The Art Of Microwave Planar Filter English Language Essay

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The microwave filter is an essential component in a huge variety of electronic systems including the telecommunication system such as in mobile radio, satellite communication and radar. This component used to select or reject signal at different frequencies. The microwave filter contained some components or a part that functions are depends on the specific applications. Besides, the desired frequency response can be obtained by the use of filters component. Filters can be designed at low cost with precise frequency response as desired and also can be fabricated either from lumped element or distributed element or combination of both elements. Thus, these all component of microwave filter is required for filter realization. In addition, the choices of topologies is depends on the characteristic of the filters such as chebyshev or elliptic, size and power handling.

For filter realization, there are two general steps are required; synthesis and technological implementation. The synthesis of filter plays important roles because it allows to identify the essential elements in the topology circuit and to define the electrical characteristics of the filter. The circuit elements of the topology include their electrical length and the value of impedances. While, the primary parameters of interest in the electrical characteristic are the bandwidth, level of rejection, attenuation, and the frequency range. At this stage, the circuit parameters are defined and the electrical characteristics can be controlled by these parameters for example, the characteristic impedance of coupled lines. In the technological implementation, the choices of substrates are very important. In practically, choosing the substrates are depends on the few factors such as size, higher-order modes, surface wave effects, dielectric loss, power handling and ect.

Therefore, in this chapter will discuss the components that contribute in the synthesis process on the development of new topologies of coupled lines filter which introduced filter with better performance in terms of selectivity and their bandwidth.

Microwave Planar Filter Design, Topology and Technology

This section will begin with a general discussion of the microwave filter theory and design which consist of synthesis method, filter implementation using transformation tools, coupled lines topologies, and planar technologies for filter implementation.

Microwave Filter Theory

Microwave filter is broadly use in many applications. It consists of a components or parts where the function is depends on the require specifications of the application. Microwave filter mostly used to control the frequency response at a certain point in microwave system by providing transmissions at frequencies within the passband of the filter and attenuation in the stopband of the filter [1]-[3]. The most common filter can be categorized into four main types which are:

Low Pass Filter

High Pass Filter

Band Stop Filter

Band Pass Filter

The frequency responses of these types of filter are illustrates in Fig. 2.1. In addition, an ideal characteristic of these filters shows zero insertion loss, constant group delay over the desired passband and infinite rejection. In practically, these characteristics are only achieved in high frequency limit for any given practical filter structure where its characteristics will degenerate due to the junction effects and resonances within the elements.


(c) (d)

Figure 2.1. Four types of filter characteristics (a) Low pass, (b) High Pass,

(c) Band Stop, (d) Band Pass

Generally, to design a filter, the following parameters are defined to characterise its frequency characteristics:

Pass bandwidth

Stop band attenuation and frequencies

Input and output impedances

Return loss

Insertion loss

Group delay

The amplitude of the filter response is the most important parameter in designing a filter which concentrates on the insertion loss and frequency characteristics.

Synthesis method of Filter Design

In microwave filter design, the most popular techniques of synthesis were used which is using parameter method and the insertion loss method. Based on these two methods, insertion loss method is more preferable and suitable for filter that is going to synthesize because it gives complete specifications of frequency characteristic which over the entire pass and stop bands.

Basically, the basic design of microwave filter such as low pass, high-pass, band-pass and band-stop operated at arbitrary frequency bands and between arbitrary resistive loads. Such basic filters are designed based on the prototype low pass filter through frequency transformation and element normalization. Normally, the element values are determined based on the low pass response approximation such as Butterworth (called as Maximally flat or Binomial) and Chebyshev or equal ripple passband response. The response shapes of the filter are controlled by the values of the element coefficients (g0, g1… gn+1) as defined in Fig. 2.2 low pass filter prototype.

Figure 2.2. Low pass filter prototype.

The Butterworth filter utilizes a maximally flat frequency response which is no ripple in the passband. Using this approximation the attenuation in the stopband constantly increased. The expression of insertion loss for Butterworth low pass filter is given by:

The passband range is from = 0 to = and the maximum insertion loss in the passband is 3 dB at where equal to 1. The angular frequency of the passband edge, ω`c and resistance r are normalized equal to unity, respectively where ω`c is measured in radians/second. The characteristic response of Butterworth is illustrates in Fig. 2.3.

Figure 2.3. The characteristic response of insertion loss for Butterworth low pass filter

Chebyshev filters have more passband ripple or stopband ripple compared to Butterworth filter. It is also called as equal ripple or minimax which have a steeper passband edge which can minimize the error between idealized and actual filter characteristic over the range of the filter. However, it exhibits a ripple in the passband. The approximation of insertion loss for Chebyshev low pass filter is given by:


n = the degree of approximation which called as number of reactive elements

am = the ripple factor

Tn () = Chebyshev polynomial of degree n

In this case, the insertion loss oscillates between 1 and in the passband response. So that becomes at the cut off frequency and increases monotonically beyond stop band . The characteristic response of Chebyshev are illustrates in Fig. 2.4.

Figure 2.4. The characteristic response of insertion loss for Chebyshev low pass filter

The element values of low pass ladder network can be derived using both type of filter Butterworth and Chebyshev, respectively. The normalization values can be calculated based on the following equation.

Prototype element values for Butterworth:

for all n

The response of n order for Butterworth function is depicted in Fig. 2.5.

Figure 2.5. The characteristic response of n order for Butterworth function

Prototype element values for Chebyshev:

for all n odd

for all even n


The response of n order for Chebyshev function is illustrates in Fig. 2.6.

Figure 2.6. The characteristic response of n order for Chebyshev function

Filter Implementation Using Transformation Tools

In section 1.2.2 discussed the types of filter response that commonly used in microwave filter. This several type of filter gives some general solutions for low pass filter transformation element. However, they generally work at low frequency. Based on the concept of these types of filter, many topologies have been proposed. The use of these concept helps to design a filter according to the specifications.

In this section, some of transformation tools are discussed where the possibility to improve the filter response at high frequencies is high. At microwave frequencies, lumped elements are generally difficult to implement due to the limited range of values and the distances between the components. Therefore, Richard's transformation and Kuroda's identities are used to convert the lumped element to transmission line and separate the filter element using the transmission line sections, respectively.

Richard's Transformation

This transformation was proposed in order to synthesize an LC network using open and short circuit transmission line stubs. The reactance of lumped element such inductor and capacitor basically have different mathematical form to that of transmission line stubs. The equation is given as follows;

For inductor;

For Capacitor;

In addition, the impedances of transmission line stubs and lumped element are different functions according to the chosen frequency. Some of the equivalent circuits derived using Richard's transformation at different length of line stubs are illustrates in Table 2.1.

Table 2.1: Equivalent Circuit of the Transmission Line at Open and Short Circuit with Different Length.

l =

l =

l =

Kuroda's Identities

The four Kuroda's Identities are used in the implementation of microwave filter in order to separate the transmission line stubs, to transform the series stubs into shunt stubs or vice versa and also to change the impractical characteristic impedances into more realizable one. The four identities are illustrates in Table 2.2 where each box represent a unit element or transmission line that indicates their characteristic impedance.

Table 2.2: Kuroda Identities (n2 = 1 + Z2 / Z1)





The definition of unit element with respective to characteristic impedance is illustrates in Fig. 2.7.

Figure 2.8: Unit element

Impedances and Admittance Inverter

These inverters essentially form the inverse of the load impedance or admittance where they can be used to transform series element to shunt element or vice versa. J and K inverter can be constructed using quarter-wave transformer of the characteristic impedance. The concept of impedance and admittance inverter is illustrated in Fig. 2.8 where this transformation is useful for bandpass and bandstop filter with narrow bandwidth (< 10%).



Figure 2.8: (a) Operations of Impedance and admittance inverter. (b) Implementation as quarter-wave transformer.

Coupled Line Theory

Coupled line is known as a coupled transmission line and largely used in microwave circuits. The coupled line consists of two unshielded transmission line where the lines are closed to each other. The interaction of electromagnetic field of each line presents a fractional of power between the lines. In general, coupled transmission line usually operates in TEM mode and it's suitable for stripline and microstrip structure. Examples of the stripline and microstrip structure are shown in Fig. 2.9.


Figure 2.9. Example of coupled transmission line;

Stripline structure (b) Microstrip structure

The structure of this coupled transmission line consist of three-wire line which can support the propagation modes where it can be use for implementation of filters and directional coupler. Fig. 2.10 shows the structure of three-wire line of coupled transmission and its equivalent capacitance network.

Figure 2.10. A three-wire coupled transmission line and its equivalent capacitance network

There are two types of line which is symmetrical (where both conductors have same dimension) and asymmetrical (have different dimension). The configurations for symmetrical coupled line, both conductors use equal width and having constant gap spacing between the conductors. This structure also called as symmetric and uniformly coupled. For asymmetrical coupled microstrip line, the spacing between the line conductors also constant same as symmetric but the different is the width of the line. This configuration use unequal width of the line conductors. This structure also called as a uniformly coupled asymmetric line. The structure of asymmetric coupled line is shown in Fig. 2.11.

Figure 2.11. Microstrip Coupled line with unequal width (asymmetrical)

For microstrip coupled line, the separation gap between the lines can be variable depends on the applications. If the separation between the lines is large, the coupling effect will reduce thus improve the electrical performances according to specifications. Generally, the fabrication for large separation is easy to fabricate. However, the filter bandwidth can only be achieving less than 20%. Hence, to design a wider bandwidth filter, the separation between the lines require tight coupling gap which are difficult to fabricate.

Next section will discuss the properties of the characteristics single quarter-wave coupled line section where it can be used to design bandpass filter such parallel coupled line filter.

Properties of Quarter-Wave Coupled Line Section

The electromagnetic coupling that interferes between the two transmission lines can be used to design a several filters. The arrangement of some cases of symmetrical coupled line are illustrates in Table 2.3. As indicated in the table, the schematic diagrams of each type coupled line section are shown together with their formula and equivalent circuit. This various circuit have different frequency responses such as low pass, bandpass, all pass and all stop.

Table 2.3: The Canonical Coupled Line Circuit

Coupled Line

Equivalent Circuit

Circuit Parameter

Band Pass

Band Pass

All Stop

All Stop

All Stop

All Pass

Band Pass

Various Filter Topologies

Various topologies have been proposed and invented based on the theory of the coupled lines. Basically, the filter based on the coupled lines more particularly work on the narrow band bandpass filter. As an example, Fig. 2.12 illustrates some of the topologies based on the coupled lines that are used; parallel coupled lines filter, interdigital filter, combline filter and ring resonator filter where the lines are coupled laterally with the ring.

Parallel coupled line filter

Interdigital filter

Combline filter

Ring resonator filter

Figure 2.12. Example of coupled line topologies. (a) Parallel coupled line filter (using lines of quarter of wave and resonator half wave), (b) Interdigital filter, (c) Combline filter, (d) Ring resonator filter

Parallel Coupled Line Filter

The relationship between the immittance inverter and coupling between the lines are very important in designing a parallel couple line filter. As discus in previous section, immittance inverters, J and K inverter can be constructed using quarter wave transformer or using lumped element. However, for the case of parallel coupled line, the resonator width and the separation gap between the lines are controller for the immittance inversion. The basic coupled line section and admittance inverter are illustrates in Fig. 2.13. It seen that, two transmission line resonator length θ are coupled together by an admittance inverter.

Figure 2.13. Equivalent circuit of coupled line section.

For parallel coupled line filter of nth section, the admittance inverter implemented at each coupling section where the value of J01, J12, and Jn+1 for each coupling are different based on the specification. The arrangement of nth section parallel coupled filter is shown in Fig. 2.14.

Figure 2.14. Parallel coupled line of nth section.

Based on this arrangement, the formula of the characteristic admittance of J-inverter can be calculated using ABCD matrix. The ideal admittance inverter can be obtained by substituted θ = -90 degree and Z0 = J in the ABCD matrix of the transmission line of electrical length and characteristic impedance Z0. Hence, the ABCD parameter of the ideal admittance inverter is computed as follows;

The ABCD parameters of this admittance inverter were calculated by considering it as quarter wave length of transmission of characteristic impedance, 1/J. At this point, the J inverter for the various section are refer to the low pass normalized elements values, g0, g1, . . . , gn+1 given as follows:

where Δ = (ω2-ω1)/ω0 is equal the fractional bandwidth of the filter. To determine the overall microstrip layout dimensions (width and spacing) of the parallel coupled line, the formula of the characteristic impedance even and odd mode are computed as follows:

For example, let consider a design parallel coupled line bandpass filter of order three (n=3) which centered at 1 GHz. The filter performance can be obtained by full wave electromagnetic simulation (EM) and an example of final layout of this design is presented in Fig. 2.15 with its EM simulated passband performance.



Figure 2.16. Overall layout with its EM simulated passband performance.

Interdigital Filter

In the past few years, interdigital line structures are commonly used as slow wave structures [1-3]. However, interdigital lines also have very interesting interdigital bandpass filter properties. As an example, the typical interdigital line filter with short and open-circuited line is shown in Fig. 2.17.



Figure 2.17. Interdigital filter (a) short-circuited lines at the ends, (b) open-circuited lines at the ends

The structure of this filter consist of arrays of TEM-mode transmission line resonator between parallel ground plane. In the Fig. 2.17(a), each resonator line is a quarter-wavelength long at the mid-band frequency. The lines are short-circuited at one end and open-circuited at the other end. This resonator element are arrange in parallel array with the positions of the short-circuited ends alternating. While in Fig. 2.17(b), the terminating lines are open circuited and particularly work for the filter with moderate to wide bandwidth which is around 30 percent or greater.

In the study, the interdigital filter is one of the most popular structures that have very attractive features. The structure of this filter is very compact and uses the available space efficiently. It can be designed either narrow or wide bandwidth (30 to 70 percent) depending on the applications. In addition, the tolerances required in their manufacturer are relatively relaxed since the spacing between the resonator elements is large. In this filter, there is no possibility of spurious response exist because the second passband is centered at three times the center frequency, 3f0, of the first passband and the rates of cutoff and strength of the stopbands can be enhanced by multiple poles of attenuation at dc and at even multiples of the center frequency of the first passband. This filter also can be fabricated without dielectrics, thereby eliminating the dielectric losses.

Combline Filter

The typical combline filter schematic in strip-line form is shown in Fig. 2.17. This resonator filter consist of TEM mode transmission line elements that are short-circuited at one end and consist of lumped capacitance Csj between the other end of the resonator line element and ground. In the schematic diagram, the lines 1 to n along with the capacitances element Cs1 to Csn comprise resonator, while lines 0 to n+1 are not comprise as a resonator since it were some part of impedance-transforming sections at the ends. In this filter, the coupling between the resonators is achieved by means of fringing field between the resonator lines.

Figure 2.17. Schematic of combline filter.

The lumped capacitances Csj allow the resonator lines to be less than λ0/4 long at resonance. In this case without these capacitances, the resonator line would be fully λ0/4 long at resonance, so that the passband would not have in the structure. This is because without some kind of reactive loading at the end of the resonator lines, the magnetic and electric coupling effects would cancel out each other so that the structure of the combline will become an all stop structure. Therefore, to achieve resonance the resonator lines with capacitively loaded the length of the lines must be less than 90 degrees long at center frequency. As an example, if the capacitance are made relatively large and the length lines are 45 degrees or less, the structure would be very compact and efficient coupling structure. In order to make the loading capacitor in this filter large so that the resonator will be λ0/8 or less. However, in this filter, if the length of the line resonator is λ0/8 long at the center frequency, the second passband will be located at slightly over four times the center frequency, 4fo.

In the theory, the attenuation through the filter will be infinite at the frequency for which the resonator lines are λ0/4 wavelength long. This is because the attenuation above the primary passband is very high and depends on the electrical length of the resonator lines. In other words, the closer to λ0/4 long the resonators are at the passband center, the steeper the rate of cutoff will be above the passband. This type of filter can be fabricated without dielectric support material and if desired the dielectric losses also can be eliminated.

Ring Resonator Filter

The ring resonator is a transmission line which form in closed loop function. The topology of ring resonator was introduced by Woff and Knoppik for microwave substrate measurement [3]. The basic circuit of ring resonator is very simple which consist of the feed lines, coupling gap and the resonator. Fig. 2.19 shows an examples circuit arrangement of ring resonator.



Figure 2.19. Examples of ring resonator (a) ring resonator with asymmetrical feed lines and notch, (b) Ring resonator side coupled via quarter wavelength lines

In this filter, the power is coupled into and out of the resonator through coupling gap and feed lines. The distance between the feed line and the resonator give an impact to the coupling gaps; thereby affect the resonant frequencies of the ring. One of the advantages of this resonator is it can support two degenerate modes which are orthogonal and have identical resonant frequencies. The uniform ring resonator is fed by an asymmetric arrangement of feeding lines or by perturbation along the ring thereby the degenerate modes become coupled and resulting in a narrow band bandpass response. Besides, there exists two transmission zeros near the fundamental frequency that located at both side of the passband.

In addition, ring resonator either end-coupled or side-coupled to the microstrip transmission line has very interesting features. The use of quarter wavelength side coupled lines to feed the ring introduced the two-tier resonance in the passband. Besides, the electric characteristics of the resonator such as matching level in the passband, bandwidth and transmission zeros frequencies can be controlled by varying the characteristic impedance of the coupled line (even- and odd-mode) and also line impedance of the ring resonator. The examples of the application ring resonator are shown in Fig. 2.20.

Figure 2.19. Application of side coupled ring resonator.

Various Planar Technologies For Filter Implementation

In the microwave systems, the transmission line media such as coaxial lines, waveguide and planar is very important elements for high frequency realization. The development of this transmission line media is characterized for low loss transmission of microwave power. Choosing the right physical elements of transmission line media is depends on the several factors such as frequency range, physical size, power handling capability and production cost [25].

In the early of microwave systems, waveguide have their own advantages in term of capability of power handling and losses. However this type of transmission line media having a bulky size and high cost during the production. High bandwidth is one of the require specification in electrical characteristic of filter. So that, coaxial line is convenient for the application that having high bandwidth. However, it is not suitable to fabricate filter that having complex microwave components [26].

Planar transmission line structures are mostly employed for microwave integrated circuits and monolithic microwave integrated circuits (MICs). The geometry of planar configuration implies that characteristics of the element can be determined by dimensions in a single plane. Basically, the complete transmission line circuit can be fabricated in one step using thin film technology and photolithography techniques. There are several transmission structures that satisfy the requirement of being planar. The most common of these configurations are:


Microstrip Lines

Coplanar Waveguide (CPW)


The symmetric stripline is reliable method for creating a transmission line. The stripline is a TEM (transverse electromagnetic) transmission line. Stripline is well known as a planar type of transmission that lends itself to microwave integrated circuit and photolithographic fabrication. The geometry of a stripline is illustrated in Fig. 2.24 where it consists of three signal layer to accommodate a single signal carrying conductor.

Figure 2.24. The geometry of a stripline.

It is constructed with a flat conductor suspended between two ground planes where the conductor and ground planes are separated by a dielectric [2, 8]. The electric field in such lines propagated perpendicular to the center and its ground conductors and also concentrated over the width of the center conductor. The propagation characteristic in such line is nearly TEM mode where Fig. 2.25 shows the fringing fields lines at the edges of the center strip.

Figure 2.25. Electric and magnetic field lines

A major advantage using strip transmission line is that the conductor is practically self-shielded. The possibility of the radiation loss would be from the sides of the stripline structure. At this point, the structure of stripline behaves in a very predictable way and the characteristic impedance of the conductor is solely controlled by width of the conductor stripline. In addition, the uses of stripline in realization of filter offer better bandwidth in their characteristics performance.

However, like other transmission line media, stripline also have some disadvantages. There are two major points that has been listed. At first, it is much harder and difficult to fabricate than other type of planar transmission line. It is noted that, the structure of stripline having some number of layers. Therefore, this type of transmission line will cause difficulties in fabrication using PCB. This is because the signal conductor must be sandwiched between two layers of dielectric. Thus, it will costly in the production process.

The second point is a stripline transmission line also requires three separate layers to be dedicated to a single transmission line. The strip width and the board thickness at the second layer ground plane are much narrower for a given impedance such 50 ohm. This can be a problem if other components need to be attached to the line [2, 7, 16]. Fig. 2.26 illustrates the stripline fabricated transmission line.

Figure 2.26. Stripline Fabricated Transmission Line


Microstrip is a type of electrical transmission line which is one of the most popular types of planar. Microstrip can be fabricated by photolithographic process and is used to convey microwave frequency signals. It is easily integrated with other passive and active microwave devices. In the general structure of this planar transmission line, microstrip consists of a single ground plane and a thin strip conductor on a low loss dielectric substrate above the ground plate. A conductor of width W is printed on a thin, and grounded with dielectric of thickness d and relative permittivity εr. The general microstrip structure is illustrates in the Fig. 2.27. While in Fig. 2.28 illustrates the field lines that consist on the microstrip conductor.

Figure 2.27. General microstrip structure

Figure 2.28 Electric and magnetic field lines

Like other planar transmission line, microstrip also has disadvantages. One of the disadvantages of this microstrip is radiation loss. Microstrip lines basically suffer more radiation loss compared to the stripline transmission line. It is note that a stripline has a minimal radiation loss. This is because the signal conductor is surrounded by a uniform dielectric material which is, in turn, confined by ground planes (see Fig. 2.29) [7, 20]. In fact, microstrip lines have a dielectric interface between dielectric material and free space at the signal conductor which causes the radiation loss [7, 18].

One major advantage of this microstrip line is the size of the circuit can be reduced because the signal conductor for microstrip line is exposed to free space of uniform dielectric constant ε0 (typically the surrounding environment is air and ε0 = 1). In addition, microstrip also easy to fabricated using standard PCB techniques because microstrip topology only requires two signal layers. The characteristic impedance (Zo) of the signal conductor is controlled by the various geometries as defined in Fig. 2.31.

Figure 2.29. Microstrip geometry definition


T = conductor thickness

W = conductor width

H = dielectric material thickness

ε0 = dielectric constant of free space

ε = dielectric constant of material

The ground plane and the signal conductor residing on separate layers is the types of coupling that can be utilized. Fig. 2.32a represents a 3-Dimension of a microstrip line and shows some of the possible coupling techniques that can be employed. While, Fig. 2.32b illustrates end coupled between the microstrip lines. At this point, the signal is capacitively coupled across the gap on the signal conductor. Fig. 2.32c illustrates the parallel coupled between the two microstrip lines where the signal is capacitively coupled between the overlapping parallel lines [7, 16, 32].

Figure 2.29. 3-Dimension of microstrip line

The main advantage to the microstrip line is the adaptability to many different coupling schemes (end coupled, parallel coupled, variations on parallel coupling). The advantages of microstrip have been well established, and it is a convenient form of transmission line structure for probe measurements of voltage, current and waves.

Coplanar Waveguide

CPW transmission lines also have advantages and disadvantages as compared to microstrip lines. CPW lines require only a single layer on which both signal conductor and ground planes reside [7, 20]. Typical CPW geometries are defined in Figure 2.33.

Figure 2.29. Coplanar waveguide geometry definition


S = spacing between conductor and ground plane

W = conductor width

ε0 = dielectric constant of free space

ε = dielectric constant of material

The geometry of the CPW line allows for convenient connection of the signal conductor to the ground layer. Although this connection is simpler to achieve as compared to the microstrip topology, the problem of parasitic inductance still persists albeit on a smaller scale. This smaller parasitic inductance is still present because any connection will still add distance to the path the signal must travel [7, 20]. As in the microstrip case, the ease of fabrication using standard PCB practices and accessibility of the signal conductor advantages still apply. A disadvantage of CPW lines from a theoretical standpoint is the area of the ground planes. According to CPW theory, these ground planes should extend to infinity as illustrated in Figure 2.34. In a practical situation, if the ground plane is greater than three times the signal width (W) the performance discrepancy is negligible [7, 16, 20].

Figure 2.29. Cross section of theoretical infinite CPW ground planes

Overall, the stripline, microstrip, and CPW transmission line technologies have many advantages and disadvantages. Table 2.6 outlines a few general differences between the three transmission line types.

Transmission Line Type





Conductor layer Required




Signal Conductor Access




Construct using standard PCB Techniques




Stripline type transmission line suffers from lack of access to signal conductor, complicated fabrication, and a high layer count as compared to the two other types. The required non standard fabrication techniques make this a less attractive transmission line option [2, 16]. The main disadvantage to the microstrip line is the parasitic inductances associated with grounding the signal conductor. The main advantage to the microstrip line is the adaptability to many different coupling schemes (end coupled, parallel coupled, variations on parallel coupling). The main disadvantage the CPW line has is the inability to utilize parallel coupled lines with a truly CPW transmission line [7, 16]. By virtue of ease of fabrication and coupling versatility, the microstrip transmission line is the best choice of the three transmission lines discussed.


In this chapter we discussed about a short state of the art of microwave planar filter. The parameters involved in development of filter synthesis are necessary in order to develop a new concept of coupled line filter topology. The topologies that proposed in this chapter introduced numerous advantages. The concept of parallel coupled lines and ring resonator that proposed in this chapter is use in designing a topology of dual-path coupled line filter.

The global synthesis of dual-path coupled lines will be discussed in the next chapter. Besides, the microstrip planar technology is used for the filter implementation.