A transmittal line is a physical construction that will steer an electromagnetic moving ridge between two ports. Basically, the transmittal systems are used to reassign energy from one point to another. It is really of import in the RF and Microwave application. The theory covered all about the field analysis and basic circuit theory which are really of import in microwave web analysis. To see the phenomenon of wave extension on a transmittal line, an attack utilizing Maxwell ‘s equations was applied. There are several type of transmittal line such as two wire line, coaxal overseas telegram, wave guide and planar transmittal lines. The alleged wave guide was used as transmittal line in this undertaking as a filter. This chapter is to give brief overview of the transmittal line theory chiefly on the wave guide to ease future treatment on other chapter.

## 2.1 Transmission Line Theory

Transmission line theory was analysed utilizing circuit theory but there is difference between them which is electrical size. Assume that the physical dimensions of a web are much smaller than the electrical length, while transmittal line may be considerable fraction of wavelength, or more. Therefore, transmittal line is a distributed-parameter web, where electromotive forces and currents can change in magnitude and stage over length. Therefore any transmittal line can be represented by a distributed electrical web as shown in figure 2.1. It comprises series inductances and resistance and shunt capacitances and resistances.

a?†z

## –

## –

## +

## +

I ( z+a?†z, T )

V ( z+a?†z, T )

V ( omega, T )

I ( omega, T )

Ca?†z

Ga?†z

La?†z

Ra?†z

## Figure 2.1 Lumped-element tantamount circuit of transmittal line

Figure 2.1 represented a two-wire line as a transmittal line where R, L, G, C defined as follows:

R=Series resistance per unit length, in a„¦/m.

L=Series inductance per unit length, in H/m.

G=Shunt conductance per unit length, in S/m.

C=Shunt electrical capacity per unit length, in F/m.

From figure 2.1, simplified utilizing Kirchhoff ‘s electromotive force jurisprudence and Kirchhoff ‘s current jurisprudence, obtained the undermentioned differential equation 2.1 and 2.2. These equations are in clip domain signifier of transmittal line equations. However, both equations being simplified into sinusoidal steady-state status, with cosine-based phasors as in equation 2.3 and equation 2.4. ( Pozar, 2005 )

## 2.1.1 Wave extension on a Transmission Line

From equation 2.3 and 2.4, both equations can be solved at the same time to deduce for wave equation in term of V ( omega ) and I ( omega ) . Equation 2.5 and 2.6 is being simplified where I? is complex extension invariable, I± is attenuation changeless and I? is phase changeless.

## 2.1.2 Lossy and Lossless Transmission Line

Equation 2.7 above was for a general transmittal line, including loss consequence. For lossy instances, the fading invariable is being considered in the extension changeless equation. However for the loss of the transmittal line is really little and can be neglected will do the fading to be about zero. Hence the equation will be simplified consequently as shown in equation 2.8 into equation 2.9.

Where

## 2.1.3 Categorization of Wave Solutions

There are three type of wave extension in cylindrical transmittal line or wave guides, TEM, TE, and TM. The geometry is characterized by music director boundaries parallel to z-axis. Hence, electric and magnetic field can be assumed that time-harmonic Fieldss with an ejwt dependance as in equation 2.10 and 2.11.

and stand for the transverse electric and magnetic field constituent, while ez and hertz are the longitudinal electric and magnetic field constituents. The equation above is for the moving ridge propagating in +z way and for -z way is can be obtained by replacing the I? with -I? . In the instances of loss nowadays, the extension invariable will be complex by replacing jI? with equation 2.7. By utilizing the Maxwell ‘s equation, for cross field constituent in term of EZ and HX can be derived as shown in equation 2.12 to equation 2.15.

Where

is defined as the cutoff wavenumber and K is wavenumber of the stuff make fulling the transmittal line or waveguide part.

Transverse electromagnetic ( TEM ) moving ridge are characterized by Ez=Hz=0. However by detecting equation 2.12 to equation 2.15, the cross field will besides be zero, unless. Transverse electric ( TE ) moving ridges, besides referred to as H-waves are characterized by Ez=0 and Hz0 while Transverse magnetic ( TM ) waves besides reffered as E-waves are characterized by Ez0 and Hz=0. Therefore all the equation derived by the features of each transverse moving ridge is simplified in table 2.1. ( Pozar, 2005 )

Transverse Electromagnetic

( TEM )

Transverse electric

( TE )

Transverse magnetic

( TM )

## Table 2.1 Simplified Transverse Wave equation.

## 2.2 Microwave Filters

Filter had played an of import function in many applications on modern universe. The application are diverse, from traditional fixed telecommunication system to mobile, pilotage, radio, satellite communicating system and remote-sensing application. Basically, the RF and micro-cook filter are widely used to know apart between wanted and unwanted frequences. The promotion of engineerings affected the RF and microwave filter became more extended in term of execution in practical system. All features need to be considered to make a filter that will give a satisfying and convenient consequence for user.

## 2.2.1 Type of Microwave Filters

By and large there are 4 types of filter map, lowpass, highpass, bandpass and bandstop filter. This filter is fundamentally to let the signal harmonizing to frequence that are wanted. For lowpass and highpass filter, the barrier of frequence depends on the cutoff frequence. Lowpass filter will let the frequence below the cutoff frequence while the highpass filter allows the frequence beyond the cutoff frequence. However for the bandpass and bandstop filter depend on the cardinal frequence. Bandpass filter will let the signal in the set of frequence but bandstop filter is otherwise.

## Figure 2.1 Type of filter

## 2.2.2 Filters Response

There are other features of filter called filter response. First type of filter response is maximally level, besides called binomial or Butterworth response. For illustration, lowpass filter is specified by equation 2.16. The representation of the equation is shown in graph signifier in figure 2.2. Second, for the response of Chebyshev or equal rippling, a Chebyshev multinomial is used to stipulate the interpolation loss of a N-order low base on balls filter as in equation 2.17.

where N is the order of the filter, and wc is the cutoff frequence. The passband is extends from tungsten = 0 to w = wc.

The equation is differing from Butterworth or binomial response because it provides the flattest possible passband response for a given order. This is shown is equation 2.17. Although the passband response will hold rippling of amplitude 1+k2, as shown in figure 2.2, since TN ( x ) will do it oscillates between for. Thus, K2 determines the passband rippling degree. For a big ten, , so far the interpolation loss becomes

PLRwhich besides increases at the rate of 20dB/decade. But the interpolation loss for the Chebyshev response is ( 22N/4 ) larger than the Butterworth response. ( Pozar, 2005 )

0 0.5 1 1.5

w/wc

Maximally level

Equal rippling

1

1 + K2

## Figure 2.2 Maximally level and equal-ripple low-pass filter responses. ( Pozar, 2005 )

## Figure 2.3 Low-pass paradigm Chebyshev response and matching band-pass filter Chebyshev response. ( G. Matthaei, 2000 )

The feature of the Chebyshev lowpass filter theoretical account is shown in figure 2.3 where the LAR represents the fading tolerance or rippling for the lowpass filter response, w1 ‘ is the cutoff frequence, w1 and w2 are the base on balls set frequence. The crisp rate of cutoff will depend on the rippling and figure of order. There are besides common filter response, elliptic map and additive map which are non used in this undertaking.

## 2.2.3 Method of Filter Design

The ideal filter web is a web that provides perfect transmittal for all frequences range in appropriate passband part. Filters designed utilizing the lumped component circuit consist of filter synthesis techniques, image parametric quantity and interpolation loss method. For image parametric quantity method consist of a cascade of simpler two-port filter subdivision to supply desired cutoff frequences and fading features, but do non let the specification of a frequence response over the complete operating scope. Therefore, although the process is comparatively simple, the design filter by the image parametric quantity method frequently must be iterated many times to accomplish the coveted consequences.

The other method is called the interpolation loss method, used web synthesis techniques to plan filters with a wholly specified frequence response. The design is simplified by get downing with low-pass filter paradigms that are normalized in term of electric resistance and frequence. Transformations are applied to change over the paradigm design to the coveted frequence scope and electric resistance degree. ( Pozar, 2005 )

## 2.3 Waveguide as Transmission Lines

## 2.3.1 Types of Waveguide

Several types of wave guides that had been used are rectangular wave guide, round wave guide, coaxal wave guide, Elliptical wave guide, Radical wave guide and spherical wave guide. All the wave guide have different type of cross-sectional country harmonizing to certain form. Each of this wave guide has their ain mathematical representation of electromagnetic field within a unvarying or unvarying part. In wave guide, merely one manner is capable of extension depend on the dimension and field excitement. However, the wave guide is wholly characterized by the behavior of the dominant manner of the wave guide, normally the lowest manner.

## 2.3.2 Rectangular Waveguides

Rectangular wave guides were one type of transmittal lines and are used in many applications presents. It has played a big assortment of constituents such as filters, couplings, sensors, isolators and attenuators. Rectangular wave guide are commercially available for assorted standard wave guide sets from 1GHz to over 220GHz as shown in appendix E. In term of development in engineering, a batch of application move towards miniaturisation and integrating. The hollow rectangular wave guide can propagate TM and TE manners, but non TEM moving ridges, since merely one music director is present.

B

I? , Iµ

a

0

## Figure 2.4 Geometry of a rectangular wave guide

Figure 2.4 shows geometry of rectangular wave guide where it is assumed that the wave guide is filled with a stuff of permittivity Iµ and permeableness I? . The breadth, a is normally longest than the high, B of the rectangular wave guide. The value of a and B will do different value of cutoff frequence and each manner ( combination m and N ) harmonizing to equation 2.19.

The manner with the lowest cutoff frequence is called the dominant manner. Hence, the lowest fc occurs for the TE10 ( thousand = 1, n = 0 ) manner harmonizing to equation 2.20 is the dominant manner of the rectangular wave guide. At a given operating frequence degree Fahrenheit, merely those manners holding fc & lt ; f will propagate and mode with fc & gt ; f will take to an fanciful I? ( or existent I± ) , intending that all field constituents will disintegrate exponentially off from the beginning of excitement as shown in equation 2.7 where complex extension changeless I? , fading invariable, I± and stage changeless I? . Such manner is referred to as cutoff, or evanescent, manners. Of more than one manner propagating, the wave guide is said to be overmoded. ( Pozar, 2005 )

Another of import parametric quantity is guide wavelength, defined as the distance between two equal stage planes along the wave guide. The value of guide wavelength can be found utilizing equation 2.21 and 2.22 below. The usher wavelength will depend on the value of frequence degree Fahrenheit.

where

## 2.4 Microwave Resonator

Microwave resonating chambers are used in assortment of application, including filters, oscillators, frequence metres, and tuned amplifier. There are assorted execution of resonating chambers at microwave frequence utilizing distributed elements such as transmittal lines, rectangular wave guide, and dielectric pits ( Pozar, 2005 ) . There are two types of resonant circuits, series and parallel. The filter construction as shown in figure 2.4 consists of series resonating chambers jumping with shunt resonating chambers, an agreement which is hard to accomplish in a practical microwave construction. In a microwave filter, it is much more practical to utilize a construction which is approximates the circuit such as shown in figure 2.6 below. In this construction all of the resonating chambers are of the same type, and an consequence like jumping series and shunt resonating chamber is achieved by the electric resistance inverters.

RA

Rubidium

Ln

Cn

C3

L1

C1

L3

## Figure 2.5 The uneven figure of order band-pass filter. ( G. Matthaei, 2000 )

By utilizing equation from 2.23 to 2.26, value of electrical capacity and induction in figure 2.5 can be calculated from value of g parametric quantity. All computation depend on the type of resonating chamber being used either shunt or parallel resonating chambers or series resonating chambers.

For shunt resonating chambers For series resonating chambers

Lumped circuit elements are hard to build at microwave frequences, hence it is normally desirable to recognize the resonating chamber in distributed-element signifiers instead than the lumped component signifiers. Basically, to set up the resonance belongingss of resonating chambers it is convenient to stipulate their resonating frequence, w0 and their incline parametric quantity. Equation 2.27 shows the reactance incline parametric quantity for series-type resonating chamber and equation 2.28 shows the susceptance incline parametric quantity for shunt or parallel-type resonating chamber.

Another of import parametric quantity for resonating circuit is its Q, or quality factor. For any resonating chamber holding series type of resonance with a reactance incline parametric quantity, a?? and series opposition, R has a Q shown in equation 2.29 but for resonating chamber holding shunt or parallel type of resonance with susceptance incline parametric quantity, I? and a shunt conductance, G has a Q shown in equation 2.30.

## 2.5 Impedance and Admittance Inverters

The construct of operation for electric resistance and entree inverters is basically organize the opposite of the burden electric resistance or entree. Basically, they can be used to transform series-connected elements to shunt-connected component or frailty versa. The Kuroda individualities can besides be used for the transition but it ‘s more utile for bandpass if utilizing electric resistance ( K ) and entree ( J ) inverters. A simplest signifier of inverters is a one-fourth wavelength of transmittal line. If the resonating chambers all exhibit series type of resonance and connected without electric resistance inverter, they will merely run like a individual series of resonating chamber. Beside a one-fourth wavelength line, there are besides other circuit that can run every bit inverter as shown in figure 2.6.

Electric resistance inverters Admittance inverters

Joule

+90a-¦

K

+90a-¦

Yin=J2/ZL

Zin=K2/ZL

I»/4

I»/4 ( a )

Y0=J

Z0=K

I?/2

I?/2

I?/2

I?/2

( B )

jB

Z0

Z0

jX

Z0

Z0

( degree Celsius )

K=1/wC

J = wC

-C

-C

-C

-C

C

C

( vitamin D )

## Figure 2.6 Electric resistance and entree inverters. ( Pozar, 2005 )

Type of entree and electric resistance inverters was shown in figure 2.6 where

Operation of electric resistance and entree inverters

Execution as quarter-wave transformers

Execution utilizing transmittal lines and reactive elements

Execution utilizing capacitance webs.

For execution utilizing transmittal lines and reactive elements in figure 2.6 ( degree Celsius ) , the parametric quantity for electric resistance inverter can be happening utilizing equation 2.31 to equation 2.33 and for entree inverter utilizing equation 2.34 to equation 2.36.

RA

Xn ( tungsten )

X2 ( tungsten )

X1 ( tungsten )

Kn.n+1

K23

K12

K01

Rubidium

## Figure 2.7 A generalised band-pass filter circuit utilizing electric resistance inverters

## Figure 2.8 Reactance of jth resonating chamber

Figure 2.7 shows a generalised circuit for a bandpass filter that have electric resistance inverter and series-type of resonating chamber. The electric resistance inverter parametric quantity K01, K12, to Kn, n+1 will match to coveted form of response harmonizing to the specification and can be happen utilizing equation 2.37 to 2.40. Equation 2.37 is reactance slope parametric quantity from figure 2.8 response for the bandpass filter and selected randomly to be of any size corresponding to convenient resonating chamber design. Normally, the value of expiration RA, RB, and the fractional bandwidth, a?† may be specified as desired. The coveted form of response is so insured by stipulating the impedance-inverter parametric quantity. If the resonating chamber of the filter consist of a lumped component, inductance and capacitance, and if the electric resistance inverter were non frequency sensitive, the equation below would be exact regardless the fractional bandwidth of the filter. ( G. Matthaei, 2000 )

J12

J01

Jn.n+1

J23

Tabun

Sarin

B1 ( tungsten )

B1 ( tungsten )

B1 ( tungsten )

## Figure 2.9 A generalised band-pass filter circuit utilizing entree inverters

## Figure 2.10 Susceptance of jth resonating chamber

Figure 2.9 shows a generalised circuit for a bandpass filter that have admittance inverter and shunt-type of resonating chamber. The electric resistance inverter parametric quantity J01, J12, to Jn, n+1 will match to coveted form of response harmonizing to the specification and can be happen utilizing equation 2.41 to 2.44. Equation 2.41 is reactance slope parametric quantity from figure 2.10 response for the bandpass filter and selected randomly to be of any size corresponding to convenient resonating chamber design. Normally, the value of expiration GA, GB, and the fractional bandwidth, a?† may be specified as desired. The coveted form of response is so insured by stipulating the admittance-inverter parametric quantity. If the resonating chamber of the filter consist of a lumped component, inductance and capacitance, and if the electric resistance inverter were non frequency sensitive, the equation below would be exact despite the fractional bandwidth of the filter. ( G. Matthaei, 2000 )

Rubidium

RA

K23

Kn, n+1

Lrn

Lr2

Crn

Cr2

K01

K12

Lr1

Cr1

## Figure 2.11 The band-pass filter in figure 2.5 converted to utilize lone series resonating chambers and electric resistance inverters. ( G. Matthaei, 2000 )

## 2.6 Iris and H-plane Offset Rectangular waveguide filter

Iris or besides known as pit rectangular wave guide bandpass filter is illustration of one type of waveguide bandpass filter as shown in figure 2.13. The iris type of rectangular wave guide bandpass filter has two different design, inductive flag and capacitive flag. Material used depends on the application of the rectangular wave guide so that the wave guide fulfilled the demand in many term and besides the specification. The stuff must hold the ability to keep the energy of the moving ridge inside the wave guide and map. H-plane offset different with the flag in term of design. Both can be called as an flag, but to distinguish between the type of flag and besides the coordination between Windowss of the waveguide filter.

## Figure 2.12 Example of rectangular wave guide bandpass filter ( Wu, 2009 )

## 2.6.1 Filter Model of series of parallel inductive and capacitive

The Iris and H-plane rectangular wave guide are design from tantamount circuit transform from the paradigm utilizing the resonating chamber and electric resistance or entree inverter. This circuit stand foring a series of parallel or shunt inductive or capacitive and between it is electrical length. The value of inductance or capacitance can be calculated utilizing the g parametric quantity depending on the specification of the filter. All the values are normalized based on the features electric resistance. Inductive flag was design where the flag metal plane is modelled as parallel inductive shunts between transmittal lines of electrical length as shown in figure 2.13 where the value of inductance is based on the resonating chamber and inverter of the response desired. Figure 2.14 shows the tantamount circuit of a capacitive flag and it is different with tantamount circuit in figure 2.13 in term of constituent used and besides the tantamount circuit parametric quantity that will be used to plan the flag filter afterword.

I?N

I?2

I?1

Z0

Z0

jXN+1

jXN

jX3

jX2

jX1

## Figure 2.13 Equivalent circuit of an Iris filter where the flag metal plane are modelled as parallel inductive shunts between transmittal line of electrical length, I?

I?N

I?2

I?1

Y0

Y0

jB3

jB2

jB1

jBN+1

jBN

## Figure 2.14 Equivalent circuit of an Iris filter where the flag metal plane are modelled as parallel capacitive shunts between transmittal line of electrical length, I?

Figure 2.13 and 2.14, show that the tantamount circuit that can be used as a modelled of an flag and H-plane offset filter. The figure of inductive or capacitive will depended on the figure of order. The figure of order determines the specification of the design. However, both inductive and capacitive will hold different type of design in term of iris form. To plan the flag, symmetrical window needed to be used to happen the value of the iris breadth. For the H-plane beginning, asymmetrical window needed to be used to happen the H-plane beginning breadth.

## 2.6.2 Iris and H-plane Offset Configuration

The circuit shown in figure 2.13 and figure 2.14 are change overing to iris design by utilizing tantamount circuit parametric quantity as shown in figure 2.17 to calculate 2.20. Iris construction contains a geometrical discontinuity and design as a four terminus or two terminal brace. The description of the propagating manners is effected by representation of the input and end product wave guides as transmittal lines and by representation of the discontinuity as a four terminal-constant circuit as in figure 2.19 to calculate 2.23. Quantitatively, the transmittal line requires the indicant of their characteristic electric resistance and extension wavelength, the four terminal circuits and the location of the input end product terminus.

## dn, n+1

## dn-1, N

## d23

## d12

## d01

## Z0

## Z0

## I?2

## I?N

## I?1

Xn, n+1

Xn-1, N

X23

X12

X01

## Figure 2.17 Top position of pit filter construction for shunt-inductance coupled waveguide filter

Figure 2.17 shows a top position of pit filter for shunt induction coupled waveguide filter. Basically, the pit filter is being converted from the shunt or parallel induction as shown in figure 2.13. Based on the figure, the of import parametric quantity needed to be calculated is the electrical length which is the length between flag and besides the breadth of the flag, d. For this instance, the flag thickness is being assumed to be about zero. Hence, the tantamount circuit that can be used to happen the of import parametric quantity is shown in figure 2.19 to calculate 2.20 utilizing the equation 2.34 to equation 2.40. The flag that can be design is either capacitive flag utilizing shunt-capacitance or inductive flag utilizing shunt-inductance.

The other design of rectangular wave guide is H-plane beginning rectangular waveguide bandpass filter. Basically, the design have the same process with the flag rectangular bandpass filter design but different in term of tantamount circuit parametric quantity. From the definition, the design is merely countervailing the H-plane and do the rectangular wave guide has different size of obstructions. The obstruction will filtrate out the unwanted frequence harmonizing to the specification.

## Z0

## I?2

## I?N

## I?1

## d23

## d12

## d01

## dn, n+1

## dn-1, N

## Z0

## X01

## X12

## X23

## Xn-1, N

## Xn, n+1

## Figure 2.18 Top position of H-plane offset filter construction for shunt-inductance coupled waveguide filter

Based on figure 2.18, the H-plane beginning filter construction are converted from figure 2.13 which is the shunt-inductance construction by utilizing the tantamount circuit parametric quantity of asymmetrical construction as shown in figure 2.21 and 2.22. The construction has the same breadth, B at all construction from input to end product despite the size of the window cause by the offsetting of H-plane. The parametric quantity of electrical length, I? can be calculated utilizing measure same with the flag rectangular wave guide.

## 2.6.3 Symmetrical Window

jB

Y0

Y0

B

vitamin D

Thymine

d’/2

Tocopherol

## Figure 2.19 Equivalent circuit parametric quantity for capacitive two obstructions and window in rectangular wave guide ( N.Marcuvitz, 1993 )

Where

For the symmetrical instance d’=b – vitamin D:

Figure 2.19 shows the tantamount circuit parametric quantity for the unsymmetrical instance where. The window or the flag is formed by two obstructions which are up and down of the rectangular wave guide. However for this equivalent, there is limitation that is of import to using this expression. The tantamount circuit on figure 2.19 and equation 2.45 to equation 2.48 is valid in the scope b/I»g & lt ; 1/2 for unsymmetrical instance and b/I»g & lt ; 1 for the symmetrical instance. For equation 2.45, its can use merely in the scope 2b/ I»g & lt ; 1 with an estimated that occur less that 5 % at the lowest wavelength scope. Equation 2.46 is applicable in the scope b/ I»g & lt ; 1 with an mistake of less than approximately 5 % and in the scope 2b/ I»g & lt ; 1 to within 1 % . Equation 2.47 is a little portion estimate that agrees with equation 2.46 to within 5 % in the scope d/b & lt ; 0.5 and b/ I»g & lt ; 0.5. The little obstruction estimate which is the equation 2.48 agrees with equation 2.46 to within 5 % in the scope d/b & gt ; 0.5 and b/ I»g & lt ; 0.4.

The measures B I»g/Y0b and Y0b/B I»g from equation 2.46 are represent in the signifier of graph as shown in appendix B. The graph is plotted as a map of d/b with b/ I»g as a parametric quantity.

## Z0

## Z0

## jX

## Thymine

Tocopherol

a

vitamin D ‘

vitamin D ‘

vitamin D

## Figure 2.20 Equivalent circuit parametric quantity for inductive two obstructions and symmetrical window in rectangular wave guide ( N.Marcuvitz, 1993 )

Where

The design of iris rectangular bandpass filter utilizing tantamount circuit parametric quantity in figure 2.20 and equation 3.49 to equation 2.51 besides have certain limitation needed to be follow. The equivalent is applicable in the wavelength scope between 2/3a & lt ; I» & lt ; 2a. Equation 2.49 is estimated to be in mistake by less that 1 % in the scope a & lt ; I» & lt ; 2a but for scope 2/3a & lt ; I» & lt ; a the mistake is larger. The estimate signifier which is equation 2.39 valid in small-aperture scope, agrees with equation 2.49 to within 4 % for vitamin D & lt ; 0.5a and a & lt ; 0.92I» . For equation 2.51 is valid in the small-obstacle scope of vitamin D ‘ & lt ; 0.2a and a & lt ; 0.9I» agrees with equation 2.49 to within 5 % .

The equation 2.49 is represented in the signifier of graph as in appendix C where XI»g/Z0a is plotted as a map of d/a for the scope 0 to 0.5 and for assorted values of a/I» .

## 2.6.4 Asymmetrical Window

## jB

## Y0

## Y0

## vitamin D

## B

Thymine

d’/2

Tocopherol

## Figure 2.21 Equivalent circuit parametric quantity for capacitive one obstructions and window in rectangular wave guide ( N.Marcuvitz, 1993 )

Based on figure 2.22, the tantamount circuit parametric quantity has the same limitation as to calculate 2.19 except that the value of I»g is replaced by I»g/2 and besides for the aforethought graph, if the I»g is replaced by I»g/2, a secret plan of B I»g/2Y0b as a map of d/b with 2d/I»g as a parametric quantity where B/Y0 is now the comparative susceptance of a window formed by one obstruction.

## Z0

## Z0

## jX

## Thymine

Tocopherol

vitamin D

a

vitamin D ‘

## Figure 2.22 Equivalent circuit parametric quantity for inductive one obstructions and asymmetrical window in rectangular wave guide ( N.Marcuvitz, 1993 )

Where

In this undertaking, figure 2.23 is being used as the tantamount circuit parametric quantity in the H-plane beginning rectangular waveguide filter since the shunt-inductive is used. For figure 2.23, the tantamount circuit is applicable in the wavelength scope a & lt ; I» & lt ; 2a. Equation 2.55 is valid in the wavelength scope a & lt ; I» & lt ; 2a with estimated mistake of approximately 1 % . Equation 2.56 valid for the little aperture scope agrees to within 5 % if d/a & lt ; 0.3 and a/I» & lt ; 0.8. Furthermore, equation 2.57 is valid in the little obstruction scope for d’/a & lt ; 0.2 and a/I» & lt ; 0.8 to within 10 % .

From equation 2.55, a graph can be obtained and plotted as shown in appendix D where the graph Z0a/XI»g is plotted as a map of d/a in the scope of 0.1 to 0.7.

## 2.7 Fabrication Procedure

There are several ways to manufacture the wave guide for case, utilizing milling machine. However, type of fiction procedure is selected based on the size, cost and clip. Milling is the procedure of machining level, curved, or irregular surfaces by feeding the work piece against revolving cutter. Milling machine is a tool that can be used to machine work piece or solid stuffs, runing from aluminum to stainless steel. Basically, it can be classified as horizontal and perpendicular. This is mentioning to the machine orientation of the spindle. The milling machine can execute several Numberss of operations such as cutting, be aftering and boring. The preciseness of the design depend on the milling cutter and besides the engineering system of the machine. It can be runing manually or automatically utilizing computing machine numerical control ( CNC ) .

Milling machine has many types and each type is characterized by category of signifier, either perpendicular or horizontal and besides the chattel of the spindle. Types of milling machine such as knee-type, cosmopolitan horizontal, ram-type, cosmopolitan ram-type, and swivel cutter caput ram-type milling machine. Milling machine tools and equipment such as milling cutters are normally made of high-velocity steel and are available in a great assortment of forms and sizes for assorted intents. Even the milling cutter may be made with assorted type such as proverb dentitions, coiling milling cutters, metal slicing saw milling cutter, side milling cutters, end milling cutter, T-slot milling cutter, waldmeister keyslot milling cutters, angle milling cutters, gear goblin, concave and convex milling cutter, corner rounding milling cutter, and particular shaped-formed milling cutter. Figure 2.23 shows the milling machine with its of import portion.

## Vertical

A: Random-access memory

Bacillus: Vertical Head

Degree centigrades: Quill

Calciferol: Table

Tocopherol: Saddle

F: Crossfeed Handle

Gram: Vertical Feed Crank

Hydrogen: Knee

## Horizontal

I: Vertical Positioning Screw

Joule: Base

Kelvin: Column

Liter: Table Handwheel

Meter: Table Transmission

Nitrogen: Ram Type Overarm

Oxygen: Arbor Support

Phosphorus: Spindle