

common elements in many microwave systems, their large size is incompatible with the

systems where size is an important consideration . The length of parallel coupled filteris too

long and it further increases with the order of filter.

To solve this problem, hairpin-line filter using folded /2 resonator

structures were developed. The traditional design of the hairpin topology has the advantage

of compact structure, but it has the limitation of wider bandwidth and poor skirt rate due to

unavoidable coupling. In addition to small size, high selectivity and narrow bandwidth;

good Return Loss (RL) and low cost are desirable features of narrowband bandpass

microstrip filters. Most of the present wireless applications are below 3 GHz . In this

spectrum, achieving narrow FBW and high quality factor (Q) while maintaining small size

and low cost is a challenging task. Using a dielectric substrate with high dielectric constant

(r) results in narrower microstrip line. However, a narrower line results in stronger

input/output coupling or a smaller external quality factor (Qe) . Narrow bandwidth and high

selectivity demands large Q, which can be achieved through larger gaps between coupled

resonators. But increasing gap between coupled resonators directly a

ffect the filter size.

In this paper a novel microstrip hairpinline narrowband bandpass filter

using Koch Fractal is presented. Resonator length has been reduced to /8 by using fractals

on coupling part of resonators thereby reducing the overall size to almost half of the

conventional hairpinline filter. Weak coupling between resonators is achieved while

maintaining relatively small spacing between resonators. It gains its simplicity from the fact

that no lumped component is used. FBW of 20 % is achieved at 1GHz while maintaining

Insertion Loss (IL) less than 3 dB and RL better than 30


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dB. For the filters with parallel coupled /2 resonators, a spurious passband around twice the

midband frequency (f0) is almost always excited

1.1 MOTIVATION

Traditionally, Microstrip coupled line filters have been used to achieve narrow

fractional bandwidth band pass filter due to their relatively weak coupling. However ,a

parasitic second harmonic contributes to an asymmetric pass band shape & degrade upper

band skirt properties. In addition to a large second harmonic signal can degrade the

performance of system components, such as mixers.

Due to the large difference between the even & odd mode effective dielectric constant of microstrip

coupled lines the phase velocity between two modes is significantly different .This problem is more

pronounced when filters are fabricated on high dielectric constant materials such as silicon or GaAs.

To overcome this problem , In this report fractal geometry have been applied. Several fractal

geometries have been widely studied to develop microwave devices ,such as antennas ,frequency

selective surfaces & photonic band gap devices .All of these fractal shape device have several

advantages including reducing resonant frequencies , & broad bandwidth. These give the fractal

shape two unique properties: SPACE FILLING & SELF SIMILARITY.

A fractal shape can be filled on a limited area as the order increases & occupies the same area

regardless of the order. This is due to the space filling property. By self similarity, a portion of the

fractal geometry always looks the same as that of the entire structure.

1.2 OBJECTIVE

The objective is to design low cost filter with reduced dimension, compact size with better

frequency response . As in microstrip coupled line filters have been used to achieve narrow

fractional bandwidth band pass filter due to their relatively weak coupling. However,a

parasitic second harmonic contributes to an asymmetric pass band shape & degrade upper

band skirt properties. In addition a large second harmonic signal can degrade the performance

of system components, such as mixers.


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To overcome this second harmonic problem , koch fractal geometry has been developed to

the coupled section of the filter . A fractal filter known as hairpin line band pass filter has

been developed to solve the above problem. It also improves the performance of microwave

devices such as superconducting resonators for layouts of microstrip filter. The proposed

design gives simple structure, and small size . This filter is fabricated on FR-4 substrate, and

its measured results are shown to be in good agreement with the simulated.


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CHAPTER : TWO

RELATED THEORY

2.1 FILTER

In circuit theory, a filter is an electrical network that change the amplitude and/or phase

characteristics of a signal with respect to frequency. Ideally, a filter will not add new fre-

quencies to the input signal, nor will it change the component frequencies of that signal, but it

will change the relative amplitudes of the various frequency components and/or their phase

relationships. Filters are often used in electronic systems to emphasize signals in certain

frequency range and reject signals in other frequency ranges. Such a filter has a gain which is

dependent on signal frequency.

The frequency-domain behaviour of a filter is described mathematically in terms of its

transfer function or network function. This is the ratio of the Laplace transforms of its output

and input signals. The voltage transfer function H(s) of a filter can therefore be written as:

(2.1)where VIN (s) and VOUT(s) are the input and output signal voltages and s is the complex

frequency variable. The transfer function defines the filter's response to any arbitrary input

signal, but we are most often concerned with its effect on continuous sine waves. Especially

important is the magnitude of the transfer function as a function of frequency, which

indicates the effect of the filter on the amplitudes of sinusoidal signals at various frequencies.

Knowing the transfer function magnitude (or gain) at each frequency allows us to determine

how well the filter can distinguish between signals at different frequencies. The transfer func-

tion magnitude versus frequency is called the amplitude response or sometimes, especially in

audio applications, the frequency response.


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Fig.1 Using A Filter To Reduce The Effect Of An Undesired Signal At Frequency F2

, While Retaining Desired Signal At Frequency F1.

2.1.1 ORDER OF FILTER

The order of a filter is the highest power of the variable s in its transfer function. The order of

a filter is usually equal to the total number of capacitors and inductors in the circuit.

2.1.2 CUT-OFF FREQUENCY

The pass band limits are usually assumed to be the frequencies where the gain has dropped by

3 decibels (0.707 of its maximum voltage gain). These frequencies are therefore called the -3

dB frequencies or the cut-off frequencies.

F fig.2. Cut-Off Frequency Fc

GAIN

FREQUENCY


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2.1.3 CENTER FREQUENCY

The center frequency is equal to the geometric mean of the - 3 dB frequency

(2.2)

where fc is the center frequency, fl is the lower -3 dB frequency ,fh is the higher -3 dB

frequency.

2.2 TYPES OF FILTER

2.2.1 LOW PASS FILTER

A low-pass filter passes low frequency signals, and rejects signals at frequencies above the

sfilter's cut-off frequency. If the components of our example circuit are rearranged .The

resultant transfer function is:

Fig.3. Frequency Response Of Low Pass Filter.

(2.3)

GAIN

FREQUENCY


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Fig.4 Simple Low Pass Filter

If a low-pass filter is placed at the output of the amplifier, and if its cutoff frequency is high

enough to allow the desired signal frequencies to pass, the overall noise level can be reduced.

2.2.2 HIGH-PASS FILTER

The opposite of the low-pass is the high-pass filter, which rejects signals below its cutoff

frequency. A high-pass filter can be made by rearranging the components of our example

network as in Figure 12. The transfer function for this filter is:

Fig.5 Simple High Pass Filter

(2.4)


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2.2.4 BAND REJECT FILTER

A filter with effectively the opposite function of the bandpass is the band-reject or notch

filter. As an example, the components in the network of Figure can be rearranged to form the

notch filter of Figure , which has the transfer function

Fig.8. Simple Band Reject Filter

(2.5)

Fig.9. Frequency Response Of Band Reject Filter


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Notch filters are used to remove an unwanted frequency from a signal, while affecting all

other frequencies as little as possible. An example of the use of a notch filter is with an audio

program that has been contaminated by 60 Hz powerline hum. A notch filter with a center

frequency of 60 Hz can remove the hum while having little effect on the audio signals.

2.2.5 ALL-PASS OR PHASE-SHIFT

The fifth and final filter response type has no effect on the amplitude of the signal at different

frequencies. Instead, its function is to change the phase of the signal without affecting its

amplitude. This type of filter is called an all-pass or phase-shift filter. The effect of a shift in

phase is illustrated in Figure . Two sinusoidal waveforms, one drawn in dashed lines, the

other a solid line, are shown. The curves are identical except that the peaks and zero crossings

of the dashed curve occur at later times than those of the solid curve. Thus, we can say that

the dashed curve has under- gone a time delay relative to the solid curve.

Fig.10. Response Of All Pass Filter

2.2.6 BUTTERWORTH FILTER

The first, and probably best-known filter approximation is the Butterworth or maximally-flat

response. It exhibits a nearly flat pass band with no ripple. The roll off is smooth and

monotonic, with a low-pass or high-pass roll off rate of 20 dB/decade (6 dB/octave) for every

pole. Thus, a 5th-order Butterworth low-pass filter would have an attenuation rate of 100 dB

for every factor of ten increase in frequency beyond the cut off frequency.


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The general equation for a Butterworth filter's amplitude response is

(2.6)

where n is the order of the filter, and can be any positive whole number (1, 2, 3, . . . ), and 0 is

the b3 dB frequency of the filter.

Fig.11. Amplitude Response Curves Of Butterworth Filter

2.2.7 CHEBYSHEV FILTER

Another approximation to the ideal filter is the Chebyshev or equal ripple response. As the

latter name implies, this sort of filter will have ripple in the passband amplitude response.

The amount of passband ripple is one of the parameters used in specifying a Chebyshev filter.

The Chebyschev characteristic has a steeper roll off near the cut off frequency when

compared to the Butterworth, but at the expense of monotonicity in the pass band and poorer

transient response. A few different Chebyshev filter responses are shown in Figure 12. The

filter responses in the figure have0.1 dB and 0.5 dB ripple in the pass band, which is small

compared to the amplitude scale in Figure.11 .


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Fig.12. Amplitude Response Of Chebyshev Filter.

2.2.8 PASSIVE FILTER

The filters used for the earlier examples were all made up of passive components: resistors,

capacitors, and inductors, so they are referred to as passive filters. A passive filter is simply a

filter that uses no amplifying elements (transistors ,operational amplifiers, etc.). In this

respect, it is the simplest (in terms of the number of necessary components) implementation

of a given transfer function. Passive filters have other advantages as well. Because they have

no active components, passive filters require no power supplies. Since they are not restricted

by the bandwidth limitations of op amps, they can work well at very high frequencies. They

can be used in applications involving larger current or voltage levels than can be handled by

active devices. Passive filters also generate little nosie when compared with circuits using

active gain elements. The noise that they produce is simply the thermal noise from the

resistive components, and, with careful design, the amplitude of this noise can be very low.

Passive filters have some important disadvantages in certain applications,

however. Since they use no active elements, they cannot provide signal gain. Input

impedances can be lower than desirable, and output impedances can be higher the optimum

for some applications, so buffer amplifiers may be needed. Inductors are necessary for the

synthesis of most useful passive filter characteristics, and these can be prohibitively

expensive if high accuracy (1% or 2%,for example), small physical size, or large value are

required. Standard values of inductors are not very closely spaced, and it is difficult to find an

off-the-shelf unit within 10%of any arbitrary value, so adjustable inductors are often used.


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Tuning these to the required values is time-consuming and expensive when producing large

quantities of filters. Furthermore, complex passive filters (higher than 2nd-order) can be

difficult and time-consuming to design.

2.2.9 ACTIVE FILTER

Active filters use amplifying elements, especially op amps, with resistors and capacitors in

their feedback loops, to synthesize the desired filter characteristics. Active filters can have

high input impedance, low output impedance, and virtually any arbitrary gain. They are also

usually easier to de-sign than passive filters. Possibly their most important attribute is that

they lack inductors, thereby reducing the problems associated with those components. Still,

the problems of accuracy and value spacing also affect capacitors, although to a lesser degree.

Performance at high frequencies is limited by the gain-bandwidth product of the amplifying

elements, but within the amplifier's operating frequency range, the op amp-based active filter

can achieve very good accuracy, provided that low-tolerance resistors and capacitors are

used. Active filters will generate noise due to the amplifying circuitry, but this can be

minimized by the use of low-noise amplifiers and careful circuit design.


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2.3 NETWORK THEORY

Most of the RF and Microwave systems and devices can be modeled as a two port network.

The two port representation basically helps in isolating either a complete circuit or a part of it

and finding its characteristic parameters. Once this is done, the isolated part of the circuit,

with a set of distinctive properties, enables us to abstract away its specific physical buildup,

thus simplifying analysis. Any circuit can be transformed into a two-port network provided

that it does not contain an independent source.

Fig.13. Two Port Network With Its Wave Variables

Where V1, V2 and I1, I2 are the voltages and currents at respective ports and Zo1 and Zo2 are

the terminal impedances. At RF and Microwave frequencies it is difficult to measure the

voltages, thus new wave variables a1, b1 and a2, b2 are introduced with a signifying the

incident wave and b implying the reflected wave. The wave variables in terms of voltage and

current are defined as follows

(2.7) for n =1 and 2 (2.8) (2.9)

for n=1 and 2 (2.10)


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Which gives power at each port Pn

(2.11)2.3.1 SCATTERING PARAMETERS

These are a set of parameters describing the scattering and reflection of traveling waves when

a network is inserted into a transmission line. S- parameters are normally used to characterize

high frequency networks, where simple models valid at lower frequencies cannot be applied.

S-parameters are normally measured as

a function of frequency, so when looking at the formulae for S-parameters it is important to

note that frequency is implied, and that the complex gain (i.e. gain and phase) is also

assumed. For this reason, S-parameters are often called complex scattering parameter

. (2.12)

(2.13)

(2.14) (2.15)S11 is the reflection coefficient of the input

S22 is the reflection coefficient of the output

S21 is the forward transmission gain

S12 is the reverse transmission gain


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These definitions can also be written in a matrix form as

[

] [

] *

+

2.3.2 OPEN CIRCUIT IMPEDANCE PARAMETERS

Impedance parameters are very useful in designing impedance matching and power

distribution systems. Two port networks can either be voltage or current driven. For the

current driven networks the input and output terminal voltage can be presented in matrix form

as follows :

Where the matrix which contain the z-parameter is also called z-matrix and is denoted by

[Z].

The Z parameters for a two port network can be mathematically defined as

(2.17) (2.18) (2.19)

(2.20)For reciprocal network Z12 = Z 21.

For asymmetrical network Z12=Z21 and Z11=Z 22.

And for lossless network,the Z parameters are imaginary.

2.3.3 SHORT-CIRCUIT ADMITTANCE PARAMETERS

Admittance parameters are very useful for describing the network when impedance

parameters may not be existing. This is solved by finding the second set of parameters by


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expressing the terminal current in terms of the voltage. The input and output terminal current

can be presented in matrix form as follows:

[] [ ] []Where the matrix which contain the Y parameter is also called Y matrix and is denoted by[y].The Y parameters for a two port network can be mathematically defined as

(2.21) (2.22) (2.23)

(2.24)2.3.4 ABCD PARAMETERS

In ABCD parameter the input port voltage and current are considered variable and equation is

formed in terms of the output voltage and current. The equation can be represented in matrix

form as follows:

[ ] *

+ [

]

The ABCD parameters for a two port network can be mathematically defined as (2.25) (2.26)

(2.27)


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(2.28)AD-BC=1 for reciprocal network

And A=D for symmetrical network

ABCD parameters are useful in analysis when the network can be broken into cascaded sub

networks.

2.3.5 IMPORTANT DEFINITION

2.3.5.1 INSERTION LOSS

The loss resulting from the insertion of a network in a transmission line, expressed as the

reciprocal of the ratio of the signal power delivered to that part of the line following the

network to the signal power delivered to that same part before insertion. It is usually

expressed in dB.

m , n = 1, 2 (m n) (2.29)Where LA denotes the insertion loss between the ports n and m.

2.3.5.2 RETURN LOSS

The Return Loss of a line is the ratio of the power reflected back from the line to the power

transmitted into the line. It is usually expressed in dB.

n = 1,2 (2.30)2.3.5.3 VOLTAGE STANDING WAVE RATIO

A standing wave may be formed when a wave is transmitted into one end of a transmission

line and is reflected from the other end by an impedance mismatch. VSWR is the ratio of the

maximum to minimum voltage in a standing wave pattern.


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n = 1,2 (2.31)2.3.5.4 PHASE DELAY

Whenever we insert a sinusoid into a filter, a sinusoid must come out. The only thing that

can change between input and output are the amplitude and the phase. Comparing a zero

crossing of the input to a zero crossing of the output measures the so-called phase delay.

To quantify this we define an input, sin() and an output sin(t- ) . Then the phase delayp is found by

(2.32) (2.33) (2.34)Where is in radians and is in radians per second. The phase delay is actually the time

delay for a steady sinusoidal signal and is not necessarily the true signal delay because a

steady sinusoidal signal doesnt carry information.

2.3.5.5 GROUP DELAY

Often the group delay is nothing more than the phase delay. This happens when the phase

delay is independent of frequency. But when the phase delay depends on frequency, then a

completely new velocity, the group velocity" appears. Curiously, the group velocity is not

an average of phase velocities. the simplest analysis of group delay begins by defining filter

input x(t) as the sum of two frequencies

(2.35)By using trigonometric identity,

(2.36)


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We see that the sum of two cosines looks like a cosine of the average frequency multiplied by

a cosine of half the difference frequency. Each of the two frequencies could be delayed a

different amount by a filter, so take the output of the filter yt to be

(2.37)In doing this, we have assumed that neither frequency was attenuated.

(The group velocity concept loses its simplicity and much of its utility in dissipative media.)

Using the same trigonometric identity, we find that

(2.38)Rewriting the beat factor in terms of a time delay tg, we now have* ( )+ (2.39)

(2.40) (2.41)For a continue frequency, the group delay is

(2.42)

This represents the baseband signal delay and is also referred to as the envelope delay.

2.3.6 IMMITTANCE INVERTER

Immittance Inverters are of two types, Impedance Inverter and Admittance inverter. The

following Block diagram shows a Immittance Inverter.


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Fig.14. Immitance Inverter

An ideal impedance inverter is a two port network that has a unique property at all frequency,

i.e. if it is terminated in impedance Z1 on one port ,the impedance Z2 seen looking in other

port is

(2.43)Where K is real and defined as characteristic impedance of the inverter.An impedance

inverter converts a capacitance into inductance and vice versa.The ABCD matrix of the

impedance inverter is

* + [ ]Similarly, an ideal admittance inverter is a two port network that if terminatd in

admittance Y1 on one port,the impedance Y2 seen looking at other port is

(2.44)Where J is real and defined as characteristics admittance of the inverter.Likewise an

admittance inverter converts a capacutance to inductance and viceversa. The ABCD matrix

of the admittance inverter is

* +


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2.3.6.1 PROPERTIES OF IMMITANCE INVERTER

If a series inductance is present between two impedance Inverters ,it looks like a

shunt capacitance from its exterior terminals.

Fig.15. Immitance Inverter Used To Convert A Shunt Capacitance Into A N Equivalent

Circuit With Series Inductance.

Similarly if a shunt capacitance is present between two admittance

inverters, it looks like a series inductance from its external terminals.

Fig.16. Immitance Inverter Used To Convert A Series Inductance Into A Equivalent Circuit

With Shunt Capacitance.

Making use of the properties of immitance inverters,band pass filters may be

realized by series LC.Resonant circuit separated by impedance inverters (K) or shunt

LC.parallel resonsnt circuit separated by Admittance inverters (J)


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2.4 MICROSTRIP BASICS

A general microstrip structure is shown in the figure 3.1, a microstrip transmission line

consists of a thin conductor strip over a dielectric substrate along with a ground plate at the

bottom of the dielectric.

Fig. 17. A Microstrip Structure

2.4.1 WAVES IN MICROSTRIP LINE

Wave travelling in microstrip line not only travel in the dielectric medium they also travel in

the air media above the microstrip line. Thus they dont support pure TEM waves . In pure

TEM transmission, the waves have only transverse component and the propogation velocity

only depends on the permittivity and the permeability of the substrate. But in the case of

microstrip line the magnetic and electric field also contain a Longitudinal component, and

their propagation velocity is dependent on the physical Dimensions of the microstrip as well.

If this longitudinal component is much smaller than the transverse

component then the microstrip line can be approximated to TEM model. And this is called

quasi TEM approximation.


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2.4.2 EFFECTIVE DIELECTRIC CONSTANT

Due to presence of two dielectric medium, air and the substrate, the

effective dielectric constant replaces the relative dielectric constant of the substrate in the

quasi TEM approximation. This effective dielectric constant is given in terms of Cd,

capacitance per unit length with the dielectric substrate present and Ca, capacitance per unit

length with dielectric constant replaced by air and is given by

= (2.45)the effective dielectric constant in terms of W (width of the Microstrip), h (height of the

substrate) and r (relative dielectric constant) given by Hammerstad and Jensen is:

(2.46)where

0

1 [

] (2.47)

(2.48)Accuracy of this model is

(2.49)

2.4.3 CHARACTERISTIC IMPEDANCECharacteristic impedance of the microstrip line is given by

(2.50)


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where c is the velocity of electromagnetic waves in free space C=2.99 10^8 m/s

Expression for characteristic impedance by hammerstad and Jensen is

0 1 (2.51)Where , ohms ( free space impedance),and [ ] (2.52)The accuracy of is better than 0.01% for and 0.03% for .2.4.4 SOME OTHERS FORMULAE

2.4.4.1 W/h

For W/h 2

(2.53)With

,

-

,

-

(2.54)

For W/h 2

, * +- (2.55)With

(2.56)


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2.4.4.2 GUIDED WAVELENGTH

(2.57)

Where is the free space wavelength at frequency f.2.4.4.3 PROPAGATION CONSTANT

(2.58)2.4.4.4 PHASE VELOCITY

(2.59)

2.4.4.5 ELECTRICAL LENGTH

(2.60) is called the electrical length whereas l is the physical length of the microstrip.Thus, when and when . Thes e are called quarter wavelength and half

wavelength microstrip line and are important in the filter design.

2.4.5 EFFECT OF METAL STRIP THICKNESS

When the strip thickness t becomes comparable to the width of the substrate then its

effect needs to be considered while designing. The following formulae show its effect on the

characteristic impedance and effective dielectric constant.

For W/h 1


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0 1 (2.61)For

* + (2.62)Where

(2.63)

(2.64)where r is the effective dielectric constant with t=0. It can be seen from the Formulae that

the effect of t is insignificant for small values of t/h ratio.

2.4.6 WAVES AND HIGHER-ORDER MODES

Despite the absence of the top conductor there exists wave on ground plate guided by the air

dielectric medium. These are called surface waves. The frequency at which these become

significantly large is

(2.65)

where the phase velocity of the two modes become equal.

To avoid excitation of higher-order modes in Microstrip the frequency of

operation is kept below the cut off frequency

(2.66)


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2.4.7 COUPLED LINES

The following figure shows the cross section of a coupled line. Widely used in the

construction of filters, they support two modes of excitation, even and odd mode.

Fig .18 A Coupled Line Structure

2.4.7.1 EVEN MODE

In even mode excitation both the microstrip coupled lines have the same voltage potential

resulting in a magnetic wall at the symmetry plane.


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Fig .19. Even Mode Of A Pair Of Coupled Microstrip Lines

Even mode capacitance is given by

(2.67)Where is the parallel plate capacitance between the microstrip line and the ground plate.Hence

(2.68) is the fringe capacitance and is given by (2.69)And is the modified fringe capacitance , with the effect of the adjacent microstripincluded. (2.70)Where

.

/ (2.71)The even mode characteristics can also be obtained from tha capacitance

() (2.72)Where is the even mode capacitance with air as dielectricAnd the effective dielectric constant for even mode is given as

(2.73)


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2.4.7.2 ODD MODE

In odd mode the coupled microstrip line possess opposite potential. This results into a electric

wall at the symmetry. The following cross section diagram shows the same.

Fig.20 Odd Mode Of A Pair Of Coupled Microstrip Line

The resulting odd mode capacitance is given as

(2.74) and represents fringe capacitance between the two microstrip line over the air andaver the dielectric,

(2.75)

Where

(2.76)

(2.77)

And the ratio of the elliptic function K(K)/K(K) is gien by


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() { (2.78)

The odd mode characteristic impedance and effective dielectric constant is given as:

() (2.79)Where is even mode capacitance with air as dielectric (2.80)


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CHAPTER-THREE

WORK DONE

3.1 PROPOSED WORK

The Main objective of our work is to design a Microstrip bandpass fractal filter for

suppression of spurious band.

In this work, a conventional hairpin-line is designed and simulatedthrough CST software . Subsequently, Koch fractal is applied to the conventional filter and

spurious band is being suppressed successfully. Finally, the proposed filters are physically

implemented on FR-4 Glass/Epoxy PCB and the simulated and measured results discussed.

3.2 MICROSTRIP FRACTAL FILTER

Microstrip filters are essential parts of the microwave system and play important role in many

communication applications especially wireless and mobile communications. These are

getting popular due their compact size, light weight, low cost and ease of fabrication .

Coupled line microstrip filters like pseudo comb line, hairpin-line, etc. possess narrow

fractional bandwidths due to their relatively weak coupling. However, due to commensurate

nature (equal electrical length of transmission-line elements), such networks have additional

spurious responses at the even-order frequencies due to the absence of homogeneous

substrate . Such spurious bands degrade the performance of system components like

generating asymmetric pass-band and reduce out-of-band rejection . To overcome this

problem, Koch fractal geometry has been applied to the coupled sections of a hairpin-line

filter, in this thesis.

Recently, the use of fractals in the design of filters have attracted a

lot of attention to achieve objectives like reduced resonant frequencies and wide bandwidth.

Fractals were first defined by Benoit Mandelbrot in 1975 as a way of classifying structures

whose dimensions were not whole numbers . Fractal means broken or irregular fragments that


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possess an inherent self-similarity in their geometrical structure. Looking at geometries

whose dimensions are not limited to integers lead to the discovery of filters with compact size

and improved characteristics. Till date several fractal geometries such as Hilbert curve,

Sierpinski carpet,Koch curve etc. have been used to develop various microwave devices .

One of the best methods to suppress spurious bands involve making optimum line structures

by inserting periodic shapes, such as grooved, wiggly and inter-digitized lines into

conventional coupled lines . These periodic structures are used to create Bragg reflections to

suppress the harmonics.

3.3 INTRODUCTION TO FRACTAL

3.3.1 DEFINITION OF FRACTAL

The formal mathematical definition of fractal is defined by Benoit Mandelbrot. It says that a

fractal is a set for which the Hausdorff Besicovich dimension strictly exceeds the

topological dimension. However, this is a very abstract definition.

Generally, we can define a fractal as a rough or fragmented geometric

shape that can be subdivided in parts, each of which is (at least approximately) a reduced-

size copy of the whole. Fractals are generally self-similar and independent of scale.

3.3.2 PROPERTIES OF FRACTAL

A fractal is a geometric figure or natural object that combines the following characteristics:

a) Its parts have the same form or structure as the whole, except that a different scaleand may be slightly deformed.

b) Its form is extremely irregular or fragmented, and remains so, whatever the scale ofexamination.

c) It contains "distinct elements" whose scales are very varied and cover a large range.d) Formation by iteration.e) Fractional dimension.


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3.4 FR4 (PRINTED CIRCUIT BOARD)

FR-4, an abbreviation for Flame Retardant 4, is a type of material used for making a printed

circuit board (PCB). It describes the board itself with no copper covering. FR-4 meets the

requirements of Underwriters Laboratories UL94-VO. The FR-4 used in PCB is typically

UV stabilized with a tetra functional epoxy resin system. It is typically a yellowish colour.

FR-4 manufactured strictly as an insulator (without copper cladding) is typically a

dysfunctional epoxy resin system and a greenish colour. FR-4 is similar to an older

material called G-10. G-10 lacked FR-4's self-extinguishing flammability-characteristics. FR-

4 has widely replaced G- 10 in most applications. Some military applications where

destruction of the circuit board is a desirable trait will still utilize G-10.A PCB needs to be an

insulator to avoid shorting the circuit, physically strong to protect the copper tracks

placed upon it, and to have certain other physical electrical qualities .FR-4 is preferred

over cheaper alternatives such as synthetic resin bonded paper (SRBP) due to several

mechanical and electrical properties; it is less loss at high frequencies, absorbs less

moisture, has greater strength and stiffness and is highly flame resistant compared to its less

costly counterpart. FR-4 is widely used to build high-end consumer, industrial, and military

electronic equipment. It is also ultra high vacuum (UHV) compatible.

3.5 HAIRPIN FILTER

Out of various band pass microstrip filters, Hairpin filter is one of the most preferred one.

The concept of hairpin filter is same as parallel coupled half wavelength resonator filters. The

advantage of hairpin filter over end coupled and parallel coupled microstrip realizations, is

the optimal space utilization. This space utilization is achieved by folding of the half

wavelength long resonators. Also the absence of any via to ground plane or any lumped

element makes the design simpler. The following figure shows a typical hairpin structure.


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Fig.21 (a) Tapped Line Input 5-Pole Hairpin Filter (B) Coupled Line Input 5-Pole Hairpin

Filter

The inter-digital and comb line filters required ground connections, which to achieve when

using microstrip line on ceramics substrates. When stripline and microstrip is used, the

hairpin filter is one of the preferred configurations. This is particularly useful when one is

interested in MIC or MMIC circuits. The hairpin-line filter can be considered basically to be

folded version of a half-wave parallel couple- line filter. It is much more compact,

though and gives approximately the same performance. As the fkquency increase, the

length-to-width ratio is smaller for a given substrate thickness, so that folding the

resonator becomes impractical. Hence this type of resonator is more suitable at lower

frequency. In general, the hairpin filter is larger than the comb-line and inter-digital filter.

But because no grounding is required, it is amenable to mass production as a larger

number of filters can be simultaneously printed on a single substrate, thereby lowering the

production cost.The hairpin filter configuration is derived from the edge-coupled filter.

To improve the aspect ratio, the resonators are folded into a

"U" shape Each resonator of the hairpin filter is 180 degrees so that the length from the center

to either end of the resonator is 90 degrees. From 90 degrees, 0 degrees are "slid" out of the

coupled section into the uncoupled segment of the resonator (fold of the resonator).

This reduces the coupled line lengths and, in effect reduces the coupling between resonators.

3.6 HAIRPIN RESONATOR

Figure 22 shows a single Hairpin Resonator. is called the slide angle. If the slide angle is

small it might lead to coupling between the arms of individual resonator. The voltage at the

end of hairpin arms is antiphase, and thus causes the arm to arm capacitance to have


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seemingly disproportionate effect. The added capacitance lowers the resonant frequency

requiring a shortening of the hairpin to compensate.

Fig 22: Hairpin Resonator

To avoid this, slide angle is kept as large as possible. But by increasing the slide angle the

coupling length between two resonators reduces, so as to attain the required coupling, the

coupling spacing needs to be reduced which posses a practical limitation. For practical design

purpose slide angle is kept twice the strip width to avoid inter-element coupling.

3.6.1 TAPPED LINE INPUT

Conventional filters employ coupled line input. Tapped line input has a space saving

advantage over coupled line input. Further while designing sometime the coupling

dimensions required for the input and output coupled line is very small and practically not

achievable which hinders the realizability of the design. Thus tapped line input is preferred

over coupled line input.


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Fig.23: Tapped Hairpin Resonator Schematic. Fig.24 Equivalent Circuit of a Tapped

Hairpin Resonator

Assuming negligible coupling between the arms of the hairpin resonator, the input

admittance at the tap point can be given as

(3.1)Provided that

and

| | * + (3.2)where f0 is the resonant frequency, f is the instantaneous frequency , Qe is singly

loaded Q and Z0 =1/Y0 is the characteristic impedance of the hairpin resonator. Comparing

the real part singly loaded Q can be obtained as

(3.3)

Where 3.7 DESIGNING OF HAIRPIN FILTER

For Designing a Hairpin filter, Full Wave EM simulation is used. For the design purpose the

low pass prototype (Butterworth, Chebyshevn, Bessel) is selected according to the design

requirement.


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3.8 HAIRPIN FILTER DESIGN

Fig.26. Equivalent Circuit o f The N-Pole Hairpin Band Pass Filter

As seen from the equivalent circuit of n pole Hairpin filter, each resonator can be modeled as

a combination of inductor and capacitor. The mutual coupling coefficient between two

resonators is Mi+1,i. Q e1 and Q en are the Quality Factor at the input and output.

Coupling coefficient and Quality Factor can be calculated as (3.4) (3.5)

for i = 1 to i = n-1 (3.6)

Where FBW is the fractional bandwidth and g0,1...........,n+1 are the normalized low pass element


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of the desired low pass filter approximation. the quality factor can be substituted and the ltap

length can be calculated as

(3.7)

(3.8)

3.8 CALCULATED PARAMETERS OF HAIRPIN-LINE BAND PASS

FRACTAL FILTER

Hairpin-line band pass filters are simple and compact in structures. They are obtained by

folding parallel-coupled resonators of half-wavelength, in to a U shape. Such resonators are

the so-called Hairpin-line resonators.

In order to fold the resonators, it is necessary to take into account the reduction of the

coupled-line lengths, which reduces the coupling between resonators . If the two arms of each

resonator are closely spaced, they function as a pair of coupled lines themselves, which has

an effect on the coupling as well.

For the 3rd order conventional Hairpin-line filter, the following are the design parameters:

Fractional Band width, Bf = 20% or 0.2 at mid band frequency 1 GHz, di-electric constant,

r = 4.4, substrate thickness, h = 1.6 mm, Loss tangent, tan = 0.02, Pass band ripple = 0.1

dB.

3.9 DESIGN PARMETERS:

PARAMETERS VALUE

Center Frequency ,fc 1 GHz Upper cut-off Frequency 1.137 GHz


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Lower cut-off Frequency 0.812 GHz Substrate thickness h 1.6 mm Loss tangent 0 .02 Pass band ripple 0.1 dB

Table1. designing parameters of filter

For 3rd

order conventional hairpin line filter,To calculate the approx length of each hairpin

resonator, the TXLINE calculator is used.

The dielectric used for this design is FR4. Its specifications are:

Properties Value

Substrate thickness 1.6mm

Relative dielectric constant 4.4

Conductor copper

Conductor thickness 35m

Loss tangent 0.022

Table 2 . specifications of FR-4

Using these specifications, we get the approx length of each hairpin resonator as given in the

figure


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Fig. 27 : Layout Of Conventinal Hairpin-Line Band Pass Filter

The lowpass prototype parameters, are g0 = g4 = 1; g1 = g3 = 1.0316; g2 = 1.1474. Having

obtained the low pass parameters , the band pass design parameters are calculated using the

following equations

(3.9)

(3.10) (3.11)For this design, we got the values as

Qe1 = 5.158,

M1,2 = M2,3 = 0.184.


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3.10 LAYOUT OF CONVENTIONAL HAIRPIN FITER

(A) PERSPECTIVE VIEW

Fig.28 perspective view of hairpin filter


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(B) FRONT VIEW

Fig.29 front view of hairpin filte

(C) HARDWARE VIEW

Fig.30 hardware snapshot of hairpin filter

3.11 1ST

ITERATION HAIRPIN BAND PASSS FRACTAL FILTER


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(A) PERSPECTIVE VIEW

Fig.31 perspective view of hairpin fractal filter

(B) FRONT VIEW

Fig.32 front view of hairpin fractal filter

(C) HARDWARE VIEW


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Fig.33 hardware snapshot of hairpin fractal filter

CHAPTER -FOUR

RESULTS

4.1 FORWARD GAIN(S21)

4.1.1 FOR CONVENTIONAL HAIRPIN FILTER


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This graph shows a band pass region from 0.6844 GHz to 1.059 GHz. The spurious band is

occuring between (1.702.053) GHz.

4.1.2 FOR 1ST

ITERATION OF FRACTAL

By use of fractal shape ,spurious band is suppressed and became narrower than before i.e.

between (2.64772.78) GHz.

4.2 INSERTION LOSS


Return loss of conventional filter is about27.65 dB at 1 GHz frequency.


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4.2.2 FOR 1ST


By using fractal , Return loss of filter is improved and is equals to30 dB at given 1 GHz

frequency.

4.3 SMITH CHART



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4.3.2 FOR 1ST


4.4 |S| PARAMETER MAGNITUDE



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4.4.2 FOR 1ST


4.5 PORT SIGNALS


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4.6 HARDWARE RESULT OF CONVENTIONAL HAIRPIN FILTER


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4.7 HARDWARE RESULT OF 1ST

ITERATION HAIRPIN FRACTAL

FILTER


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This graph shows a filters frequency response with a pass band between 885.4 MHz and

1159.1 MHz and a suppressed 2nd

harmonic.

UNIT: FIVE


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5. CONCLUSION AND FUTURE SCOPE

5.1 CONCLUSION

As we have taken a conventional hairpin band pass filter with the

specifications like center frequency of 1 GHz ,lower frequency of 0.6844 GHz ,higher

frequency of value 1.0567 GHz with a return loss of 27.65 dB.this conventional filter

contains spurioud bands ,generally called 2nd

harmonics,between (1.70292.056) GHz.

By using koch fractal geometry to the conventional hairpin filter,we found that 2nd

harmonic

or spurious band is suppressed and band becoame narroweer than before. Now the spurious

band exists between (2.64772.78) GHz frequency only.

So,we got an improvement in forward gain and return loss of filter along

with the suppression of spurious band due to use of fractal geometry to the conventional hair

pin band pass filter.

5.2 FUTURE SCOPE

Scope of this filter is very wide .Now a days broadband wireless access communications

system is a rapidly expanding market such system commonly employ filters in microwave &

mm-wave transceivers as channel separators. Theirs is an increasing demand for low cost,

light weight & compact size filters. To meet such demands , this filter is very much efficient .

These filters are used in different applications according to their requirements.

Fractal electrodynamics is the application of fractal concepts to the electromagnetic theory

and in this field , fractal description of natural geometries allowed the characterization of

interaction between these structures and electromagnetic waves , leading to the solution of

problems such as land or ocean surfaces , diffraction or random media propagation. By

utilizing a hilbert pattern , it is possible to design very compact resistors, which minimizes

the parasitic inductance per unit surface , and at the same time maximize the capacitance for a

fixed area in microstrip capacitor.

REFERENCES


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1. HONG JIA-SHEN, G., LANCASTER, M. J. Microstrip Filters for RF/ MicrowaveApplications. John Wiley & Sons Inc., 2001

2. POZAR, D. M. Microwave Engg. John Wiley, 2000.3. HSIEH, Y., WANG, S.-M., CHANG, C.-Y. Bandpass filters with resistive

attenuators being located at 2nd and 4th spurious. In Proc. 34 rd EuMC, 2004, vol.

2, p. 729732.

4. JAGGARD, D. L. On Fractal Electrodynamics. Recent Advances in ElectromagneticTheory. Ed. H N Kriticos and D L Jaggard. NewYork: Springer-Verlag, 1990.

5. KWON KIM, IL., et. al. Fractal-shaped microstrip coupled-line bandpass filters forsuppression of second harmonic. IEEE Transactions on Microwave Theory and

Techniques, 2005, vol. 53, no. 9, p. 29432948.

6. COHEN, N., HOHFELD, R. G. Fractal loops and small loop approximation.Commun. Quart., Winter 1996, p. 7778.

7. MATHAEI, G., YOUNG, L., JONES, E. M. T. Microwave Filter ImpedanceMatching Networks and Coupling Structures. Norwood: Artech House, 1980

8. J. S. WONG, Microstrip tapped-line filter design, IEEE Trans. Microwave TheoryTech., vol. MTT-27, pp. 44-50, Jan. 1979.

9. J. S. HONG and M. J. LANCASTER, Canonical microstrip filter using square open-loop resonators, Elec. Lett., vol. 31, pp. 2020-2022, 1995.

10.R. LEVY, Filters with single transmission zeros at real or imaginary frequencies,IEEE Trans. Microwave Theory Tech., vol. MTT-24, pp.172181, 1976.

11.J. S. HONG and M. J. LANCASTER, Couplings of microstrip square open-loopresonators for cross-coupled planar microwave filters, IEEE Trans. Microwave

Theory Tech., vol. 44, pp. 20992109, 1996.

12.Xiao, J.-K. and Y. Li, Novel microstrip square ring bandpass filters, JournaElectromagnetic Waves and Applications, Vol. 20, No. 13, 18171826, 2006.

13.Hong, J.-S. and M. J. Lancaster, Development of new microstrip pseudo-interdigitalband pass filters, IEEE Microwave and Guided Wave Letters, Vol. 5, No. 8, 261

263, August 1995.

14.Hong, J.-S. and M. J. Lancaster, Cross-coupled microstrip hairpin-resonator filters,15.IEEE Transactions on Microwave Theory and Techniques, Vol. 46, No. 1, 118122,

January 1998.

16.Gu, Q. RF System Design of Transceivers for Wireless Communications, Springer,2005.


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17.Jantaree, J. S. Kerdsumang and P. Akkaraekthalin , A microstrip bandpass filterusing a symmetrical parallel coupled-line structure, The 9th Asia Pacific Conference

on Communications,Vol. 2, 784788, 2003.

18.Deng, P.H., Y.S. Lin, C.H. Wang, and C. H. Chen, Compact microstrip bandpassfilters with good selectivity and stopband rejection, IEEE Transactions on

Microwave Theory and Techniques, Vol. 54, No. 2, 533539, February 2006.

19.Zhao, L.P., X.W. Chen, and C.H. Liang, Novel design of dual-mode dual-bandbandpass filter with triangular resonators,Progress In Electromagnetics Research,

PIER 77, 417424, 2007.

20.Xiao, J.K., S.W. Ma, S. Zhang, and Y. Li, Novel compact split ring steppedimpedance resonators (SIR) bandpass filters with transmission zeros, Journal of

Electromagnetic Waves and Applications, Vol. 21, No. 3, 329339, 2007.

21.Wang, Y. X., BZ. Wang, and J. Wang, A compact square loop dual-mode bandpassfilter with wide stop-band, Progress In Electromagnetics Research, PIER 77, 6773,

2007.

22. Xiao, J.K., Novel microstrip dual-mode bandpass filter using isosceles triangularpatch resonator with fractal-shaped structure, Journal of Electromagnetic Waves and

Applications, Vol. 21, No. 10, 13411351, 2007.

23.Swanson, D. G., Jr., Grounding microstrip lines with via holes, IEEE Transactionson Microwave Theory and Techniques, Vol. 40 No. 8, 17191721, August 1992.

24.Kinayman, N. and M. I. Aksun, Modern Microwave Circuits, Artech House, Boston,London, 2005.

25. Pak, J. S., M. Aoyagi, K. Kikuchi, and J. Kim, Band-sto filter effect ofpower/ground plane on through-hole signal via in multilayer PCB, IEICE Trans.

Electron, Vol. E89-C, No. 4, 551559, April 2006.

CONSULTED INTERNET SITES

1. www.wikipedia.com

2. www.cst.com

3. www.google.com

APPENDIX
http://www.cst.com/http://www.cst.com/


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1. WHAT IS MICROWAVE STUDIO?CST MICROWAVE STUDIO is a full-featured software package for electromagnetic

analysis and design in the high frequency range. It simplifies the process ofinputting the

structure by providing a powerful solid 3D modeling front end. Strong graphic feedback

simplifies the definition of your device even further. After the component has been

modeled, a fully automatic meshing procedure is applied before a simulation engine is

started.

CST MICROWAVE STUDIO is part of the CST DESIGN STUDIO suite and offers a

number of different solvers for different types of application. Since no method works

equally well in all application domains, the software contains four different simulation

techniques (transient solver, frequency domain solver, integral equation solver, Eigen

mode solver) to best fit their particular applications.

The most flexible tool is the transient solver, which

can obtain the entire broadband frequency behaviour of the simulated device from

only one calculation run (in contrast to the frequency step approach of many other

simulators). It is based on the Finite Integration Technique (FIT) introduced in

electrodynamics more than three decades ago. This solver is efficient for most kinds of

high frequency applications such as connectors, transmission lines, filters, antennas and

more.

In this tutorial w e will make use of the transient solver for designing

a microstrip hairpin band pass fractal filter as shown in figure.


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Fig 1: Graphical User Interface of CST MICROWAVE

1.2 SIMULATION WORKFLOW

After starting CST DESIGN ENVIRONMENT, choose to create

a new CST MICROWAVE STUDIO project. You will be asked to select a template f o r

a structure which is closest to your device of interest, but you can also start from

scratch opening an empty project. An interesting feature of the on-line help system is

the Quick Start Guide, an electronic assistant that will guide you through yo u r

simulation. You can open this assistant by


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Selecting Help QuickStart Guide if it does not show up automatically

If you are unsure of how to access a certain op er a t i on , c l i c k on the

corresponding line. The Quick Start Guide will then either run an animation

showing the location of the related menu entry or open the corresponding help

page. As shown in the Quick Start-dialog box which should now be positioned in the

upper right corner of the mainview, the following steps have to be accomplished for a

successful simulation:

1.3 DEFINE THE UNITS

Choose the settings which make defining the dimensions, frequencies and time steps foryour problem most comfortable. The defaults for this structure type are geometrical

lengths in mm and frequencies in GHz.

1.4 DEFINE THE BACKGROUND MATERIAL

By default, the modelled structure will be described within a perfectly conducting

world. For an filter problem, these settings have to be modified because the structure

typically attenuates the undesired signals. In order to change these settings, you can

make changes in the corresponding dialogue box (Solve Background Material).

1.5 MODELTHE STRUCTURE

Now the actual filter structure has to be built. For modeling the filter structure, a

number of different geometrical design tools for typical geometries such as plates,

cylinders, spheres etc., are provided in the CAD section of CST MICROWAVE

STUDIO. Theses shapes can be added or intersected using Boolean operators to build upmore complex shapes. An overview of the different methods available in the tool-set

and their properties is included in the on-line help.

1.6 DEFINE THE FREQUENCY RANGE

The next setting for the simulation is the frequency range of interest. You can specify the

frequency by choosing Solve Frequency from the main menu: Since you have already set

the frequency units (to GHz for example), you need to define only the absolute numbershere (i.e Without un its). The frequency settings are important because the mesh


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generator will adjust the mesh refinement (spatial sampling) to the frequency range

specified.

1.7 DEFINEPORTS

Every filter structure needs a source of high-frequency energy for excitation of the

desired electromagnetic waves. Structures may be excited e.g. using impressed

currents or voltages between discrete points or by wave-guide ports. The latter are

pre-defined surfaces in which a limited number of Eigen modes are calculated and

may be stimulated. The correct definition of ports is very important for obtaining

accurate S-parameters.

1.8 DEFINE BOUNDARY AND SYMMETRY

CONDITIONS

The simulation of this structure will only be performed within the bounding box of

the structure. You may, however, specify certain boundary conditions for each plane

(xmin, xmax, ymin etc.) of the bounding box taking advantage of the symmetry in

your specific problem. The boundary conditions are specified in a dialogue box that

opens by choosing

Solve Boundary Conditions from the main menu.

1.9 SET FI E L D MONITORS

In addition to the port impedance and S-parameters which are calculated automatically

for each port, field quantities such as electric or magnetic currents, power flow,

equivalent current den s i t y or radiated f a r -field may be calculated. To invoke

thcalculation ofthese output data, use the command Solve Field Monitors.

1.10 START THE SIMULATION

After defining all necessary parameters, you are ready to start your first simulation. Start

the simulation from the transient solver control dialogue box: SolveTransient Solver. In

this dialogue box, you can specify which column of the S-matrix should be calculated.

Therefore, select the Source type port for which the couplings to all other ports will

then be calculated during a single simulation run.


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1.11 USING PARAMETERS

CST MICROWAVE STUDIO has a built-in parametric optimizer that c a n help to

find appropriate dimensions in your design. To take advantage of this feature you

need to declare one or more parameters in the parameter list (bottom left part of

the program window) and use the symbols in almost every input field of the program

(dimensions, port settings etc.) Also simple calculations us ing these pre-defined

symbols are possible (e.g.4*x+y).

1.12 SIMULATION RESULTS

After a successful simulation run , you will be able to access various calculation

results and retrieve the obtained output data from the problem object tree at the

right hand side of the program window.

1.13 ANALYSES THE PORT MODES

After the solver has completed the port mode calculation, you can view the results

(even if the transient analysis is still running). In order to visualize a particular port

mode, you must choose the solution from the navigation tree. If you open the specific

sub-folder, you may select the electric or the magnetic mode field. Selecting the folder

for the electric field of the first mode e1 will display the port mode and its relevant

parameters in the main view: Besides information on the type of mode, you will also

find the propagation constant at a central frequency.


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Fig 2 Typical Patch Geomet ry and Dimensions

1.14 ANALYSES S-PARAMETERS AND FIELD QUANTITIES

At the end of a successful simulation run you may also retrieve the other outpu t datafrom the navigation tree, e.g. S-Parameters and electromagnetic field quantities.

1.15 EXERCISE

1.15.1 INTRODUCTION AND MODEL DIMENSIONS

In this tutorial you will learn how to simulate planar devices. As a typical example for a

planar device, you will analyze a Microstrip Line. The following explanations on how tomodel and analyze this device can be applied to other planar devices, as well. CST

MICROWAVE STUDIO can provide a wide variety of results. This tutorial, however,

concentrates solely on the surface currents.


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The structure depicted above consists of two different materials: The aluminum oxide

substrate (Al2O3) and the stripline metallization. There is no need to model the ground

plane since it can easily be described using a perfect electric boundary condition.

1.15.2 GEOMETRIC CONSTRUCTION STEPS

The tutorial will take you step by step through the construction of your model, and relevant

screen shots will be provided so that you can double-check your entries along the way.

Select a Template Once you have started CST DESIGN ENVIRONMENT and have

chosen to create a new CST MICROWAVE STUDIO project, you are requested to select a

template that best fits your current device. Here, the Planar Filter template should be

selected.


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This template automatically sets the units to mm and GHz, the background material to

vacuum and all boundaries to perfect electrical conductors. Because the background

material has been set to vacuum, the structure can be modeled just as it appears.

Furthermore, the automatic mesh strategy is optimized for planar structures and the

solver settings are adjusted to resonant behaviour.

1.15.3SET THE UNITS

As mentioned, the template has automatically set the geometrical units to mm. However,

since all geometrical dimensions are given in mil for this example, you should change

this setting manually. Therefore, open the units dialog box by selecting Solve -> Units

from the main menu:


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1.15.4 DRAW THE SUBSTRATE BRICK

The first construction step for modeling a planar structure is usually to define the

substrate layer. This can be easily achieved by creating a brick made of the substrates

material. Please activate the brick creation mode (Objects -> Basic Shapes -> Brick, ).

When you are prompted to define the first point, you can enter the coordinates

numerically by pressing the Tab key that will open the following dialog box:

In this example, you should enter a substrate block that has an extension of 300 mil in


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each of the transversal directions. The transversal coordinates can thus be described by

X = -150, Y = -150 for the first corner and X = 150, Y = 150 for the opposite corner,

assuming that the brick is modeled symmetrically to the origin. Please enter the first

points coordinates X = -150 and Y = -150 in the dialog box and press the OK button.

You can repeat these steps for the second point:

1 Press the Tab key

2 Enter X = 150, Y = 150 in the dialog box and press OK.

Now you will be requested to enter the height of the brick. This can also be numerically

specified by pressing the Tab key again, entering the Height of 25 and pressing the OK

button. Now the following dialog box will appear showing you a summary of your

previous input:

In this example, you should enter a substrate block that has an extension of 300 mil in

each of the transversal directions. The transversal coordinates can thus be described by

X = -150, Y = -150 for the first corner and X = 150, Y = 150 for the opposite corner,

assuming that the brick is modeled symmetrically to the origin. Please enter the first

points coordinates X = -150 and Y = -150 in the dialog box and press the OK button.

You can repeat these steps for the second point:

1 Press the Tab key

2 Enter X = 150, Y = 150 in the dialog box and press OK.

Now you will be requested to enter the height of the brick. This can also be numerically

specified by pressing the Tab key again, entering the Height of 25 and pressing the OK

button. Now the following dialog box will appear showing you a summary of your

previous input:


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Please check all these settings carefully. If you encounter any mistake, please change the

value in the corresponding entry field.

You should now assign a meaningful name to the brick by entering e.g. substrate in the


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Name field. Since the brick is the first object you have modeled thus far, you can keep

the default settings for the first Component (component1).

Please note: The use of different components allows you to combine several solids into

specific groups, independent of their material behavior.

The Material setting of the brick must be changed to the desired substrate material.

Because no material has yet been defined for the substrate, you should open the layer

definition dialog box by selecting [New Material] from the Material dropdown list:

In this dialog box you should define a new Material name (e.g. Al2O3) and set the Type

to a Normal dielectric material. Afterwards, specify the material properties in the

Epsilon and Mue fields. Here, you only need to change the dielectric constant Epsilon to


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9.9. Finally, choose a color for the material by pressing the Change button. Your dialog

box should now look similar to the picture above before you press the OK button.

Please note: The defined material Al2O3 will now be available inside the current

project for the creation of other solids. However, if you also want to save this specific

material definition for other projects, you may check the button Add to material library.

You will have access to this material database by clicking on Load from Material Library

in the Materials context menu in the navigation tree.

Back in the brick creation dialog box you can also press the OK button to finally create

the substrate brick. Your screen should now look as follows (you can press the Space key

in order to zoom the structure to the maximum possible extent):

1.15.5 MODEL THE STRIPLINE METALLIZATION

The next step is to model the stripline metallization on top of the substrate. This can also

be easily achieved by creating a brick made of the PEC material. Please check all the

settings carefully as shown below before click OK button.


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1.15.6 DEFINE PORT 1

The next step is to add the ports to the microstrip device. Each port will simulate an

infinitely long waveguide (here stripline) structure that is connected to the structure at

the ports plane. Waveguide ports are the most accurate way to calculate the microstrip

devices and should thus be used here.

A waveguide port extends the structure to infinity. Its transversal

extension must be large enough to sufficiently cover the microstrip mode. On the other

hand, it should not be chosen excessively large in

order to avoid higher order mode propagation in the port. A good choice for the width of

the port is roughly ten times the width of the stripline. A proper height is about five

times the height of the substrate.

Applying these guidelines to the example here, you find that the optimum

ports width is roughly 250 mil and that its height should be about 125 mil. In this

example, the whole model has a width of 300 mil and a height of 150 mil. Because these

dimensions are close to the optimal port size you can simply take these dimensions and

apply the port to the full extension of the model.


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Please open the waveguide port dialog box (Solve -> Waveguide Ports, ) to define the

first port:

Here, you should set the Normal of the ports plane to the Y-direction and its Orientation

in the positive Y-direction (Positive). Because the port should extend across the entire

boundary of the model, you can simply keep the Full plane setting for the transversal

position. Without the Free normal position check button activated, the port will be

allocated as default on the boundary of the calculation domain.

The next step is to choose how many modes should be considered by the port. For

microstrip devices, a single mode usually propagates along the line. Therefore, you


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should keep the default setting of one mode.

Please finally check the settings in the dialog box and press the OK button to create the

port: You can now repeat the same steps for the definition of the opposite port 2:

1 Open the waveguide port dialog box. (Solve -> Waveguide Ports,

2 Set the Normal to Y.

3 Set the Orientation to Negative.

4 Press OK to store the ports settings.

Your model should now look as follows:

1.15.7 DEFINE THE BOUNDARY CONDITIONS

In this case, the structure is not embedded within a perfect electrically conducting

enclosure, Therefore you need to change the boundary conditions to Open for all six

boundaries by clicking Solve -> Boundary Conditions.


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1.15.8 DEFINE THE FREQUENCY RANGE

The frequency range for the simulation should be chosen with care. The performance of

a transient solver can be degraded if the chosen frequency range is too small. We

recommend using reasonably large bandwidths of 20% to 100% for the transient

simulation. In this example, the frequency range is between 6 and 17 GHz. With the

center frequency being 11.5 GHz, the bandwidth (17 GHz 6 GHz = 11 GHz) is about

96% of the center frequency, which is sufficiently large. Thus, you can simply choose

the frequency range as desired between 6 and 17 GHz.

Please note: Assuming that you were interested primarily in a frequency range of e.g.

11.5 to 12.5 GHz (for a narrow band filter), then the bandwidth would only be about

8.3%. In this case, it would make sense to increase the frequency range (without losing

accuracy) to a bandwidth of 30% that corresponds to a frequency range of 10.2 13.8

GHz. This extension of the frequency range could speed up your simulation by more

than a factor of three! Also the lower frequency can be set to zero without any problems!

The calculation time can often be reduced by half if the lower frequency is set to zero

rather than e.g. to 0.01 GHz.

After the proper frequency band for this device has been chosen, you can simply open

the frequency range dialog box (Solve -> Frequency, ) and enter the range from 6 to 17

(GHz) before pressing the OK button (the frequency unit has previously been set to GHz

and is displayed in the status bar):

One interesting result for microstrip devices is the current distribution as a function of

frequency. The transient solver in CST MICROWAVE STUDIO is able to obtain the

surface current distribution for an arbitrary number of frequency samples from a single

calculation run. You can define field monitors to specify the frequencies at which the


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field data shall be stored.

Please open the monitor definition dialog box by selecting Solve -> Field Monitors ( ):

In this dialog box you should select the Type H-Field/Surface current before you specify

the frequency for this monitor in the Frequency field. Afterwards, you should press theApply button to store the monitors data. Please define monitors for the following

frequencies: 6, 9, 12, 15 (with GHz being the currently active frequency unit). Please

make sure that you press the Apply button for each

monitor. The monitor definition is then added in the Monitors folder in the navigation

tree. The volume in which the fields are recorded is indicated by a box.

After the monitor definition is complete, you can close this dialog box by pressing the

OK button.Field Calculation

A key feature of CST MICROWAVE STUDIO is the Method on Demand approach

that allows a simulator or mesh type that is best suited for a particular problem. In this

case, we choose the transient simulation with a hexahedral mesh.

Transient Solver z Transient Solver Settings The transient solver parameters are

specified in the solver control dialog box that can be opened by selecting Solve ->

Transient Solver from the main menu or by pressing the Transient solver icon in

the toolbar.


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Because the structure is fully symmetric, so change the Source type to Port 1.

Finally, press the Start button to start the calculation. A progress bar and

abort button appear in the status bar, displaying some information about the solver

stages.

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