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Abstract-This document is an explanation about the Band stop Filter design in a range of 1910MHz-1930MHz using an equal ripple. This filter design is fully explain based on calculation, design and simulation.
HE Personal Communications Services (PCS) is an advance wireless mobile technologies and services which promises to permit communications to anyone, anyplace, and anytime while on the move. The FCC defines PCS as a family of mobile or portable radio communications services that encompass mobile and ancillary fixed communications services to individuals and businesses and can be integrated with a variety of competing networks.
Unlicensed PCS will accommodate a wide range of services for small areas such as data networking within office buildings with wireless Local Area Networks (LANs), personal digital assistants, laptop computers, portable facsimile machines, wireless replacements for portions of the wire line telephone network, and other kinds of short-range communications. Terminal devices will be a new generation of cordless telephones that operate without centralized base stations and will be limited to very low power and range enabling spectrum to be reused efficiently.
Unlicensed PCS is preferable to be used at office-wide and campus-wide services. Equipment manufacturers do not have to wait for the development of standards since they can design proprietary products for their clients. The FCC has allocated spectrum for unlicensed PCS in the 1910 to 1930 MHZ band. For this Band stop Filter design, it is required to follows the requirement which need to design an Unlicensed PCS device with a range of 1910MHz to 1930MHz. The order of filter is 5 elements must be in equal ripple 3dB. 
Filter can be defined as a signal processing system which output signal is different from the input signal which called the stimulation; the output signal has some determined properties. In more practical terms an electric filter is a device that designed to suppress, pass, or separate a group of signals from a signal according to the specification in a particular application. The application areas of filtering are manifold, for example to band-limit signals before sampling to reduce aliasing, to eliminate unwanted noise in communication systems, to resolve signals into their frequency components, to convert discrete-time signals into continuous-time signals and to demodulate signal. Filters are generally classified into three broad classes which are continuous-time, sampled- data and discrete-time filters depending on the type of signal being processed by the filter. Therefore, the concept of signals is fundamental in the design of filters. A signal is a function of one or more independent variables such as time, space, temperature, etc. that carries information. The independent variables of a signal can either be continuous or discrete. Assuming that the signal is a function of time, in the first case the signal is called continuous-time and in the second, discrete-time. A continuous-time signal is defined at every instant of time over a given interval, whereas a discrete-time signal is defined only at discrete-time instances. Similarly, the values of a signal can also be classified in either continuous or discrete. 
Filters are commonly classified according to the filter function they perform. The basic functions are: low-pass, high-pass, band pass, and band stop. If a filter passes frequencies from zero to its cut off frequency and stops all frequencies higher than the cut off frequencies, then this filter type is called an ideal low pass filter. A circuit designed to perform this frequency selection is called a filter circuit. Filter is desirable to have circuits capable of selectively filtering one frequency or range of frequencies out of a mix of different frequencies in a circuit. Band-stop filters is also called band-elimination, band-reject, or notch filters, this kind of filter passes all frequencies above and below a particular range set by the component values. It can be made out of a low-pass and a high-pass filter, just like the band-pass design. 
A band stop filter passes most unaltered frequencies and attenuates those frequencies in a specific range to very low levels. A band stop filter is the notch filter which is a narrowband band stop filter. At any frequency outside the defined band or range, band stop filters have a theoretical gain of 1. At any frequency within the defined range, band stop filters have a theoretical gain of 0. The cutoff frequencies, or the points at which the theoretical gain switches between 1 and 0 or 0 and 1, is determined by filter components and application.
Calculation and Design
The order of a filter is important for several reasons. It is directly related to the number of components in the filter and the complexity of the design task. Therefore, higher-order filters are more expensive, take up more space, and are more difficult to design. The primary advantage of a higher-order filter is that it will have a steeper roll off slope than a similar lower- order filter. Based on 3dB equally ripple graph, value of elements n=5 is used in order to design a 5 element of band stop filter.
The basic 5 element low pass filter design is used as figure 1 shows, before convert it the band stop design. In low pass filter, the value of inductor and capacitor is depends on the 3dB equally ripple graph, which are the value of L1 is equal to L5, C2 is equal to C4.
Figure 1: Low Pass Filter
After convert the low pass filter to band stop filter as figure 2, the value of L1, L2, L3, C1, C2 and C3 is calculated by using the formula given. The value of L4, L5, C4 and C5 no need to be calculated since L4=L2, L5=L1, C4=C2 and C5=C1.
Figure 2: Band Stop Filter
For the calculation, formula used as below:
L1= âˆ†LZo/ωo C1= 1/ωoâˆ†LZo
L2= Zo/ωoCâˆ† C2= Câˆ†/ωoZo
L3= âˆ†LZo/ωo C3= 1/ωoâˆ†LZo
The value of âˆ† is calculated through the value of (ω2-ω1)/ωo whichωo=√ω1ω2.
The value of ω is calculated based on the value of frequency of Unlicensed PCS which are in a range of 1910MHz to 1930MHz. The range considered as ω1and ω2 respectively.
Simulation using ADS is used in order to prove that the Band Stop Filter is similarly as a theoretical. Below is the result of Band Stop Filter after the simulation.
Figure 3: Band Stop Filter Design using ADS
Figure 4: Band Stop Filter Equal Ripple
Based on this simulation result, it shows that the equal ripple for Band Stop Filter is exist in the top of curve of an amplitude or phase characteristic whose local maxima and local minima all have the same value within a specified frequency range.
Ripple in this frequency response which referring to the periodic signal with an insertion loss of a filter or some other two-port network designed. The ripple existed is not usually strictly a linear periodic signal as can see in the plotted graph. The ripple of this filter design is not similar to other regular filters which never reach 0dB at minimum loss if the filter designed is for transmission across the pass band.
The amount of ripple can be minimized for other parameters and characteristic of a filter design. By increasing the ripple, the rate of pass band to the stop band can be increased. It also can be done without increasing the order of the filter. On the other hand, the ripple can be reduced by increasing the order of the filter while at the same time maintaining the same rate of roll-off.
Throughout the filter design process, we noticed that in order to design a basic filter, first and foremost student need to verify their bandwidth or range of frequency. From the basic design of Low pass filter, students convert it to the Band Stop filter design with 5 elements and refer it to 3dB equal ripple graph. From the graph, student can verify the value of each 5 elements for inductor and capacitor. Based on the value given, students are able to calculate the exact value of inductor and capacitor for Band Stop Filter either in series or parallel refers to Low Pass Filter circuit. The calculation is based on suitable formula for designing Band Stop Filter.
In order to simulate the filter design, Advance Design System (ADS) software is used. The ADS software helps student to get the equal ripple response. First, to design the circuit in ADS, student selects the lumped-component toolbar, states the calculated value and arranges the component according to the Band Stop filter circuit. S-Parameter is used to place the start and stop frequency for the filter response. In this case, 1910 Mhz is stated as start frequency and 1930 Mhz is used as stop frequency. S-Parameter can be changed and it depends on the range of frequency for filter design needed.
The Display Template is used to display the result of Smith Chart and also the response curve for the particular filter design. For Smith Chart the Display Template used S11 and S22 parameter while frequency response used S12 and S21. After placing the lumped-component, student simulates the circuit and Display Template displayed the equal ripple response. Start and stop frequency in S-parameter value can be changed in order to get the ripple on the frequency curve.
Student are able to implement a PCS band stop filter using five elements using the 0.3 dB equal-ripple low-pass filter prototype to achieve fractional bandwidth at 1910 MHz to 1930 MHz attenuation level with center frequency at 1920 MHz. However, it suffers from some drawbacks such as large circuit size, an asymmetry between low and high frequency pass bands, undesirable stop band and lack OF FLEXIBILITY. THESE can be further improved using different configurations and principles such as combination of open stub and spur line or with additional cross coupling which can provide more desirable characteristics and flexibility for the practical design of wideband band stop filters.