Research Article, J Electr Eng Electron Technol Vol: 7 Issue: 2
UHF Band-Pass Filter Based on Parallel Coupled Resonators
*Corresponding Author : Mounir Belattar
Department of Electrical Engineering and Computer Engineering, University 20 Août 1955 University, Skikda, Algeria
E-mail: [email protected]
Received: June 04, 2018 Accepted: July 07, 2018 Published: July 14, 2018
Citation: Belattar M, Lashab M, Benhabrou A (2018) UHF Band-Pass Filter Based on Parallel Coupled Resonators. J Electr Eng Electron Technol 7:2. doi: 10.4172/2325-9833.1000163
The proposed microstrip filter is based on parallel coupled lines whose propagation mode is quasi-TEM, this type of filter take an important part in various communication systems. In this work we will study the procedure of design and realization of an UHF band-pass filter with centre frequency of 868.5 MHz and bandwidth of 1 MHz based on Coupled parallel lines, the obtained theoretical results are in good agreement with the literature.
Keywords: Characteristic impedance; Coupled lines; Dispersion; Even mode; Odd mode; Permittivity
In very high frequencies, inductors and capacitors lose their intrinsic characteristics. In addition, a limited range of component values is available from manufacturers. Therefore, for these frequencies, the passive filters are generally made using the distributed elements such as transmission line sections. Many works have been based on the use of waveguides for the design of filters [1,2]. However, waveguide systems are cumbersome and costly and of low power, compared to those designed from planar structures. In this work we are going to calculate the elements of a UHF micro ribbon filter with 868.5 MHz bandwidth 1 MHZ center frequency resonators, serving UHF transmitters to filter signals from a very close network that The GSM network, whose central frequency is 890 MHz.
Filter Elements Calculation
For a central frequency filter f0 equal to 868.5 MHz and 1 MHz bandwidth, we obtain: by transposing the prototype of a bandpass filter to that of a low pass filter. The components values can be calculated as follows.
g0 =1 (1)
Where bandpass filter parameters of order n=2 are given in Table 1.
Table 1: Bandpass filter parameter of order n=2.
Where g0, g1 ... gn are the elements of a prototype of a low pass filter with normalized cut-off frequency Ωc=1, and FBW is the passband of the bandpass filter. Jj, j + 1 are the characteristic admittances of J-inverters and Y0 is the characteristic admittance of the termination lines.
Odd and even characteristic impedances
All these impedances are given in Table 2.
|n||Value 1||Value 2|
Table 2: Odd and even characteristic impedances.
Calculation of the ratios W/h even and W/h odd
To present the odd and odd modes of the desired impedances, we determine the ratios of the simple equivalent microstrip lines (W/h) s, which are responsible for connecting the coupled line relationships to single-line relationships for a single microstrip line (Figure 1) .
Thus, the requires resonator:
For a single microstrip line, the approximate expressions for W/h in terms of Zc and εr, drawn by Hammerstad  are given as follows:
For W/h ≥ 2
Calculation of W/h and S/h ratios
At this point he is able to find (W/h) se and (W/h) so, by applying Z0se and Z0so (as Zc) to the equations of simple microstrip lines . Now, the ratios w/h and s/h can be expressed for the desired coupled microstrip line using a set of approximate equations (4,7):
Calculation of the microstrip length
For each pair of coupled quarter wave sections, the guided wavelength of the quasi-TEM microstrip mode can be given by:
Thus, the required resonator:
The expressions giving better precision  are as follows:
For broad microstrip lines, where W/h ≥ 1
For narrow microstrip lines, where W/h ≤ 1
Accurate Method for Calculating Filter Parameters
The static microstrip line model gives accurate results for low frequencies (up to about 868.5 MHz). It uses physical dimensions of the microstrip line as normalized parameters .
In n homogeneous medium. The equations here use air, as a homogeneous material. The impedance is given by:
The effective shielded impedance represented by the expression:
In order to take into account the shielding, effects, a fill factor q is introduced : The effective relative permittivity is therefore given by:
The characteristic impedance of the microstrip line placed on a dielectric with relative permittivity εr is given by:
Dispersive model of coupled parallel microstrip lines
A symmetric pair of coupled microstrip lines is composed of two parallel lines of equal widths W with a spacing S and of length L mounted on a non-magnetic dielectric substrate of thickness h (Tables 3 and 4). And having a permittivity relate εr
Table 3: Widths W and separation S of the lines filter.
Table 4: Length of value of parallel lines.
The equations expressing the effective permittivity are given by the following expressions:
Where fn GHz.mm is the normalized frequency with respect to the substrate height, the effective characteristic impedance due to the dispersion is given by Jansen and Kirschning :
Evaluation of characteristic impedances and effective relative permittivity
The physical dimensions of the structure were again standardized with respect to the substrate height
The results are accurate to 1 percent in the range:
Where εr is the relative permittivity of the substrate material for the same static mode (f=0) whereas the effective permittivity is calculated according to Hammerstad  as follows:
Kirschning and Jansen  have reshaped the equations Hammerstad and Jensen for the odd mode of static permittivity, in order to improve the accuracy, to obtain:
The term odd-shielding correction is expressed as: The quantity εeff (0) is the effective permittivity of a single microstrip of thickness w and the relative effective permittivity in the case of a zero-width conductor is calculated. The indices "e" and "o" designate the even and odd modes, respectively, and the argument 0 implies static parameters. For the even mode, the characteristic impedance is expressed as:
The shielding effects are again counted, where the characteristic impedances of the even and odd modes of a symmetric pair of microstrip lines coupled in a homogeneous air dielectric (εr=1) are calculated and the ΔZ0 correction term (0) is computed from another set of expressions for even and odd modes. Whereas, for the same modes, the correction is expressed by:
And for the odd mode the correction is given by:
In order to obtain the corrections made on the impedances of the coupled lines on a dielectric substrate different from air, the corrections have been obtained in the case of air; this must be divided by the square root of the effective permittivity:
The impedance dispersion in the even mode is obtained from the expression
Synthesis of coupled microstrip lines
In the synthesis procedure, Ze and Zo for the coupled lines are known and it is necessary to find W/h and S/h. The first step is to find the two single line shape ratios (w/h)se and (w/h)so corresponding to the impedance Ze/2 and Zo/2, Wheeler's theory  provides curves , for obtaining the ratios graphically. The W/h, and S/h ratios for the coupled lines are now solved simultaneously by the following formulas (Figure 2):
For εr >6
After all the calculations, we arrive at the design of the filter UHF of order 2 (Figure 3 and Table 5) with a substrate Duroid of height h=0.79 mm and of relative permittivity εr=2.35, operating at the central frequency f0=868.5 MHz with 1 MHZ bandwidth.
Table 5: Characteristic impedances and effective relative permittivity’s and dimensions computed for a frequency f0=868.5 MHz in even and odd mode.
ZL (f) is the dependent frequency of powering up a single microstrip with a characteristic impedance width W This calculation gives the impedances of the even and odd modes as well as the even and odd efficient dielectric constants of the microstrip coupled lines on a Duroid substrate illustrated in Figure 4. Figure 5 shows the variations of the ratio W/h as a function of S/h in the even odd coupling modes of the microstrip line coupled for the Duroid case.
In this work, one of our objectives was to present the design procedure of a Tchebychev-type microstrip UHF bandpass filter based on parallel coupled lines. The design of these filters requires the determination of widths Wi of coupled parallel micro-line lines, the widths li of the resonators as well as the Si distances separating these lines. In this context, a calculation program has been developed to calculate these elements accurately.
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