# Theoretical Background WIMAX Background Computer Science Essay

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The rising demand for internet and wireless multimedia applications has encouraged the development of broadband wireless technologies in the last few years [1]. In June 2004, the Institute of Electrical and Electronic Engineers (IEEE) developed standard 802.16, more generally known as the Worldwide Interoperability for Microwave Access, or WiMAX. WiMAX will change the principle of telecommunications as it is currently known all over the world. It eradicates the lack of resources that has plagued current service providers for the last century.

WiMAX mainly offers a throughput of 72 Mbps for up to 30 miles (50km) point to point and also it supports a non-line-of-sight (NLOS) within 4 miles (6.7km) using a point to multipoint distribution technology. It can distribute to almost any number of subscribers nearly to any bandwidth, depending on network architecture and subscriber density [2].

With the possible exception of terminating a voice call via a PSTN number, calls may not use the PSTN. As Voice over Internet Protocol (VoIP) technologies can be used for mobile telephony as well, it will soon be possible to replace the cell phone infrastructure for only a small fraction of the cost needed to build the cell-phone network in the first place. This can simply be done by use of a WiMAX mobile phone and access to a WiMAX base station (the same base stations that delivers VoIP, broadband internet access, and TvoIP to residences and businesses). WiMAX will be able to use the TV over Internet Protocol (TvoIP) technology; this technology does for cable TV exactly what VoIP technology does for telephone companies. It will be possible to transmit a cable TV program with a broadband Internet connection like WiMAX, displayed on a normal TV set with no extra skills required. Finally, WiMAX can beam 72 Mbps for 30 miles with an infrastructure cost of a few thousand only compared to multibillion fiber optic networks thus making it the perfect idea or solution for a backbone.

## WiMAX Frequency Spectrum

Till now no uniform global licensed spectrum for WiMAX, however the WiMAX forum has published three licensed spectrum profiles: 2.3Â GHz, 2.5Â GHz and 3.5Â GHz, in an effort to drive standardisation and decrease cost.

Figure 2.1: WiMax spectrum profiles

## WiMax Transceiver

BandPass Filters

Figure 2.2: WiMax Transceiver

General WiMax transceiver as shown in fig - 2.2 above usually has two filters (one at the Trasmitter terminal and one at the Receiver terminal), the porpuse of these filters is to select the signal having frequency which is within the system desired frequencies and to filter out signals having frequencies out of the desired range, thus the filter used for this condition is a Bandpass filter which allows signals to be trasmitted or received only if they are within a spesific frequency band.

The reason for using a Bandpass filter is that the WiMax system will not interface with the other wireless systems such as Wi-Fi, Bluetooth and others which using another frequency bands.

## Microwaev Filter

Microwave filters are two-port network used to control the frequency response at a point in a microwave system by providing transmission at frequencies within the Passband of the filter (zero attenuation) and attenuation in the Stopband of the filter (infinite attenuation) , typical frequency responses include Lowpass, Highpass, Bandpass and Bandstop filter [3], and their characteristics are:

Lowpass filter: Allows trasmission of signals having frequencies ranging from zero to a spesific frequency called Cutoff frequency (fc) , and rejects frequencies above fc

Highpass filter: Allows transmission of signals having frequencies ranging from Cutoff frequency fc and above, and rejects frequencies below fc.

Bandpass filter: Allows transmission of signals having frequencies ranging from f1( lower frequency) to f2(higher frequency), and rejects frequencies out of this range.

Bandstop filter: Rejects transmission of signals having frequencies ranging from f1(lower frequency) to f2(higher frequency), and allows frequencies out of this range.

In reality an ideal filter with zero attenuation at Passband and infinite attenuation at Stopband cannot be achieved, so in practice the aim is to design a filter with high approximately to the ideal filter by using different approaches and different techniques.

Lowpass filter Highpass filter

Bandpass filter Bandstop filter

Figure 2.3: typical frequency responses

Microwave filter is also divided into two types:

Passive filter: Passive implementations of linear filters are based on combinations ofÂ resistorsÂ (R), inductorsÂ (L) andÂ capacitorsÂ (C). These types are collectively known asÂ passive filters [4].

The output power of a Passive filter is smaller less than the Input power due to the loss in the filter components (Resistors, Inductors and Capacitors).

Figure 2.3: Passive filter

Active filter: An active filter contains resistors, capacitors, and an active element such as voltage amplifier, microwave active devices such as field effect transistor, is used to provide filters with gain or tunable response characteristics.

The output power of an active filter is usually larger than the Input power due to the filter itself which works as an amplifier to amplify the input power.

Figure 2.4: Active filter

## Filter design Methods

There are two commonly used methods to design a Microwave filter:

## Image Parameter Method

The image parameter method of filter design absorb the specification of Passband and Stopband characteristics for a cascade of two port networks; the method is relatively simple but has the disadvantage that an arbitrary frequency response cannot be included into the design.

The image parameter method may yield a usable filter response, but if doesn't, there is no clear cut way to improve the design. The image parameter method is useful for simple filters design and provides a link between infinite periodic structures and practical filter design [3].

The two port sections are arranged into aÂ ladder network, the quantity of the required sections typically determined by StopbandÂ rejection required. In its simplest form, the microwave filter may consist of identical sections, yet it is more common to use a composite filter consists of different types of sections to improve different parameters. The main parameter considered is the Stopband Attenuation parameter.

## Insertion Loss Method

As described above for the case of Image Parameter Method, the final designed system cannot further be improved, another design technique which is called the insertion loss method is used is to design a microwave filter, it has an advantage over the Image parameter method that permits a high degree of control over the Passband and Stopband amplitude and phase characteristics, with an efficient way to construct the desired response [3].

A filter response designed by the Insertion loss method is identified by the power loss ratio:

(2.1)

ï‡: Reflection coefficient looking into the filter

## Normalized Low Pass Filter Types (Filter transfer function)

Different approaches were developed by mathematicians and each was designed to optimize some filter properties, these are few commonly used filters types used to design a normalized Lowpass filter:

## Buuterworth (Maximly flat) Filter

It is the most common filter approximation. The figure below shows the response of the Butterworth filter which it has an almost flat response at the Passband of the filter and very smooth transition from the Passband to the Stopband and vice versa.

The Lowpass filter response for N order is specified by:

N = filter order, wc = cutoff frequency

For w = wc and = 1 , it shows that the insertion loss increases at the rate of 20N dB/decade

Figure 2.5: butterworth filter amplitude response

## Chebyshev (Equal ripple) Filter

The Chebyshev approach differs from the Butterworth approach in a way that it has a sharper transition from Passband to Stopband and vice versa, but it has a drawback over the Butterworth such that it has ripples in the Passband or in the Stopband, the figures below illustrate the changes:

Chebyshev type I Chebyshev type II

Figure 2.6: Chebyshev filter amplitude responses

The low pass filter response for N order is specified by:

The insertion loss is also increases at a rate of 20N dB/decade

## Elliptic Filter

The Elliptic approach differs from the Butterworth and Chebyshev that is concern mostly on the transition from the Passband to the Stopband and vice versa, but it has a drawback that it has equal ripples in both the Passband and the Stopband.

Figure 2.7: Elliptic filter amplitude response

## Linear phase filter

The linear phase filter differs from the other filters in a way that it focuses on the phase response linearity rather than the amplitude to avoid signal distortion.

C:\Users\Zaid\Desktop\Bessel4_GainDelay.png

Figure 2.8: Linear filter amplitude response

The table below compares the characteristics of each approach

Transfer Function

Butterworth

Chebyshev

Elliptic

Bessel

Characteristic

Smooth attenuation in Passband

Contains no ripple

Moderate attenuation steepness

Acceptable linear phase response

Easy to implement

Passband response no longer flat

Contains ripples in Passband

More rectangular attenuation curve

Bad phase response

Passband and Stopband responses no longer flat Contains ripples in Passband and Stopband

Very fast cutoff

Smooth attenuationin Passband

Frequency response is less selective, very slow cutoff

Good linear phase response

Table 2.1: Characteristics of the different filter transfer function

## Microwave Filter Design Procedures

The general procedures for designing a filter using the insertion loss method can be summarized in four steps:

Filter specifications: These include the cutoff frequency, the Stopband attenuation, the Passband insertion loss and Passband behavior.

Design a low pass "prototype" circuit: in such a protoype, R = 1 Î© and wc = 1 rad/s.

Filter tables are used for this step.

Scale and conversion: The filter is scaled to the proper impedance level and frequency level such as to a Highpass, Bandpass, or Bandstop topology.

Filter realization: Finally, the final desigend filter is realized by using trasmission lines whose reactance correspond to those of distributed circuit elements.

## Low Pass Filter Design Using Insertion Loss Method

As mentioned in (section 2.5.2), the insertion loss method has an advantage that permits a high degree of control over the Passband and Stopband amplitude and phase characteristics, made it the most common technique to design a Microwave filter.

After obtaining all the required specifications which is the first procedure in designing a microwave filter, the second procedure is to construct a Lowpass prototype filter.

There are two types of circuits that can be used as shown in the figure below:

Figure 2.9: Prototypes of low-pass filter circuits

Figure - 2.9 shows a prototype Lowpass circuit where g1, g2, g3, â€¦., gN+1 are called (Elements), the element values are designed from standard Lowpass response approximations such as Butterworth, Chebyshev and Bessel approach. The angular cut-off frequency Î©c and the termination resistance R are both normalized to unity in the prototype filter derived from these approximations, by using any of the circuits above, same results will be obtained.

Das, A. and Das, S.K mentioned in "Microwave Engineering" [5] that by knowing the order of the filter, these elements (for example using the Butterworth approach) can be calculated using the following Formulas:

g0 = 1

gk = 2 sin {(2k - 1) }, k = 1,2,3â€¦â€¦N

gN+1 = 1 , for all N

The table below summarized the elements values from N=1 to N = 10 [6]:

N

g1

g2

g3

g4

g5

g6

g7

g8

g9

1

2.0000

1.0000

2

1.4142

1.4142

1.0000

3

1.0000

2.0000

1.0000

1.0000

4

0.7654

1.8478

1.8478

0.7654

1.0000

5

0.6180

1.6180

2.0000

1.6180

0.6180

1.0000

6

0.5176

1.4142

1.9318

1.9318

1.4142

0.5176

1.0000

7

0.4450

1.2470

1.8019

2.0000

1.8019

1.2470

0.4450

1.0000

8

0.3902

1.1111

1.6629

1.9615

1.9615

1.6629

1.1111

0.3902

1.0000

Table 2.2: Elements values for filters with maximally flat attenuation

The attenuation for frequencies higher than the cutoff frequency is proportional to the order of the filter, so if the required designed filter is to have higher attenuation, the filter order should be higher and vice versa. The figure below shows the attenuation vs. the normalized frequency for Butterworth approach for filter order from N = 1, to N = 10 [3]:

Figure 2.10: attenuation vs. normalized frequency for Butterworth approach

The discussion above is for Butterworth maximally flat approach, for Chebyshev I and II and for the Linear approach, you can refer to pozar [3].

## Filter Transformations

In the previous section, the constructed circuit prototype is just a normalized model of a Lowpass filter, to obtain the practical Lowpass, Highpass, Bandpass and Bandstop filters, a transformation of the low-pass prototype filters with normalized angular cut-off frequency Î©c and the termination resistance R are both normalized to unity are made into the desired type.

The transformation process contains two stages:

Frequency transformation: Convert the normalized frequency Î© from unity to the actual frequency wc.

Impedance transformation: Convert the normalized input and output resistance from unity to the actual values.

As we are only concern with Bandpass filter, only the steps to transform the normalized Lowpass to Bandpass filter will be discussed, for more information refer to [3].

Lowpass prototype is transformed to the Bandpass filter by first using the following frequency transformation technique:

w = =

Where;

Î” is the fractional bandwidth of the Passband. The centre frequency, wo could be chosen arithmetic mean of w1 and w2, but the equations are simpler if it is chosen as the geometric mean;

Applying the impedance transformation and frequency transformation to the series inductances and shunt capacitances of the Lowpass prototype gives:

A series inductor, Lk is transformed to a series LC circuit with element values:

L'k = (2.7a)

C'k = (2.7b)

A shunt capacitor, Ck is transformed to a parallel LC circuit with element values:

L'k = (2.8a)

C'k = (2.8b)

The element transformations from a LPP (Lowpass prototype) to various types of filter are summarized as shown below [7]:

Figure 2.11: Impedance and Frequency Transformation of LPP

## Filter Realization

At this point the first 3 procedures of the design procedures have been illustrated, the final step is to realize the final design by using transmission lines whose reactance correspond to those of distributed circuit elements. There are number of techniques used to realize a filter, each type corresponds to different requirements.

Examples of realization techniques:

Stepped Impedance filter

Capacitive Gap Coupled Transmission Line filter

Parallel Coupled Strip Line filter

Comb-Line filter

Hairpin Line filter

The Parallel Coupled Strip Line filter and Hairpin Line filter will be discussed, these two techniques are implemented using planer Transmission line structure (Microstrip), Before goes into the details of these two techniques, the theory behind planer Transmission line structure will next be discussed.

## Planer Transmission Line

Planer Transmission Lines are the simplest and the most commonly used transmission lines, they can support TM, TE and TEM mode, and they can be constructed easily using low cost printed circuit board materials and processes. They are comprised from a solid dielectric substrate material with permittivity and permeability with single sided or double sided metallization, where the first side for signal current flowing, and the second side is for grounding.

Examples of common used types are shown in Figure - 2.12, Such as Microstrip, , Coplanar waveguide Stripline and Slotline, each topology has its own characteristics such as the distribution of its fields, characteristic impedance, phase velocity, and number of modes supported by the structure of the filter.

These Planer Transmission Lines can be used to produce such circuit elements as delay lines, crossovers, resonators, transitions, power combiners, and filters.

Figure 2.12: Â Common, multiconductor, planar transmission lines and their TEM mode E-field distributions: (a) parallel-plate, (b) microstrip, (c) stripline, (d) coplanar waveguide, and (e) slot line

Microstrip planar transmission line is the most widely used today for the design of microwave components and devices , it can be easily fabricated usingÂ printed circuit boardÂ [PCB] technology, and is used to conveyÂ microwave-frequency signals. It consists of two conducting Materials separated by aÂ dielectricÂ layer known as theÂ substrate. It is used to construct different types of microwave devices such as Microwave antennas,Â couplers,Â filters,Â power dividersÂ etc. Microstrip planar transmission line has advantages over the other transmission line types such as it is much cheaper than traditionalÂ waveguideÂ technology, as lighter in weight and more compact and can be used to design distributed circuit at frequencies from below 1 GHz through some tens of gigahertz.

The geometry of Microstrip is shown in Figure - 2.13, dielectric substrate having relative permittivity and thickness of d is sandwiched between the main conductor which carry the signal having a width W, and ground plate, the upper dielectric is typically air.

Figure 2.13: Microstrip geometry

## Microstrip Wave Propogation Mode

Unlike Stripline, where all the fields are enclosed within a homogeneous dielectric region, the behavior and analysis of Microstrip line is complicated for the reason that the dielectric (air) does not completely surround the region above the conducting strip, theÂ dielectric constant Â of the dielectric substrate is different (greater) than that of the air, so the TEM phase velocity of the air differs from the TEM phase velocity of the dielectric, thus the wave is travelling in an inhomogeneous medium. at frequencies > 0, both Electric (E) and Magnetic (H) fields have longitudinal components. We conclude from that, that a pure TEM wave is impossible to attained, and the dominant mode is referred to as quasi-TEM mode.

Figure 2.14: Wave propagation modes

Additional outcomes of an inhomogeneous medium includes:

TheÂ phase velocityÂ gradually decreases by increasing frequency.

TheÂ characteristic impedanceÂ of the line changes slightly with frequency.

TheÂ wave impedanceÂ varies over the length of the line.

Figure 2.15: Electric E & Magnatic H fields of Microstep

## Microsrtrip Discontinuities

Microstrip planer transmission line suffers from discontinuities like the other types of planer transmission lines, Discontinuities are the result of mechanical or electrical transitions from one medium to another or as steps, open-ends, bends, gaps, and junctions. Discontinuities can cause reflection and mismatching and its undesirable.

If the transmission is in low frequencies, the effect of discontinuities is low, but if the transmission is in high frequency, the effect of discontinuities is significant and it may change the characteristics of the device significantly, the reason for that is each discontinuity can be implemented by an equivalent electric circuit, figure 2.16 illustrate the situation.

As illustrated in figure - 2.16 each discontinuity is implemented by an electric circuit with inductors and capacitors, in low frequencies the impedance and admittance of each component is , but in high frequency, impedance and admittance of each component is large.

Similar Discontinuities are also exist for Stripline and the other printed transmission lines such as Slotline, Coplanar waveguide and others.

Figure 2.16: Some Common microstrip discontinuities. (a) Open-ended microstrip. (b) Gap in Microstrip. (c) Change in width. (d) T-junction. (e) Coax-to-Microstrip junction [3].

## Microstrip Parallel Coupled Lines

Coupling between parallel conductors exist in many types of Strip Lines components, such components as directional couplers, filters, Baluns and delay lines such as inter digital lines.

Figure - 2.17 illustrate the cross section of coupled Microstrip lines, two Microstrip lines of the width W and length l and thickness t are in the parallel coupled configuration, and they are separated by s, this coupled line structure supports two quasi-TEM modes, which are even mode and odd mode.

Figure 2.17: Microstrip Coupled Liens cross section

The characteristics of these coupled lines are specified in terms of even impedance Zoe, and odd impedance Zoo. Zoe is identified as the characteristic impedance of one line to ground when equal currents are flowing in the two lines. Zoo is identified as the characteristic impedance of one line to ground when equal and opposite currents is flowing in the two lines. Figure - 2.18 illustrate the electric field configuration over the cross section of the line [6].

Figure 2.18: Even and Odd modes electric field orientation

## Parallel Coupled Line Filter

In this section, the half wavelength resonator filter will be illustrated, the length of each resonator is half wavelength at the centre frequency, and they are positioned so that adjacent resonators parallel to each other along half of their length (Î»/4) which gives relatively large coupling for a spacing s between them. Parallel coupled configuration is preferred than other configurations such as end coupled configuration for the reason that parallel coupled can achieve more compact structure, this structure is particularly suitable for printed circuit filters bandwidth to up to about 10 - 15 percent [6].

Figure - 2.19 illustrate an example of a parallel coupled half wavelength resonator filter.

Figure 2.19: cross sections of various Coupled transmission line configurations. (a)Thin Strip Line. (b) thin Lines Coupled Through a Slot. (c) Round Wires. (d) Thin Lines Vertical to the Ground Planes. (e)Thin Lines Superimposed. (f) Interleaved thin Lines. (g) Thick Rectangular Bars [6]:

## Parallel Coupled Half Wavelength Resonator Filter Design

The steps below illustrate the flow to design a Parallel Coupled Half Wavelength Resonator Filter:

Determine filter Specifications.

Determine the normalized circuit elements.

Determine the Inverter Constants.

Determine the even and odd characteristics impedances.

Determine the parallel coupled lines width W and separation s.

Determine the length l of the parallel coupled lines.

Detailed procedures will be discussed in Chapter 3

## Hairpin -Line Bandpass Filter

A Hairpin Line is a Micrstrip structure used to construct a Microstrip filter, and it can be considered as an improve version of a parallel coupled line filter, it is mainly used to design Bandpass filters, for a filter having N coupled-line sections will produce N-1 order filter response.

The Hairpin Line filter is preferred over the common parallel Coupled Line filter for the reason that it reduces the size of the overall filter circuit.

The Hairpin Coupled Line filter, the Parallel coupled sections have lengths of quarter wavelengths, the transformation process starts with introducing a sliding factor (b) to allow for bending of the Parallel Coupled Lines to make the design more compact. The next step in the design is to fold the resonators of the parallel coupled lines to "U" shape, by folding the Resonators, the area of the designed circuit is compressed to a much smaller size having the same characteristics of the Parallel Coupled Line filter.

The same dimensions of the Parallel Coupled line resonators may be used to design the Hairpin Line filter or changes may be made for tuning and perfection purpose. The conclusion is that the same equations used to design the Parallel Coupled Line filter can be used to design the Hairpin filter.

Some CAD (Computer Aided Design) softwares can be used to directly design the Hairpin Line filter without first designing the Parallel Coupled Line filter first just by inserting the required filter specifications.

such software like ADS (Advanced Design System) which is very reliable to use.

The details of designing a Hairpin Line filter are described below:

(a)

(b)

(c)

Figure 2.20: Designing of a hairpin-line filter:

(a) Parallel-coupled filter - notice that the coupling section is Î»/4 long (depicted by rectangular bracket) (b) The resonators are moved to provide for a slide factor, b (depicted by rectangular bracket where length < Î»/4) (c) The Î»/2 resonators are bent at the slide factor area to produce the hairpin resonator structure.